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Equality scale-based and sound horizon-based analysis of the Hubble tension
Abstract
The Hubble horizon at matter-radiation equality (keq−1) and the sound horizon at the last scattering surface [rs(z*)] provides an interesting consistency check for the standard Λ Cold Dark Matter (ΛCDM) model and its extensions. It is well known that the reduction of rs can be compensated by the increase of H0, while the same is true for the standard rulers keq. Adding extra radiational component to the early Universe can reduce keq. The addition of early dark energy (EDE), however, tends to increase keq. We perform keq- and rs-based analyses in both the EDE model and the Wess-Zumino dark radiation (WZDR) model. In the latter case, we find ΔH0=0.4 between the rs- and keq-based datasets, while in the former case, we find ΔH0=1.2. This result suggests that the dark radiation scenario is more consistent in the fit of the two standard rulers (keq and rs). As a forecast analyses, we fit the two models with a mock keq prior derived from Planck best-fit ΛCDM model. Compared with the best-fit H0 in baseline ΛCDM model, we find ΔH0=1.1 for the WZDR model and ΔH0=−2.4 for EDE model.
... It should be noted that the full resolution of the Hubble tension would require going beyond providing new degrees of freedom and would involve a fit to all of the CMB data that are consistent with all cosmological and particle physics constraints. For some recent related work on the Hubble tension, see [63][64][65][66][67][68]. ...
While the standard model accurately describes data at the electroweak scale without the inclusion of gravity, beyond the standard model, physics is increasingly intertwined with gravitational phenomena and cosmology. Thus, the gravity-mediated breaking of supersymmetry in supergravity models leads to sparticle masses, which are gravitational in origin, observable at TeV scales and testable at the LHC, and supergravity also provides a candidate for dark matter, a possible framework for inflationary models and for models of dark energy. Further, extended supergravity models and string and D-brane models contain hidden sectors, some of which may be feebly coupled to the visible sector, resulting in heat exchange between the visible and hidden sectors. Because of the couplings between the sectors, both particle physics and cosmology are affected. The above implies that particle physics and cosmology are intrinsically intertwined in the resolution of essentially all of the cosmological phenomena, such as dark matter and dark energy, and in the resolution of cosmological puzzles, such as the Hubble tension and the EDGES anomaly. Here, we give a brief overview of the intertwining and its implications for the discovery of sparticles, as well as the resolution of cosmological anomalies and the identification of dark matter and dark energy as major challenges for the coming decades.
... It should be noted that the full resolution of the Hubble tension would require going beyond providing new degrees of freedom and would involve a fit to all of the CMB date consistent with all cosmological and particle physics constraints. For some recent related work on Hubble tension see [63][64][65][66][67][68]. ...
While the standard model accurately describes data at the electroweak scale without inclusion of gravity, beyond the standard model physics is increasingly intertwined with gravitational phenomena and cosmology. Thus gravity mediated breaking of supersymmetry in supergravity models lead to sparticles masses, which are gravitational in origin, observable at TeV scales and testable at the LHC, and supergravity also provides candidate for dark matter, a possible framework for inflationary models and for models of dark energy. Further, extended supergravity models, and string and D-brane models contain hidden sectors some of which may be feebly coupled to the visible sector resulting in heat exchange between the visible and hidden sectors. Because of the couplings between the sectors both particle physics and cosmology are effected. The above implies that particle physics and cosmology are intrinsically intertwined in the resolution of essentially all of the cosmological phenomena such as dark matter and dark energy and in the resolution of cosmological puzzles such as Hubble tension and EDGES anomaly. Here we give a brief overview of the intertwining and implications for the discovery of sparticles, and the resolution of the cosmological anomalies and identification of dark matter and dark energy as major challenges for the coming decades.
The Hubble tension has now grown to a level of significance which can no longer be ignored and calls for a solution which, despite a huge number of attempts, has so far eluded us. Significant efforts in the literature have focused on early-time modifications of ΛCDM, introducing new physics operating prior to recombination and reducing the sound horizon. In this opinion paper I argue that early-time new physics alone will always fall short of fully solving the Hubble tension. I base my arguments on seven independent hints, related to (1) the ages of the oldest astrophysical objects, (2) considerations on the sound horizon-Hubble constant degeneracy directions in cosmological data, (3) the important role of cosmic chronometers, (4) a number of “descending trends” observed in a wide variety of low-redshift datasets, (5) the early integrated Sachs-Wolfe effect as an early-time consistency test of ΛCDM, (6) early-Universe physics insensitive and uncalibrated cosmic standard constraints on the matter density, and finally (7) equality wavenumber-based constraints on the Hubble constant from galaxy power spectrum measurements. I argue that a promising way forward should ultimately involve a combination of early- and late-time (but non-local—in a cosmological sense, i.e., at high redshift) new physics, as well as local (i.e., at z∼0) new physics, and I conclude by providing reflections with regards to potentially interesting models which may also help with the S8 tension.
We present constraints on cosmological parameters from the Pantheon+ analysis of 1701 light curves of 1550 distinct Type Ia supernovae (SNe Ia) ranging in redshift from z = 0.001 to 2.26. This work features an increased sample size from the addition of multiple cross-calibrated photometric systems of SNe covering an increased redshift span, and improved treatments of systematic uncertainties in comparison to the original Pantheon analysis, which together result in a factor of 2 improvement in cosmological constraining power. For a flat ΛCDM model, we find Ω M = 0.334 ± 0.018 from SNe Ia alone. For a flat w 0 CDM model, we measure w 0 = −0.90 ± 0.14 from SNe Ia alone, H 0 = 73.5 ± 1.1 km s ⁻¹ Mpc ⁻¹ when including the Cepheid host distances and covariance (SH0ES), and w 0 = − 0.978 − 0.031 + 0.024 when combining the SN likelihood with Planck constraints from the cosmic microwave background (CMB) and baryon acoustic oscillations (BAO); both w 0 values are consistent with a cosmological constant. We also present the most precise measurements to date on the evolution of dark energy in a flat w 0 w a CDM universe, and measure w a = − 0.1 − 2.0 + 0.9 from Pantheon+ SNe Ia alone, H 0 = 73.3 ± 1.1 km s ⁻¹ Mpc ⁻¹ when including SH0ES Cepheid distances, and w a = − 0.65 − 0.32 + 0.28 when combining Pantheon+ SNe Ia with CMB and BAO data. Finally, we find that systematic uncertainties in the use of SNe Ia along the distance ladder comprise less than one-third of the total uncertainty in the measurement of H 0 and cannot explain the present “Hubble tension” between local measurements and early universe predictions from the cosmological model.
The black hole observations obtained so far indicate one thing: similar “donuts” exist in the sky. But what if some of the observed black hole shadows that will obtained in the future are different from the others? In this work the aim is to show that a difference in the shadow of some observed black holes in the future, might explain the H0-tension problem. In this letter we investigate the possible effects of a pressure cosmological singularity on the circular photon orbits and the shadow of galactic supermassive black holes at cosmological redshifts. Since the pressure singularity is a global event in the Universe, the effects of the pressure singularity will be imposed on supermassive black holes at a specific redshift. As we show, the pressure singularity affects the circular photon orbits around cosmological black holes described by the McVittie metric, and specifically, for some time before the time instance that the singularity occurs, the photon orbits do not exist. We discuss the possible effects of the absence of circular photon orbits on the shadow of these black holes. Our idea indicates that if a pressure singularity occurred in the near past, then this could have a direct imprint on the shadow of supermassive galactic black holes at the redshift corresponding to the time instance that the singularity occurred in the past. Thus, if a sample of shadows is observed in the future for redshifts z 0.01, and for a specific redshift differences are found in the shadows, this could be an indication that a pressure singularity occurred, and this global event might resolve the H0-tension as discussed in previous work. However, the observation of several shadows at redshifts z 0.01 is rather a far future task.
We report observations from the Hubble Space Telescope (HST) of Cepheid variables in the host galaxies of 42 Type Ia supernovae (SNe Ia) used to calibrate the Hubble constant ( H 0 ). These include the complete sample of all suitable SNe Ia discovered in the last four decades at redshift z ≤ 0.01, collected and calibrated from ≥1000 HST orbits, more than doubling the sample whose size limits the precision of the direct determination of H 0 . The Cepheids are calibrated geometrically from Gaia EDR3 parallaxes, masers in NGC 4258 (here tripling that sample of Cepheids), and detached eclipsing binaries in the Large Magellanic Cloud. All Cepheids in these anchors and SN Ia hosts were measured with the same instrument (WFC3) and filters ( F555W , F814W , F160W ) to negate zero-point errors. We present multiple verifications of Cepheid photometry and six tests of background determinations that show Cepheid measurements are accurate in the presence of crowded backgrounds. The SNe Ia in these hosts calibrate the magnitude–redshift relation from the revised Pantheon+ compilation, accounting here for covariance between all SN data and with host properties and SN surveys matched throughout to negate systematics. We decrease the uncertainty in the local determination of H 0 to 1 km s ⁻¹ Mpc ⁻¹ including systematics. We present results for a comprehensive set of nearly 70 analysis variants to explore the sensitivity of H 0 to selections of anchors, SN surveys, redshift ranges, the treatment of Cepheid dust, metallicity, form of the period–luminosity relation, SN color, peculiar-velocity corrections, sample bifurcations, and simultaneous measurement of the expansion history. Our baseline result from the Cepheid–SN Ia sample is H 0 = 73.04 ± 1.04 km s ⁻¹ Mpc ⁻¹ , which includes systematic uncertainties and lies near the median of all analysis variants. We demonstrate consistency with measures from HST of the TRGB between SN Ia hosts and NGC 4258, and include them simultaneously to yield 72.53 ± 0.99 km s ⁻¹ Mpc ⁻¹ . The inclusion of high-redshift SNe Ia yields H 0 = 73.30 ± 1.04 km s ⁻¹ Mpc ⁻¹ and q 0 = −0.51 ± 0.024. We find a 5 σ difference with the prediction of H 0 from Planck cosmic microwave background observations under ΛCDM, with no indication that the discrepancy arises from measurement uncertainties or analysis variations considered to date. The source of this now long-standing discrepancy between direct and cosmological routes to determining H 0 remains unknown.
Motivated by the large observed diversity in the properties of extragalactic extinction by dust, we reanalyze the Cepheid calibration used to infer the Hubble constant, H 0 , from Type Ia supernovae, using Cepheid data in 19 Type Ia supernova host galaxies from Riess et al. and anchor data from Riess et al. Unlike the SH0ES team, we do not enforce a fixed universal color–luminosity relation to correct the Cepheid magnitudes. Instead, we focus on a data-driven method, where the optical colors and near-infrared magnitudes of the Cepheids are used to derive individual color–luminosity relations for each Type Ia supernova host and anchor galaxy. We present two different analyses, one based on Wesenheit magnitudes, resulting in H 0 = 73.2 ± 1.3 km s ⁻¹ Mpc ⁻¹ , a 4.2 σ tension with the value inferred from the cosmic microwave background. In the second approach, we calibrate an individual extinction law for each galaxy, with noninformative priors using color excesses, yielding H 0 = 73.9 ± 1.8 km s ⁻¹ Mpc ⁻¹ , in 3.4 σ tension with the Planck value. Although the two methods yield similar results, in the latter approach, the Hubble constants inferred from the individual Cepheid absolute distance calibrator galaxies range from H 0 = 68.1 ± 3.5 km s ⁻¹ Mpc ⁻¹ to H 0 = 76.7 ± 2.0 km s ⁻¹ Mpc ⁻¹ . Taking the correlated nature of H 0 inferred from individual anchors into account, and allowing for individual extinction laws, the Milky Way anchor is in 2.1–3.1 σ tension with the NGC 4258 and Large Magellanic Cloud anchors, depending on prior assumptions regarding the color–luminosity relations and the method used for quantifying the tension.
Dark radiation (DR) appears as a new physics candidate in various scenarios beyond the Standard Model. While it is often assumed that perturbations in DR are adiabatic, they can easily have an isocurvature component if more than one field was present during inflation, and whose decay products did not all thermalize with each other. By implementing the appropriate isocurvature initial conditions (IC), we derive the constraints on both uncorrelated and correlated DR density isocurvature perturbations from the full Planck 2018 data alone, and also in combination with other cosmological data sets. Our study on free-streaming DR (FDR) updates and generalizes the existing bound on neutrino density isocurvature perturbations by including a varying number of relativistic degrees of freedom, and for coupled DR (CDR) isocurvature, we derive the first bound. We also show that for CDR qualitatively new physical effects arise compared to FDR. One such effect is that for isocurvature IC, FDR gives rise to larger CMB anisotropies compared to CDR — contrary to the adiabatic case. More generally, we find that a blue-tilt of DR isocurvature spectrum is preferred. This gives rise to a larger value of the Hubble constant H 0 compared to the standard ΛCDM+Δ N eff cosmology with adiabatic spectra and relaxes the H 0 tension.
It has recently been suggested that a gravitational transition of the effective Newton’s constant Geff by about 10%, 50–150 Myrs ago could lead to the resolution of both the Hubble crisis and the growth tension of the standard ΛCDM model. Hints for such an abrupt transition with weaker gravity at times before the transition, have recently been identified in Tully–Fisher galactic mass-velocity data, and also in Cepheid SnIa calibrator data. Here we use Monte-Carlo simulations to show that such a transition could significantly increase (by a factor of 3 or more) the number of long period comets (LPCs) impacting the solar system from the Oort cloud (semi-major axis of orbits ≳104AU). This increase is consistent with observational evidence from the terrestrial and lunar cratering rates, indicating that the impact flux of kilometer sized objects increased by at least a factor of 2 over that last 100 Myrs compared to the long term average. This increase may also be connected with the Chicxulub impactor event that produced the Cretaceous–Tertiary (K-T) extinction of 75% of life on Earth (including dinosaurs) about 66 Myrs ago. We use Monte-Carlo simulations to show that for isotropic Oort cloud comet distribution with initially circular orbits, random velocity perturbations (induced e.g., by passing stars and/or galactic tidal effects), lead to a deformation of the orbits that increases significantly when Geff increases. A 10% increase in Geff leads to an increase in the probability of the comets to enter the loss cone and reach the planetary region (pericenter of less than 10 AU) by a factor that ranges from 5% (for velocity perturbation much smaller than the comet initial velocity) to more than 300% (for total velocity perturbations comparable with the initial comet velocity).
The recent analysis from the SH0ES collaboration has confirmed the existence of a Hubble tension between measurements at high redshift ( z > 1000) and at low redshift ( z < 1) at the 5 σ level with the low redshift measurement giving a higher value. In this work we propose a particle physics model that can help alleviate the Hubble tension via an out-of-equilibrium hidden sector coupled to the visible sector. The particles that populate the dark sector consist of a dark fermion, which acts as dark matter, a dark photon, a massive scalar and a massless pseudo-scalar. Assuming no initial population of particles in the dark sector, feeble couplings between the visible and the hidden sectors via kinetic mixing populate the dark sector even though the number densities of hidden sector particles never reach their equilibrium distribution and the two sectors remain at different temperatures. A cosmologically consistent analysis is presented where a correlated evolution of the visible and the hidden sectors with coupled Boltzmann equations involving two temperatures, one for the visible sector and the other for the hidden sector, is carried out. The relic density of the dark matter constituted of dark fermions is computed in this two-temperature formalism. As a consequence, BBN predictions are upheld with a minimal contribution to Δ N eff . However, the out-of-equilibrium decay of the massive scalar to the massless pseudo-scalar close to the recombination time causes an increase in Δ N eff that can help weaken the Hubble tension.
The standard Λ Cold Dark Matter (ΛCDM) cosmological model provides a good description of a wide range of astrophysical and cosmological data. However, there are a few big open questions that make the standard model look like an approximation to a more realistic scenario yet to be found. In this paper, we list a few important goals that need to be addressed in the next decade, taking into account the current discordances between the different cosmological probes, such as the disagreement in the value of the Hubble constant H0, the σ8–S8 tension, and other less statistically significant anomalies. While these discordances can still be in part the result of systematic errors, their persistence after several years of accurate analysis strongly hints at cracks in the standard cosmological scenario and the necessity for new physics or generalisations beyond the standard model. In this paper, we focus on the 5.0σ tension between the Planck CMB estimate of the Hubble constant H0 and the SH0ES collaboration measurements. After showing the H0 evaluations made from different teams using different methods and geometric calibrations, we list a few interesting new physics models that could alleviate this tension and discuss how the next decade's experiments will be crucial. Moreover, we focus on the tension of the Planck CMB data with weak lensing measurements and redshift surveys, about the value of the matter energy density Ωm, and the amplitude or rate of the growth of structure (σ8,fσ8). We list a few interesting models proposed for alleviating this tension, and we discuss the importance of trying to fit a full array of data with a single model and not just one parameter at a time. Additionally, we present a wide range of other less discussed anomalies at a statistical significance level lower than the H0–S8 tensions which may also constitute hints towards new physics, and we discuss possible generic theoretical approaches that can collectively explain the non-standard nature of these signals. Finally, we give an overview of upgraded experiments and next-generation space missions and facilities on Earth that will be of crucial importance to address all these open questions.
In the recent literature it has been shown that the H0 tension may be eliminated if an abrupt physics transition changed the Cepheid parameters in the near past of the Universe, nearly 70 -150Myrs ago. In this letter we stress the possibility that this abrupt transition was caused by the smooth passage of our Universe through a pressure finite-time cosmological singularity. Being a non-crushing type singularity the pressure singularity can leave its imprints in the Universe, since it occurs globally and literally everywhere. We discuss how this scenario could easily be realized by F (R) gravity, with the strong energy conditions being satisfied without the need for a scalar field or specific matter fluids. We also stress the fact that the pressure singularity can affect the effective gravitational constant of F (R) gravity. Moreover, we stress the fact that pressure singularities can disrupt the trajectories of bound objects in the Universe, which is also pointed out in the literature, even in the context of general relativity. We also show numerically in a General Relativistic framework that elliptic trajectories are distorted and changed to different elliptic trajectories when the Universe passes through the pressure singularity. Such a disruption of the trajectories could have tidal effects on the surface of the earth, for example on sea waters and oceans, regarding the distortion of moons elliptic trajectory. Accordingly, the distortion of earth's trajectory around the sun could have affected climatologically earth 70 - 150Myrs ago.
The tension among inferences of Hubble constant (H0) is found in a large array of datasets combinations. Modification to the late expansion history is the most direct solution to this discrepancy. In this work, we examine the viability of restoring the cosmological concordance with a novel version of transitional dark energy (TDE). The main anchors for the cosmic distance scale: cosmic microwave background (CMB) radiation, baryon acoustic oscillation (BAO), and Type Ia supernova (SNe Ia) calibrated by Cepheids form a “impossible trinity”, i.e., it’s plausible to reconcile with any two of the three but unlikely to accommodate them all. Particularly, the tension between BAO and the calibrated SNe Ia can not be reconciled within the scenarios of late dark energy. Nevertheless, our analysis suggests that the TDE model can reconcile with CMB and SNe Ia calibrated by its absolute magnitude (MB). when the equation of state (EoS) of DE transits around z ∼ 1. Meanwhile, we see a positive sign that the EoS transits with the inclusion of a local prior on MB, whereas the opposite is true without the MB prior.
We use an up-to-date compilation of Tully–Fisher data to search for transitions in the evolution of the Tully–Fisher relation. Using an up-to-date data compilation, we find hints at ≈3σ level for a transition at critical distances Dc≃9 Mpc and Dc≃17 Mpc. We split the full sample in two subsamples, according to the measured galaxy distance with respect to splitting distance Dc, and identify the likelihood of the best-fit slope and intercept of one sample with respect to the best-fit corresponding values of the other sample. For Dc≃9 Mpc and Dc≃17 Mpc, we find a tension between the two subsamples at a level of Δχ2>17(3.5σ). Using Monte Carlo simulations, we demonstrate that this result is robust with respect to random statistical and systematic variations of the galactic distances and is unlikely in the context of a homogeneous dataset constructed using the Tully–Fisher relation. If the tension is interpreted as being due to a gravitational strength transition, it would imply a shift in the effective gravitational constant to lower values for distances larger than Dc by ΔGG≃−0.1. Such a shift is of the anticipated sign and magnitude but at a somewhat lower distance (redshift) than the gravitational transition recently proposed to address the Hubble and growth tensions (ΔGG≃−0.1 at the transition redshift of zt≲0.01 (Dc≲40 Mpc)).
Measurement of the distances to nearby galaxies has improved rapidly in recent decades. The ever-present challenge is to reduce systematic effects, especially as greater distances are probed and the uncertainties become larger. In this paper, we combine several recent calibrations of the tip of the red giant branch (TRGB) method. These calibrations are internally self-consistent at the 1% level. New Gaia Early Data Release 3 data provide an additional consistency check at a (lower) 5% level of accuracy, a result of the well-documented Gaia angular covariance bias. The updated TRGB calibration applied to a sample of Type Ia supernovae from the Carnegie Supernova Project results in a value of the Hubble constant of H0 = 69.8 ± 0.6 (stat) ± 1.6 (sys) km s⁻¹Mpc⁻¹. No statistically significant difference is found between the value of H0 based on the TRGB and that determined from the cosmic microwave background. The TRGB results are also consistent to within 2σ with the SHoES and Spitzer plus Hubble Space Telescope (HST) Key Project Cepheid calibrations. The TRGB results alone do not demand additional new physics beyond the standard (λCDM) cosmological model. They have the advantage of simplicity of the underlying physics (the core He flash) and small systematic uncertainties (from extinction, metallicity, and crowding). Finally, the strengths and weaknesses of both the TRGB and Cepheids are reviewed, and prospects for addressing the current discrepancy with future Gaia, HST, and James Webb Space Telescope observations are discussed. Resolving this discrepancy is essential for ascertaining if the claimed tension in H0between the locally measured and CMB-inferred values is physically motivated.
New physics increasing the expansion rate just prior to recombination is among the least unlikely solutions to the Hubble tension and would be expected to leave an important signature in the early integrated Sachs-Wolfe (eISW) effect, a source of cosmic microwave background (CMB) anisotropies arising from the time variation of gravitational potentials when the Universe was not completely matter dominated. Why, then, is there no clear evidence for new physics from the CMB alone, and why does the Λ cold dark matter (ΛCDM) model fit CMB data so well? These questions and the vastness of the Hubble tension theory model space provide the motivation for general consistency tests of ΛCDM. I perform an eISW-based consistency test of ΛCDM introducing the parameter AeISW, which rescales the eISW contribution to the CMB power spectra. A fit to Planck CMB data yields AeISW=0.988±0.027, in perfect agreement with the ΛCDM expectation AeISW=1 and posing an important challenge for early-time new physics, which I illustrate in a case study focused on early dark energy (EDE). I explicitly show that the increase in ωc needed for EDE to preserve the fit to the CMB, which has been argued to worsen the fit to weak lensing and galaxy clustering measurements, is specifically required to lower the amplitude of the eISW effect, which would otherwise exceed ΛCDM’s prediction by ≈20%: this is a generic problem beyond EDE that likely applies to most models enhancing the expansion rate around recombination. Early-time new physics models invoked to address the Hubble tension are therefore faced with the significant challenge of making a similar prediction to ΛCDM for the eISW effect while not degrading the fit to other measurements in doing so.
The mismatch between the locally measured expansion rate of the universe and the one inferred from the cosmic microwave background measurements by Planck in the context of the standard ΛCDM, known as the Hubble tension, has become one of the most pressing problems in cosmology. A large number of amendments to the ΛCDM model have been proposed in order to solve this tension. Many of them introduce new physics, such as early dark energy, modifications of the standard model neutrino sector, extra radiation, primordial magnetic fields or varying fundamental constants, with the aim of reducing the sound horizon at recombination r ⋆ . We demonstrate here that any model which only reduces r ⋆ can never fully resolve the Hubble tension while remaining consistent with other cosmological datasets. We show explicitly that models which achieve a higher Hubble constant with lower values of matter density Ω m h ² run into tension with the observations of baryon acoustic oscillations, while models with larger Ω m h ² develop tension with galaxy weak lensing data.
This paper investigates whether changes to late-time physics can resolve the ‘Hubble tension’. It is argued that many of the claims in the literature favouring such solutions are caused by a misunderstanding of how distance ladder measurements actually work and, in particular, by the inappropriate use of a distance ladder H0 prior. A dynamics-free inverse distance ladder shows that changes to late-time physics are strongly constrained observationally and cannot resolve the discrepancy between the SH0ES data and the base ΛCDM cosmology inferred from Planck. We propose a statistically rigorous scheme to replace the use of H0 priors.
The simplest ΛCDM model provides a good fit to a large span of cosmological data but harbors large areas of phenomenology and ignorance. With the improvement of the number and the accuracy of observations, discrepancies among key cosmological parameters of the model have emerged. The most statistically significant tension is the 4σ to 6σ disagreement between predictions of the Hubble constant, H 0, made by the early time probes in concert with the 'vanilla' ΛCDM cosmological model, and a number of late time, model-independent determinations of H 0 from local measurements of distances and redshifts. The high precision and consistency of the data at both ends present strong challenges to the possible solution space and demands a hypothesis with enough rigor to explain multiple observations - whether these invoke new physics, unexpected large-scale structures or multiple, unrelated errors. A thorough review of the problem including a discussion of recent Hubble constant estimates and a summary of the proposed theoretical solutions is presented here. We include more than 1000 references, indicating that the interest in this area has grown considerably just during the last few years. We classify the many proposals to resolve the tension in these categories: early dark energy, late dark energy, dark energy models with 6 degrees of freedom and their extensions, models with extra relativistic degrees of freedom, models with extra interactions, unified cosmologies, modified gravity, inflationary models, modified recombination history, physics of the critical phenomena, and alternative proposals. Some are formally successful, improving the fit to the data in light of their additional degrees of freedom, restoring agreement within 1-2σ between Planck 2018, using the cosmic microwave background power spectra data, baryon acoustic oscillations, Pantheon SN data, and R20, the latest SH0ES Team Riess, et al (2021 Astrophys. J. 908 L6) measurement of the Hubble constant (H 0 = 73.2 1.3 km s-1 Mpc-1 at 68% confidence level). However, there are many more unsuccessful models which leave the discrepancy well above the 3σ disagreement level. In many cases, reduced tension comes not simply from a change in the value of H 0 but also due to an increase in its uncertainty due to degeneracy with additional physics, complicating the picture and pointing to the need for additional probes. While no specific proposal makes a strong case for being highly likely or far better than all others, solutions involving early or dynamical dark energy, neutrino interactions, interacting cosmologies, primordial magnetic fields, and modified gravity provide the best options until a better alternative comes along.
The disagreement between direct late-time measurements of the Hubble constant from the SH0ES collaboration, and early-universe measurements based on the ΛCDM model from the Planck collaboration might, at least in principle, be explained by new physics in the early universe. Recently, the application of the Effective Field Theory of Large-Scale Structure to the full shape of the power spectrum of the SDSS/BOSS data has revealed a new, rather powerful, way to measure the Hubble constant and the other cosmological parameters from Large-Scale Structure surveys. In light of this, we analyze two models for early universe physics, Early Dark Energy and Rock 'n' Roll, that were designed to significantly ameliorate the Hubble tension. Upon including the information from the full shape to the Planck, BAO, and Supernovae measurements, we find that the degeneracies in the cosmological parameters that were introduced by these models are well broken by the data, so that these two models do not significantly ameliorate the tension.
The increasingly significant tensions within ΛCDM, combined with the lack of detection of dark matter (DM) in laboratory experiments, have boosted interest in non-minimal dark sectors, which are theoretically well-motivated and inspire new search strategies for DM. Here we consider, for the first time, the possibility of DM having simultaneous interactions with photons, baryons, and dark radiation (DR). We have developed a new and efficient version of the Boltzmann code class that allows for one DM species to have multiple interaction channels. With this framework we reassess existing cosmological bounds on the various interaction coefficients in multi-interacting DM scenarios. We find no clear degeneracies between these different interactions and show that their cosmological effects are largely additive. We further investigate the possibility of these models to alleviate the cosmological tensions, and find that the combination of DM-photon and DM-DR interactions can at the same time reduce the S8 tension (from 2.3σ to 1.2σ) and the H0 tension (from 4.3σ to 3.1σ). The public release of our code will pave the way for the study of various rich dark sectors.
We present an expanded sample of 75 Milky Way Cepheids with Hubble Space Telescope ( HST ) photometry and Gaia EDR3 parallaxes, which we use to recalibrate the extragalactic distance ladder and refine the determination of the Hubble constant. All HST observations were obtained with the same instrument (WFC3) and filters (F555W, F814W, F160W) used for imaging of extragalactic Cepheids in Type Ia supernova (SN Ia) hosts. The HST observations used the WFC3 spatial scanning mode to mitigate saturation and reduce pixel-to-pixel calibration errors, reaching a mean photometric error of 5 millimags per observation. We use new Gaia EDR3 parallaxes, greatly improved since DR2, and the period–luminosity (P–L) relation of these Cepheids to simultaneously calibrate the extragalactic distance ladder and to refine the determination of the Gaia EDR3 parallax offset. The resulting geometric calibration of Cepheid luminosities has 1.0% precision, better than any alternative geometric anchor. Applied to the calibration of SNe Ia, it results in a measurement of the Hubble constant of 73.0 ± 1.4 km s ⁻¹ Mpc ⁻¹ , in good agreement with conclusions based on earlier Gaia data releases. We also find the slope of the Cepheid P–L relation in the Milky Way, and the metallicity dependence of its zero-point, to be in good agreement with the mean values derived from other galaxies. In combination with the best complementary sources of Cepheid calibration, we reach 1.8% precision and find H 0 = 73.2 ± 1.3 km s ⁻¹ Mpc ⁻¹ , a 4.2 σ difference with the prediction from Planck CMB observations under ΛCDM. We expect to reach ∼1.3% precision in the near term from an expanded sample of ∼40 SNe Ia in Cepheid hosts.
We present a new open-source code that calculates one-loop power spectra and cross spectra for matter fields and biased tracers in real and redshift space. These spectra incorporate all ingredients required for a direct application to data: nonlinear bias and redshift-space distortions, infrared resummation, counterterms, and the Alcock-Paczynski effect. Our code is based on the Boltzmann solver class and inherits its advantageous properties: user friendliness, ease of modification, high speed, and simple interface with other software. We present detailed descriptions of the theoretical model, the code structure, approximations, and accuracy tests. A typical end-to-end run for one cosmology takes 0.3 seconds, which is sufficient for Markov chain Monte Carlo parameter extraction. As an example, we apply the code to the Baryon Oscillation Spectroscopic Survey (BOSS) data and infer cosmological parameters from the shape of the galaxy power spectrum.
We present cosmological parameter results from the final full-mission Planck measurements of the cosmic microwave background (CMB) anisotropies, combining information from the temperature and polarization maps and the lensing reconstruction. Compared to the 2015 results, improved measurements of large-scale polarization allow the reionization optical depth to be measured with higher precision, leading to significant gains in the precision of other correlated parameters. Improved modelling of the small-scale polarization leads to more robust constraints on many parameters, with residual modelling uncertainties estimated to affect them only at the 0.5σ level. We find good consistency with the standard spatially-flat 6-parameter ΛCDM cosmology having a power-law spectrum of adiabatic scalar perturbations (denoted “base ΛCDM” in this paper), from polarization, temperature, and lensing, separately and in combination. A combined analysis gives dark matter density Ωch2 = 0.120 ± 0.001, baryon density Ωbh2 = 0.0224 ± 0.0001, scalar spectral index ns = 0.965 ± 0.004, and optical depth τ = 0.054 ± 0.007 (in this abstract we quote 68% confidence regions on measured parameters and 95% on upper limits). The angular acoustic scale is measured to 0.03% precision, with 100θ* = 1.0411 ± 0.0003. These results are only weakly dependent on the cosmological model and remain stable, with somewhat increased errors, in many commonly considered extensions. Assuming the base-ΛCDM cosmology, the inferred (model-dependent) late-Universe parameters are: Hubble constant H0 = (67.4 ± 0.5) km s−1 Mpc−1; matter density parameter Ωm = 0.315 ± 0.007; and matter fluctuation amplitude σ8 = 0.811 ± 0.006. We find no compelling evidence for extensions to the base-ΛCDM model. Combining with baryon acoustic oscillation (BAO) measurements (and considering single-parameter extensions) we constrain the effective extra relativistic degrees of freedom to be Neff = 2.99 ± 0.17, in agreement with the Standard Model prediction Neff = 3.046, and find that the neutrino mass is tightly constrained to ∑mν < 0.12 eV. The CMB spectra continue to prefer higher lensing amplitudes than predicted in base ΛCDM at over 2σ, which pulls some parameters that affect the lensing amplitude away from the ΛCDM model; however, this is not supported by the lensing reconstruction or (in models that also change the background geometry) BAO data. The joint constraint with BAO measurements on spatial curvature is consistent with a flat universe, ΩK = 0.001 ± 0.002. Also combining with Type Ia supernovae (SNe), the dark-energy equation of state parameter is measured to be w0 = −1.03 ± 0.03, consistent with a cosmological constant. We find no evidence for deviations from a purely power-law primordial spectrum, and combining with data from BAO, BICEP2, and Keck Array data, we place a limit on the tensor-to-scalar ratio r0.002 < 0.06. Standard big-bang nucleosynthesis predictions for the helium and deuterium abundances for the base-ΛCDM cosmology are in excellent agreement with observations. The Planck base-ΛCDM results are in good agreement with BAO, SNe, and some galaxy lensing observations, but in slight tension with the Dark Energy Survey’s combined-probe results including galaxy clustering (which prefers lower fluctuation amplitudes or matter density parameters), and in significant, 3.6σ, tension with local measurements of the Hubble constant (which prefer a higher value). Simple model extensions that can partially resolve these tensions are not favoured by the Planck data.
The Hubble tension between the ΛCDM-model-dependent prediction of the current expansion rate H0 using Planck data and direct, model-independent measurements in the local universe from the SH0ES collaboration disagree at >3.5σ. Moreover, there exists a milder ∼ 2σ tension between similar predictions for the amplitude S8 of matter fluctuations and its measurement in the local universe. As explanations relying on unresolved systematics have not been found, theorists have been exploring explanations for these anomalies that modify the cosmological model, altering early-universe-based predictions for these parameters. However, new cosmological models that attempt to resolve one tension often worsen the other. In this paper, we investigate a decaying dark matter (DDM) model as a solution to both tensions simultaneously. Here, a fraction of dark matter density decays into dark radiation. The decay rate Γ is proportional to the Hubble rate H through the constant αdr, the only additional parameter of this model. Then, this model deviates most from ΛCDM in the early universe, with αdr being positively correlated with H0 and negatively with S8. Hence, increasing αdr (and allowing dark matter to decay in this way) can then diminish both tensions simultaneously. When only considering Planck CMB data and the local SH0ES prior on H0, ∼ 1% dark matter decays, decreasing the S8 tension to 0.3σ and increasing the best-fit H0 by 1.6 km/s/Mpc. However, the addition of intermediate-redshift data (the JLA supernova dataset and baryon acoustic oscillation data) weakens the effectiveness of this model. Only ∼ 0.5% of the dark matter decays bringing the S8 tension back up to ∼ 1.5 σ and the increase in the best-fit H0 down to 0.4 km/s/Mpc.
Many theoretical resolutions to the so-called “Hubble tension” rely on modifying the sound horizon at recombination, rs, and thus the acoustic scale used as a standard ruler in the cosmic microwave background (CMB) and large scale structure (LSS) datasets. As shown in a number of recent works, these observables can also be used to compute rs-independent constraints on H0 by making use of the horizon scale at matter-radiation equality, keq, which has different sensitivity to high redshift physics than rs. As such, rs- and keq-based measurements of H0 (within a ΛCDM framework) may differ if there is new physics present pre-recombination. In this work, we present the tightest constraints on the latter from current data, finding H0=64.8−2.5+2.2 km s−1 Mpc−1 at 68% CL from a combination of BOSS galaxy power spectra, Planck CMB lensing, and the newly released pantheon+ supernova constraints, as well as physical priors on the baryon density, neutrino mass, and spectral index. The BOSS and Planck measurements have different degeneracy directions, leading to the improved combined constraints, with a bound of H0=67.1−2.9+2.5 (63.6−3.6+2.9) from BOSS (Planck) alone in km s−1 Mpc−1 units. The results show some dependence on the neutrino mass bounds, with the constraint broadening to H0=68.0−3.2+2.9 km s−1 Mpc−1 if we instead impose a weak prior on ∑mν from terrestrial experiments rather than assuming ∑mν<0.26 eV, or shifting to H0=64.6±2.4 kms−1 Mpc−1 if the neutrino mass is fixed to its minimal value. Even without dependence on the sound horizon, our results are in ≈3σ tension with those obtained from the Cepheid-calibrated distance ladder, which begins to cause problems for new physics models that vary H0 by changing acoustic physics or the expansion history immediately prior to recombination.
The Hubble tension seems to be a crisis with ∼5σ discrepancy between the most recent local distance ladder measurement from type Ia supernovae calibrated by Cepheids and the global fitting constraint from the cosmic microwave background data. To narrow down the possible late-time solutions to the Hubble tension, we have used in a recent study [Phys. Rev. D 105, L021301 (2022)] an improved inverse distance ladder method calibrated by the absolute measurements of the Hubble expansion rate at high redshifts from the cosmic chronometer data, and found no appealing evidence for new physics at the late time beyond the ΛCDM model characterized by a parametrization based on the cosmic age. In this paper, we further investigate the perspective of this improved inverse distance ladder method by including the late-time matter perturbation growth data. Independent of the dataset choices, model parametrizations, and diagnostic quantities (S8 and S12), the new physics at the late time beyond the ΛCDM model is strongly disfavored so that the previous late-time no-go guide for the Hubble tension is further strengthened.
Despite the remarkable success of the Λ Cold Dark Matter (ΛCDM) cosmological model, a growing discrepancy has emerged (currently measured at the level of ∼4−6σ) between the value of the Hubble constant H0 measured using the local distance ladder and the value inferred using the cosmic microwave background and galaxy surveys. While a vast array of ΛCDM extensions have been proposed to explain these discordant observations, understanding the (relative) success of these models in resolving the tension has proven difficult — this is a direct consequence of the fact that each model has been subjected to differing, and typically incomplete, compilations of cosmological data. In this review, we attempt to make a systematic comparison of seventeen different models which have been proposed to resolve the H0 tension (spanning both early- and late-Universe solutions), and quantify the relative success of each using a series of metrics and a vast array of data combinations. Owing to the timely appearance of this article, we refer to this contest as the “H0 Olympics”; the goal being to identify which of the proposed solutions, and more broadly which underlying mechanisms, are most likely to be responsible for explaining the observed discrepancy (should unaccounted for systematics not be the culprit). This work also establishes a foundation of tests which will allow the success of novel proposals to be meaningfully “benchmarked”.
We investigate constraints on early dark energy (EDE) using ACT DR4, SPT-3G 2018, Planck polarization, and restricted Planck temperature data (at ℓ<650), finding a 3.3σ preference (Δχ2=−16.2 for three additional degrees of freedom) for EDE over ΛCDM. The EDE contributes a maximum fractional energy density of fEDE(zc)=0.163−0.04+0.047 at a redshift zc=3357±200 and leads to a CMB inferred value of the Hubble constant H0=74.2−2.1+1.9 km/s/Mpc. We find that Planck and ACT DR4 data provide the majority of the improvement in χ2, and that the inclusion of SPT-3G pulls the posterior of fEDE(zc) away from ΛCDM. This is the first time that a moderate preference for EDE has been reported for these combined CMB datasets including Planck polarization. We find that including measurements of supernovae luminosity distances and the baryon acoustic oscillation standard ruler only minimally affects the preference (3.0σ), while measurements that probe the clustering of matter at late times—the lensing potential power spectrum from Planck and fσ8 from BOSS—decrease the significance of the preference to 2.6σ. Conversely, adding a prior on the H0 value as reported by the SH0ES collaboration increases the preference to the 4−5σ level. In the absence of this prior, the inclusion of Planck TT data at ℓ>1300 reduces the preference from 3.0σ to 2.3σ and the constraint on fEDE(zc) becomes compatible with ΛCDM at 1σ. We explore whether systematic errors in the Planck polarization data may affect our conclusions and find that changing the TE polarization efficiencies significantly reduces the Planck preference for EDE. More work will be necessary to establish whether these hints for EDE within CMB data alone are the sole results of systematic errors or an opening to new physics.
Emerging high-redshift cosmological probes, in particular quasars (QSOs), show a preference for larger matter densities, Ωm≈1, within the flat ΛCDM framework. Here, using the Risaliti-Lusso relation for standardizable QSOs, we demonstrate that the QSOs recover the same Planck-ΛCDM universe as type Ia supernovae (SN), Ωm≈0.3 at lower redshifts 0<z≲0.7, before transitioning to an Einstein–de Sitter universe (Ωm=1) at higher redshifts z≳1. We illustrate the same trend, namely increasing Ωm and decreasing H0 with redshift, in SN but poor statistics prevent a definitive statement. We explain physically why the trend may be expected and show the intrinsic bias through non-Gaussian tails with mock SN data. Our results highlight an intrinsic bias in the flat ΛCDM universe, whereby Ωm increases, H0 decreases and S8 increases with effective redshift, thus providing a new perspective on ΛCDM tensions; even in a Planck-ΛCDM universe the current tensions may be expected.
A number of challenges to the standard ΛCDM model have been emerging during the past few years as the accuracy of cosmological observations improves. In this review we discuss in a unified manner many existing signals in cosmological and astrophysical data that appear to be in some tension (2σ or larger) with the standard ΛCDM model as specified by the Cosmological Principle, General Relativity and the Planck18 parameter values. In addition to the well-studied 5σ challenge of ΛCDM (the Hubble H0 tension) and other well known tensions (the growth tension, and the lensing amplitude AL anomaly), we discuss a wide range of other less discussed less-standard signals which appear at a lower statistical significance level than the H0 tension some of them known as ’curiosities’ in the data) which may also constitute hints towards new physics. For example such signals include cosmic dipoles (the fine structure constant α, velocity and quasar dipoles), CMB asymmetries, BAO Lyα tension, age of the Universe issues, the Lithium problem, small scale curiosities like the core-cusp and missing satellite problems, quasars Hubble diagram, oscillating short range gravity signals etc. The goal of this pedagogical review is to collectively present the current status (2022 update) of these signals and their level of significance, with emphasis on the Hubble tension and refer to recent resources where more details can be found for each signal. We also briefly discuss theoretical approaches that can potentially explain some of these signals.
As cosmological data have improved, tensions have arisen. One such tension is the difference between the locally measured Hubble constant H0 and the value inferred from the cosmic microwave background (CMB). Interacting radiation has been suggested as a solution, but studies show that conventional models are precluded by high-ℓ CMB polarization data. It seems at least plausible that a solution may be provided by related models that distinguish between high- and low-ℓ multipoles. When interactions of strongly-coupled radiation are mediated by a force carrier that becomes nonrelativistic, the dark radiation undergoes a “step” in which its relative energy density increases as the mediator deposits its entropy into the lighter species. If this transition occurs while CMB-observable modes are inside the horizon, high- and low-ℓ peaks are impacted differently, corresponding to modes that enter the horizon before or after the step. These dynamics are naturally packaged into the simplest supersymmetric theory, the Wess-Zumino model, with the mass of the scalar mediator near the eV scale. We investigate the cosmological signatures of such Wess-Zumino dark radiation (WZDR) and find that it provides an improved fit to the CMB alone, favoring larger values of H0. If supernovae measurements from the SH0ES Collaboration are also included in the analysis, the inferred value of H0 is yet larger, but the preference for dark radiation and the location of the transition is left nearly unchanged. Utilizing a standardized set of measures, we compare to other models and find that WZDR is among the most successful at addressing the H0 tension and is the best of those with a Lagrangian formulation.
In this work, we shall provide an F(R) gravity theoretical framework for solving the H0-tension. Specifically, by exploiting the F(R) gravity correspondence with a scalar-tensor theory, we shall provide a condition in which when it is satisfied, the H0-tension is alleviated. The condition that remedies the H0-tension restricts the corresponding F(R) gravity, and we present in brief the theoretical features of the constrained F(R) gravity theory in both the Jordan and Einstein frames. The condition that may remedy the H0-tension is based on the existence of a metastable de Sitter point that occurs for redshifts near the recombination. This metastable de Sitter vacuum restricts the functional form of the F(R) gravity in the Jordan frame. We also show that by appropriately choosing the F(R) gravity, along with the theoretical solution offered for the H0-tension problem, one may also provide a unified description of the inflationary era with the late-time accelerating era, in terms of two extra de Sitter vacua. We propose a new approach to F(R) gravity by introducing a new class of integral F(R) gravity functions, which may be wider than the usual class expressed in terms of elementary F(R) gravity functions. Finally, the Einstein frame inflationary dynamics formalism is briefly discussed.
Gravitational transitions at low redshifts (zt < 0.1) have been recently proposed as a solution to the Hubble and growth tensions. Such transitions would naturally lead to a transition in the absolute magnitude M of type Ia supernovae (SnIa) at zt (Late M Transitions - LMT) and possibly in the dark energy equation of state parameter w (Late w − M Transitions - LwMT). Here, we compare the quality of fit of this class of models to cosmological data, with the corresponding quality of fit of the cosmological constant model (ΛCDM) and some of the best smooth H(z) deformation models (wCDM, CPL, PEDE). We also perform model selection via the Akaike Information Criterion and the Bayes factor. We use the full CMB temperature anisotropy spectrum data, the baryon acoustic oscillations (BAO) data, the Pantheon SnIa data, the SnIa absolute magnitude M as determined by Cepheid calibrators and the value of the Hubble constant H0 as determined by local SnIa calibrated using Cepheids. We find that smooth H(z) deformation models perform worse than transition models for the following reasons: 1) They have a worse fit to low-z geometric probes (BAO and SnIa data); 2) They favor values of the SnIa absolute magnitude M that are lower as compared to the value Mc obtained with local Cepheid calibrators at z < 0.01; 3) They tend to worsen the Ωm,0−σ8,0 growth tension. We also find that the w−M transition model (LwMT) does not provide a better quality of fit to cosmological data than a pure M transition model (LMT) where w is fixed to the ΛCDM value w = −1 at all redshifts. We conclude that the LMT model has significant statistical advantages over smooth late-time H(z) deformation models in addressing the Hubble crisis.
H0 constraints from galaxy surveys are sourced by the geometric properties of two standardizable rulers: the sound horizon scale, rs, and the matter-radiation equality scale, keq. While most analyses over the past decade have focused on the first scale, recent work has emphasised that the second can provide an independent source of information about the expansion rate of the Universe. In this work, we demonstrate an improved method for performing such a measurement with future galaxy surveys such as Euclid. Previous approaches have avoided rs-based information by removing the prior on the baryon density, and thus the sound-horizon calibration. Here, we present a new method to marginalize over rs; this allows baryon information to be retained, which enables tighter parameter constraints. For a Euclid-like spectroscopic survey, we forecast sound-horizon independent H0 constraints of σH0=0.7 km s−1 Mpc−1 for our method using the equality scale, compared with σH0=0.5 km s−1 Mpc−1 from the sound horizon. Upcoming equality scale H0 measurements thus can be highly competitive, although we caution that the impact of observational systematics on such measurements still needs to be investigated in detail. Applying our new approach to the BOSS power spectrum gives H0=69.5−3.5+3.0 km s−1 Mpc−1 from equality alone, somewhat tighter than previous constraints. Consistency of rs- and keq-based H0 measurements can provide a valuable internal consistency test of the cosmological model; as an example, we consider the change in H0 created by early dark energy. Assuming the Planck+SH0ES best-fit early dark energy model we find a 2.6σ shift (ΔH0=2.6 km s−1 Mpc−1) between the two measurements for Euclid; if we instead assume the ACT best-fit model, this increases to 9.0σ (ΔH0=7.8 km s−1 Mpc−1).
Sterile neutrinos can affect the evolution of the universe, and thus using the cosmological observations can search for sterile neutrinos. In this work, we use the cosmic microwave background anisotropy data from the Planck 2018 release, combined with the latest baryon acoustic oscillation, type Ia supernova, and Hubble constant data, to constrain the cosmological models with considering sterile neutrinos. In order to test the influences of the properties of dark energy on the results of searching for sterile neutrinos, in addition to the Λ cold dark matter (ΛCDM) model, we also consider the wCDM model and the holographic dark energy (HDE) model. We find that the existence of sterile neutrinos is not preferred when the H0 local measurement is not included in the data combination. When the H0 measurement is included in the joint constraints, it is found that ΔNeff>0 is favored at about 2.7σ level for the ΛCDM model and at about 1–1.7σ level for the wCDM model. However, mν,sterileeff still cannot be well constrained and only upper limits can be given. In addition, we find that the HDE model is definitely ruled out by the current data. We also discuss the issue of the Hubble tension, and we conclude that involving sterile neutrinos in the cosmological models cannot truly resolve the Hubble tension.
We reanalyze the Cepheid data used to infer the value of the Hubble constant H0 by calibrating type Ia supernovae. We do not enforce a universal value of the empirical Cepheid calibration parameters RW (Cepheid Wesenheit color-luminosity parameter) and MHW (Cepheid Wesenheit H-band absolute magnitude). Instead, we allow for variation of either of these parameters for each individual galaxy. We also consider the case where these parameters have two universal values: one for low galactic distances D Dc, where Dc is a critical transition distance. We find hints for a 3σ level mismatch between the low and high galactic distance parameter values. We then use model selection criteria [Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC)], which penalize models with large numbers of parameters, to compare and rank the following types of RW and MHW parameter variations: Base models: Universal values for RW and MHW (no parameter variation), I: Individual fitted galactic RW with one universal fitted MHW, II: One universal fixed RW with individual fitted galactic MHW, III: One universal fitted RW with individual fitted galactic MHW, IV: Two universal fitted RW (near and far) with one universal fitted MHW, V: One universal fitted RW with two universal fitted MHW (near and far), and VI: Two universal fitted RW (near and far) with two universal fitted MHW (near and far). We find that the AIC and BIC model selection criteria consistently favor model IV instead of the commonly used Base model, where no variation is allowed for the Cepheid empirical parameters. The best-fit value of the SnIa absolute magnitude MB and of H0 implied by the favored model IV is consistent with the inverse distance ladder calibration based on the cosmic microwave background sound horizon H0=67.4±0.5 km s−1 Mpc−1. Thus, in the context of the favored model IV the Hubble crisis is not present. This model may imply the presence of a fundamental physics transition taking place at a time more recent than 100 Myr ago.
We study an expanding two-fluid model of nonrelativistic dark matter and radiation, which are allowed to interact during a certain time span and to establish an approximate thermal equilibrium. Such an interaction, which generates an effective bulk viscous pressure at background level, is expected to be relevant for times around the transition from radiation to matter dominance. We quantify the magnitude of this pressure for dark-matter particle masses within the range 1 eV≲mχ≲10 eV around the matter-radiation equality epoch (i.e., redshift zeq∼3400) and demonstrate that the existence of a transient bulk viscosity has consequences which may be relevant for addressing current tensions of the standard cosmological model: (i) the additional (negative) pressure contribution modifies the expansion rate around zeq, yielding a larger H0 value, and (ii) large-scale structure formation is impacted by suppressing the amplitude of matter overdensity growth via a new viscous friction-term contribution to the Mészáros effect. As a result, the H0 and S8 tensions of the current standard cosmological model are both significantly alleviated.
The mismatch in the value of the Hubble constant from low- and high-redshift observations may be recast as a discrepancy between the low- and high-redshift determinations of the luminosity of Type Ia supernovae, the latter featuring an absolute magnitude which is ≈0.2 mag lower. Here, we propose that a rapid transition in the value of the relative effective gravitational constant μG≡GeffGN at zt≃0.01 could explain the lower luminosity (higher magnitude) of local supernovae, thus solving the H0 crisis. In other words, here the tension is solved by featuring a transition at the perturbative rather than background level. A model that features μG=1 for z≲0.01 but μG≃0.9 for z≳0.01 is trivially consistent with local gravitational constraints but would raise the Chandrasekhar mass and so decrease the absolute magnitude of type Ia supernovae at z≳0.01 by the required value of ≈0.2 mag. Such a rapid transition of the effective gravitational constant would not only resolve the Hubble tension but it would also help resolve the growth tension as it would reduce the growth of density perturbations without affecting the Planck/ΛCDM background expansion.
We present a novel scenario in which light (∼few eV) dark fermions (sterile neutrinos) interact with a scalar field as in mass-varying neutrino dark energy theories. As the eV sterile states naturally become nonrelativistic before the matter-radiation equality (MRE), we show that the neutrino-scalar fluid develops strong perturbative instability followed by the formation of neutrino nuggets, and the early dark energy (EDE) behavior disappears around MRE. The stability of the nugget is achieved when the Fermi pressure balances the attractive scalar force, and we numerically find the mass and radius of heavy cold nuggets by solving for the static configuration for the scalar field. We find that for the case when dark matter nugget density is subdominant and most of the EDE go into scalar field dynamics, it can in principle relax the Hubble anomaly. Especially when a kinetic-energy-dominated phase appears after the phase transition, the DE density dilutes faster than radiation and satisfies the requirements for solving the H 0 anomaly. In our scenario, unlike in originally proposed early DE theory, the DE density is controlled by (eV) neutrino mass and it does not require a fine-tuned EDE scale. We perform a Markov Chain Monte Carlo analysis and confront our model with Planck + SHOES and baryon acoustic oscillation data and find evidence for a nonzero neutrino-scalar EDE density during MRE. Our analysis shows that this model is in agreement to nearly 1.3σ with SHOES measurement, which is H 0 = 74.03 1.42 km s-1 Mpc-1. © 2021. The American Astronomical Society. All rights reserved..
A shorter sound horizon scale at the recombination epoch, arising from introducing extra energy components such as extra radiation or early dark energy (EDE), is a simple approach to resolving the so-called Hubble tension. We compare EDE models, an extra radiation model, and a model in which EDE and extra radiation coexist, paying attention to the fit to big bang nucleosynthesis (BBN). We find that the fit to BBN in EDE models is somewhat poorer than that in the ΛCDM model, because the increased inferred baryon asymmetry leads to a smaller deuterium abundance. We find that an extra radiation–EDE coexistence model gives the largest present Hubble parameter H0 among the models studied. We also examine the differences between the results obtained with and without consideration of the BBN. The difference in the extra radiation model is 3.22<Neff<3.49(68%) for data sets without BBN and 3.16<Neff<3.40(68%) for data sets with BBN, which is so large that the 1σ border of the larger side becomes the 2σ border.
Hubble tension is routinely presented as a mismatch between the Hubble constant H0 determined locally and a value inferred from the flat ΛCDM cosmology. In essence, the tension boils down to a disagreement between two numbers. Here, assuming the tension is cosmological in origin, we predict that within flat ΛCDM there should be other inferred values of H0, and that a “running of H0 with redshift” can be expected. These additional determinations of H0 may be traced to a difference between the effective equation of state (EoS) of the Universe within the Friedmann-Lemaître-Robertson-Walker (FLRW) cosmology framework and the current standard model. We introduce a diagnostic that flags such a running of H0.
A dark-energy which behaves as the cosmological constant until a sudden phantom transition at very-low redshift (z < 0.1) seems to solve the >4σ disagreement between the local and high-redshift determinations of the Hubble constant, while maintaining the phenomenological success of the ΛCDM model with respect to the other observables. Here, we show that such a hockey-stick dark energy cannot solve the H0 crisis. The basic reason is that the supernova absolute magnitude MB that is used to derive the local H0 constraint is not compatible with the MB that is necessary to fit supernova, BAO and CMB data, and this disagreement is not solved by a sudden phantom transition at very-low redshift. We make use of this example to show why it is preferable to adopt in the statistical analyses the prior on MB as an alternative to the prior on H0. The three reasons are: i) one avoids potential double counting of low-redshift supernovae, ii) one avoids assuming the validity of cosmography, in particular fixing the deceleration parameter to the standard model value q0 = −0.55, iii) one includes in the analysis the fact that MB is constrained by local calibration, an information which would otherwise be neglected in the analysis, biasing both model selection and parameter constraints. We provide the priors on MB relative to the recent Pantheon and DES-SN3YR supernova catalogs. We also provide a Gaussian joint prior on H0 and q0 that generalizes the prior on H0 by SH0ES.
A rapid phantom transition of the dark energy equation of state parameter w at a transition redshift zt<0.1 of the form w(z)=−1+Δw Θ(zt−z) with Δw<0 can lead to a higher value of the Hubble constant while closely mimicking a Planck18/ΛCDM form of the comoving distance r(z)=∫0zdz′H(z′) for z>zt. Such a transition however would imply a significantly lower value of the SnIa absolute magnitude M than the value MC imposed by local Cepheid calibrators at z<0.01. Thus, in order to resolve the H0 tension it would need to be accompanied by a similar transition in the value of the SnIa absolute magnitude M as M(z)=MC+ΔM Θ(z−zt) with ΔM<0. This is a late w−M phantom transition (LwMPT). It may be achieved by a sudden reduction of the value of the normalized effective Newton constant μ=Geff/GN by about 6% assuming that the absolute luminosity of SnIa is proportional to the Chandrasekhar mass which varies as μ−3/2. We demonstrate that such an ultra low z abrupt feature of w−M provides a better fit to cosmological data compared to smooth late time deformations of H(z) that also address the Hubble tension. For zt=0.02 we find Δw≃−4, ΔM≃−0.1. This model also addresses the growth tension due to the predicted lower value of μ at z>zt. A prior of Δw=0 (no w transition) can still resolve the H0 tension with a larger amplitude M transition with ΔM≃−0.2 at zt≃0.01. This implies a larger reduction of μ for z>0.01 (about 12%). The LwMPT can be generically induced by a scalar field nonminimally coupled to gravity with no need of a screening mechanism since in this model μ=1 at z<0.01.
A constant early dark energy (EDE) component contributing a fraction fEDE(zc)∼10% of the energy density of the universe around zc≃3500 and diluting as or faster than radiation afterwards, can provide a simple resolution to the Hubble tension, the ∼5σ discrepancy—in the ΛCDM context—between the H0 value derived from early- and late-universe observations. However, it has been pointed out that including Large-Scale Structure (LSS) data, which are in ∼3σ tension with ΛCDM and EDE cosmologies, might break some parameter degeneracy and alter these conclusions. We reassess the viability of the EDE against a host of high- and low-redshift measurements, by combining LSS observations from recent weak lensing (WL) surveys with CMB, baryon acoustic oscillation (BAO), growth function (FS) and Supernova Ia (SNIa) data. Introducing a model whose only parameter is fEDE(zc), we report in agreement with past work a ∼2σ preference for nonzero fEDE(zc) from Planck CMB data alone, while the tension with the local H0 measurement from sh0es is reduced below 2σ. Adding BAO, FS and SNIa does not affect this conclusion, while the inclusion of a prior on H0 from sh0es increase the preference for EDE over ΛCDM to the ∼3.6σ level. After checking the EDE nonlinear matter power spectrum as predicted by standard semi-analytical algorithms via a dedicated set of N-body simulations, we test the 1-parameter EDE cosmology against WL data. We find that it does not significantly worsen the fit to the S8 measurement as compared to ΛCDM, and that current WL observations do not exclude the EDE resolution to the Hubble tension. We also caution against the interpretation of constraints obtained from combining statistically inconsistent datasets within the ΛCDM cosmology. In light of the CMB lensing anomalies, we show that the lensing-marginalized CMB data also favor nonzero fEDE(zc) at ∼2σ, predicts H0 in 1.4σ agreement with sh0es and S8 in 1.5σ and 0.8σ agreement with kids-viking and des respectively. There still exists however a ∼2.5σ tension with the joint results from kids-viking and des. With an eye on Occam’s razor, we finally discuss promising extensions of the EDE cosmology that could allow us to fully restore cosmological concordance.
Two sources of geometric information are encoded in the galaxy power spectrum: the sound horizon at recombination and the horizon at matter-radiation equality. Analyzing the BOSS 12th data release galaxy power spectra using perturbation theory with Ωm priors from Pantheon supernovae but no priors on Ωb, we obtain constraints on H0 from the second scale, finding H0=65.1−5.4+3.0 km s−1 Mpc−1; this differs from the best fit of SH0ES at 95% confidence. Similar results are obtained if Ωm is constrained from uncalibrated baryon acoustic oscillations: H0=65.6−5.5+3.4 km s−1 Mpc−1. Adding the analogous lensing results from Baxter and Sherwin from 2020, the posterior shifts to 70.6−5.0+3.7 km s−1 Mpc−1. Using mock data, Fisher analyses, and scale cuts, we demonstrate that our constraints do not receive significant information from the sound horizon scale. Since many models resolve the H0 controversy by adding new physics to alter the sound horizon, our measurements are a consistency test for standard cosmology before recombination. A simple forecast indicates that such constraints could reach σH0≃1.6 km s−1 Mpc−1 in the era of Euclid.
Measurements of the Hubble constant, H0, from the cosmic distance ladder are currently in tension with the value inferred from Planck observations of the CMB and other high redshift datasets if a flat ΛCDM cosmological model is assumed. One of the few promising theoretical resolutions of this tension is to invoke new physics that changes the sound horizon scale in the early universe; this can bring CMB and BAO constraints on H0 into better agreement with local measurements. In this paper, we discuss how a measurement of the Hubble constant can be made from the CMB without using information from the sound horizon scale, rs. In particular, we show how measurements of the CMB lensing power spectrum can place interesting constraints on H0 when combined with measurements of either supernovae or galaxy weak lensing, which constrain the matter density parameter. The constraints arise from the sensitivity of the CMB lensing power spectrum to the horizon scale at matter-radiation equality (in projection); this scale could have a different dependence on new physics than the sound horizon. From an analysis of current CMB lensing data from Planck and Pantheon supernovae with conservative external priors, we derive an rs-independent constraint of H0 = 73.5 ± 5.3 km/s/Mpc. Forecasts for future CMB surveys indicate that improving constraints beyond an error of σ(H0) = 3 km/s/Mpc will be difficult with CMB lensing, although applying similar methods to the galaxy power spectrum may allow for further improvements.
We consider a low redshift (z<0.7) cosmological data set comprising megamasers, cosmic chronometers, type Ia supernovae and baryon acoustic oscillations, which we bin according to their redshift. For each bin, we read the value of H0 by fitting directly to the flat ΛCDM model. Doing so, we find that H0 descends with redshift, allowing one to fit a line with a nonzero slope of statistical significance 2.1σ. Our analysis rests on the use of cosmic chronometers to break a degeneracy in baryon acoustic oscillations data and it will be imperative to revisit this feature as data improves. Nevertheless, our results provide the first independent indication of the descending trend reported by the H0LiCOW Collaboration. If substantiated going forward, early Universe solutions to the Hubble tension will struggle explaining this trend.
We measure cosmic weak lensing shear power spectra with the Subaru Hyper Suprime-Cam (HSC) survey first-year shear catalog covering 137 deg2 of the sky. Thanks to the high effective galaxy number density of ∼17 arcmin−2, even after conservative cuts such as a magnitude cut of i < 24.5 and photometric redshift cut of 0.3 ≤ z ≤ 1.5, we obtain a high-significance measurement of the cosmic shear power spectra in four tomographic redshift bins, achieving a total signal-to-noise ratio of 16 in the multipole range 300 ≤ ℓ ≤ 1900. We carefully account for various uncertainties in our analysis including the intrinsic alignment of galaxies, scatters and biases in photometric redshifts, residual uncertainties in the shear measurement, and modeling of the matter power spectrum. The accuracy of our power spectrum measurement method as well as our analytic model of the covariance matrix are tested against realistic mock shear catalogs. For a flat Λ cold dark matter model, we find $S\,_{8}\equiv \sigma _8(\Omega _{\rm m}/0.3)^\alpha =0.800^{+0.029}_{-0.028}$ for α = 0.45 ($S\,_8=0.780^{+0.030}_{-0.033}$ for α = 0.5) from our HSC tomographic cosmic shear analysis alone. In comparison with Planck cosmic microwave background constraints, our results prefer slightly lower values of S8, although metrics such as the Bayesian evidence ratio test do not show significant evidence for discordance between these results. We study the effect of possible additional systematic errors that are unaccounted for in our fiducial cosmic shear analysis, and find that they can shift the best-fit values of S8 by up to ∼0.6 σ in both directions. The full HSC survey data will contain several times more area, and will lead to significantly improved cosmological constraints.
We present measurements of cosmic shear two-point correlation functions (TPCFs) from Hyper Suprime-Cam Subaru Strategic Program (HSC) first-year data, and derive cosmological constraints based on a blind analysis. The HSC first-year shape catalog is divided into four tomographic redshift bins ranging from $z=0.3$ to 1.5 with equal widths of $\Delta z =0.3$. The unweighted galaxy number densities in each tomographic bin are 5.9, 5.9, 4.3, and $2.4\:$arcmin$^{-2}$ from the lowest to highest redshifts, respectively. We adopt the standard TPCF estimators, $\xi _\pm$, for our cosmological analysis, given that we find no evidence of significant B-mode shear. The TPCFs are detected at high significance for all 10 combinations of auto- and cross-tomographic bins over a wide angular range, yielding a total signal-to-noise ratio of 19 in the angular ranges adopted in the cosmological analysis, $7^{\prime }<\theta <56^{\prime }$ for $\xi _+$ and $28^{\prime }<\theta <178^{\prime }$ for $\xi _-$. We perform the standard Bayesian likelihood analysis for cosmological inference from the measured cosmic shear TPCFs, including contributions from intrinsic alignment of galaxies as well as systematic effects from PSF model errors, shear calibration uncertainty, and source redshift distribution errors. We adopt a covariance matrix derived from realistic mock catalogs constructed from full-sky gravitational lensing simulations that fully account for survey geometry and measurement noise. For a flat $\Lambda$ cold dark matter model, we find $S\,_8 \equiv \sigma _8\sqrt{\Omega _{\rm m}/0.3}=0.804_{-0.029}^{+0.032}$, and $\Omega _{\rm m}=0.346_{-0.100}^{+0.052}$. We carefully check the robustness of the cosmological results against astrophysical modeling uncertainties and systematic uncertainties in measurements, and find that none of them has a significant impact on the cosmological constraints.
Recently, a phenomenologically emergent dark energy (PEDE) model was presented with a dark energy density evolving as $\widetilde{\Omega }_{\rm {DE}}(z) = \Omega _{\rm {DE,0}}[ 1 - {\rm {tanh}}({\log }_{10}(1+z))]$, i.e. with no degree of freedom. Later on, a generalized model was proposed by adding one degree of freedom to the PEDE model, encoded in the parameter Δ. Motivated by these proposals, we constrain the parameter space ($h,\Omega _m^{(0)}$) and ($h,\Omega _m^{(0)}, \Delta$) for PEDE and generalized emergent dark energy (GEDE), respectively, by employing the most recent observational (non-)homogeneous and differential age Hubble data. Additionally, we reconstruct the deceleration and jerk parameters and estimate yield values at z = 0 of $q_0 = -0.784^{+0.028}_{-0.027}$ and $j_0 = 1.241^{+0.164}_{-0.149}$ for PEDE and $q_0 = -0.730^{+0.059}_{-0.067}$ and $j_0 = 1.293^{+0.194}_{-0.187}$ for GEDE using the homogeneous sample. We report values on the deceleration–acceleration transition redshift with those reported in the literature within 2σ CL. Furthermore, we perform a stability analysis of the PEDE and GEDE models to study the global evolution of the Universe around their critical points. Although the PEDE and GEDE dynamics are similar to the standard model, our stability analysis indicates that in both models there is an accelerated phase at early epochs of the Universe evolution.
Current cosmological data exhibit a tension between inferences of the Hubble constant, H0, derived from early and late-Universe measurements. One proposed solution is to introduce a new component in the early Universe, which initially acts as “early dark energy” (EDE), thus decreasing the physical size of the sound horizon imprinted in the cosmic microwave background (CMB) and increasing the inferred H0. Previous EDE analyses have shown this model can relax the H0 tension, but the CMB-preferred value of the density fluctuation amplitude, σ8, increases in EDE as compared to Λ cold dark matter (ΛCDM), increasing tension with large-scale structure (LSS) data. We show that the EDE model fit to CMB and SH0ES data yields scale-dependent changes in the matter power spectrum compared to ΛCDM, including 10% more power at k=1 h/Mpc. Motivated by this observation, we reanalyze the EDE scenario, considering LSS data in detail. We also update previous analyses by including Planck 2018 CMB likelihoods, and perform the first search for EDE in Planck data alone, which yields no evidence for EDE. We consider several data set combinations involving the primary CMB, CMB lensing, supernovae, baryon acoustic oscillations, redshift-space distortions, weak lensing, galaxy clustering, and local distance-ladder data (SH0ES). While the EDE component is weakly detected (3σ) when including the SH0ES data and excluding most LSS data, this drops below 2σ when further LSS data are included. Further, this result is in tension with strong constraints imposed on EDE by CMB and LSS data without SH0ES, which show no evidence for this model. We also show that physical priors on the fundamental scalar field parameters further weaken evidence for EDE. We conclude that the EDE scenario is, at best, no more likely to be concordant with all current cosmological data sets than ΛCDM, and appears unlikely to resolve the H0 tension.