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H_0$ Ex Machina: Vacuum Metamorphosis and Beyond $H_0
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Abstract
We do not solve tensions with concordance cosmology; we do obtain $H_0\approx 74\,$km/s/Mpc from CMB+BAO+SN data in our model, but that is not the point. Discrepancies in Hubble constant values obtained by various astrophysical probes should not be viewed in isolation. While one can resolve at least some of the differences through either an early time transition or late time transition in the expansion rate, these introduce other changes. We advocate a holistic approach, using a wide variety of cosmic data, rather than focusing on one number, $H_0$. Vacuum metamorphosis, a late time transition physically motivated by quantum gravitational effects and with the same number of parameters as \lcdm, can successfully give a high $H_0$ value from cosmic microwave background data but fails when combined with multiple distance probes. We also explore the influence of spatial curvature, and of a conjoined analysis of cosmic expansion and growth.
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We present a joint analysis of the Planck cosmic microwave background (CMB) and Baryon Oscillation Spectroscopic Survey (BOSS) final data releases. A key novelty of our study is the use of a new full-shape (FS) likelihood for the redshift-space galaxy power spectrum of the BOSS data, based on an improved perturbation theory template. We show that the addition of the redshift-space galaxy clustering measurements breaks degeneracies present in the CMB data alone and tightens constraints on cosmological parameters. Assuming the minimal ΛCDM cosmology with massive neutrinos, we find the following late-Universe parameters: the Hubble constant H0=67.95−0.52+0.66 km s−1 Mpc−1, the matter density fraction Ωm=0.3079−0.0085+0.0065, the mass fluctuation amplitude σ8=0.8087−0.0072+0.012, and an upper limit on the sum of neutrino masses Mtot<0.16 eV (95% C.L.). This can be contrasted with the Planck-only measurements: H0=67.14−0.72+1.3 km s−1 Mpc−1, Ωm=0.3188−0.016+0.0091, σ8=0.8053−0.0091+0.019, and Mtot<0.26 eV (95% C.L.). Our bound on the sum of neutrino masses relaxes once the hierarchy-dependent priors from the oscillation experiments are imposed. The addition of the new FS likelihood also constrains the effective number of extra relativistic degrees of freedom, Neff=2.88±0.17. Our study shows that the current FS and the pure baryon acoustic oscillation data add a similar amount of information in combination with the Planck likelihood. We argue that this is just a coincidence given the BOSS volume and efficiency of the current reconstruction algorithms. In the era of future surveys FS will play a dominant role in cosmological parameter measurements.
The tip of the red giant branch (TRGB) method provides one of the most accurate and precise means of measuring the distances to nearby galaxies. Here we present a multi-wavelength, VIJHK absolute calibration of the TRGB based on observations of TRGB stars in the Large Magellanic Cloud (LMC), grounded on a geometric distance, determined by detached eclipsing binaries (DEBs). This paper presents a more detailed description of the method first presented by Freedman et al. for measuring corrections for the total line-of-sight extinction and reddening to the LMC. In this method, we use a differential comparison of the red giant population in the LMC, first with red giants in the Local Group galaxy IC 1613, and then with those in the Small Magellanic Cloud (SMC). As a consistency check, we derive an independent calibration of the TRGB sequence using the SMC alone, invoking its geometric distance also calibrated by DEBs. An additional consistency check comes from near-infrared observations of Galactic globular clusters covering a wide range of metallicities. In all cases we find excellent agreement in the zero-point calibration. We then examine the recent claims by Yuan et al., demonstrating that, in the case of the SMC, they corrected for extinction alone while neglecting the essential correction for reddening. In the case of IC 1613, we show that their analysis contains an incorrect treatment of (over-correction for) metallicity. Using our revised (and direct) measurement of the LMC TRGB extinction, we find a value of H 0 = 69.6 ± 0.8 (±1.1% stat) ± 1.7 (±2.4% sys) km s ⁻¹ Mpc ⁻¹ .
We present cosmological constraints based on the cosmic microwave background (CMB) lensing potential power spectrum measurement from the recent 500 deg² SPTPOL survey, the most precise CMB lensing measurement from the ground to date. We fit a flat ΛCDM model to the reconstructed lensing power spectrum alone and in addition with other data sets: baryon acoustic oscillations (BAO), as well as primary CMB spectra from Planck and SPTPOL. The cosmological constraints based on SPTPOL and Planck lensing band powers are in good agreement when analyzed alone and in combination with Planck full-sky primary CMB data. With weak priors on the baryon density and other parameters, the SPTPOL CMB lensing data alone provide a 4% constraint on σ₈Ω^(0.25)_m = 0.593 ± 0.025. Jointly fitting with BAO data, we find σ₈ = 0.779±0.023, Ω_m = 0.368^(+0.032)_(−0.037), and H₀ = 72.0^(+2.1)_(−2.5)kms⁻¹ Mpc⁻¹, up to 2σ away from the central values preferred by Planck lensing + BAO. However, we recover good agreement between SPTPOL and Planck when restricting the analysis to similar scales. We also consider single-parameter extensions to the flat ΛCDM model. The SPTPOL lensing spectrum constrains the spatial curvature to be Ω_K = −0.0007±0.0025 and the sum of the neutrino masses to be ∑m_ν < 0.23 eV at 95% C.L. (with Planck primary CMB and BAO data), in good agreement with the Planck lensing results. With the differences in the signal-to-noise ratio of the lensing modes and the angular scales covered in the lensing spectra, this analysis represents an important independent check on the full-sky Planck lensing measurement.
The recent Planck Legacy 2018 release has confirmed the presence of an enhanced lensing amplitude in cosmic microwave background power spectra compared with that predicted in the standard Λ cold dark matter model, where Λ is the cosmological constant. A closed Universe can provide a physical explanation for this effect, with the Planck cosmic microwave background spectra now preferring a positive curvature at more than the 99% confidence level. Here, we further investigate the evidence for a closed Universe from Planck, showing that positive curvature naturally explains the anomalous lensing amplitude, and demonstrating that it also removes a well-known tension in the Planck dataset concerning the values of cosmological parameters derived at different angular scales. We show that since the Planck power spectra prefer a closed Universe, discordances higher than generally estimated arise for most of the local cosmological observables, including baryon acoustic oscillations. The assumption of a flat Universe could therefore mask a cosmological crisis where disparate observed properties of the Universe appear to be mutually inconsistent. Future measurements are needed to clarify whether the observed discordances are due to undetected systematics, or to new physics or simply are a statistical fluctuation. The standard cosmological model assumes a flat Universe, but some model inconsistencies appear when curvature is allowed, as supported by the latest Planck Legacy 2018 power spectra. Is it time to consider new physics?
We investigate constraints on the Hubble constant (H_{0}) using Baryon Acoustic Oscillations (BAO) and baryon density measurements from Big Bang Nucleosynthesis (BBN). We start by investigating the tension between galaxy BAO measurements and those using the Lyman-α forest, within a Bayesian framework. Using the latest results from eBOSS DR14 we find that the probability of this tension being statistical is sime6.3% assuming flat ΛCDM. We measure H_{0} = 67.6±1.1 km s^{−1} Mpc^{−1}, with a weak dependence on the BBN prior used, in agreement with results from Planck Cosmic Microwave Background (CMB) results and in strong tension with distance ladder results. Finally, we forecast the future of BAO + BBN measurements of H^{0}, using the Dark Energy Spectroscopic Instrument (DESI). We find that the choice of BBN prior will have a significant impact when considering future BAO measurements from DESI.
We present an improved determination of the Hubble constant from Hubble Space Telescope (HST) observations of 70 long-period Cepheids in the Large Magellanic Cloud (LMC). These were obtained with the same WFC3 photometric system used to measure extragalactic Cepheids in the hosts of SNe Ia. Gyroscopic control of HST was employed to reduce overheads while collecting a large sample of widely separated Cepheids. The Cepheid period–luminosity relation provides a zero-point-independent link with 0.4% precision between the new 1.2% geometric distance to the LMC from detached eclipsing binaries (DEBs) measured by Pietrzyński et al. and the luminosity of SNe Ia. Measurements and analysis of the LMC Cepheids were completed prior to knowledge of the new DEB LMC distance. Combined with a refined calibration of the count-rate linearity of WFC3-IR with 0.1% precision, these three improved elements together reduce the overall uncertainty in the geometric calibration of the Cepheid distance ladder based on the LMC from 2.5% to 1.3%. Using only the LMC DEBs to calibrate the ladder, we find H 0 = 74.22 ± 1.82 km s⁻¹ Mpc⁻¹ including systematic uncertainties, 3% higher than before for this particular anchor. Combining the LMC DEBs, masers in NGC 4258, and Milky Way parallaxes yields our best estimate: H 0 = 74.03 ± 1.42 km s⁻¹ Mpc⁻¹, including systematics, an uncertainty of 1.91%–15% lower than our best previous result. Removing any one of these anchors changes H 0 by less than 0.7%. The difference between H 0 measured locally and the value inferred from Planck CMB and ΛCDM is 6.6 ± 1.5 km s⁻¹ Mpc⁻¹ or 4.4σ (P = 99.999% for Gaussian errors) in significance, raising the discrepancy beyond a plausible level of chance. We summarize independent tests showing that this discrepancy is not attributable to an error in any one source or measurement, increasing the odds that it results from a cosmological feature beyond ΛCDM.
The Einstein equations with quantum one-loop contributions of conformally covariant matter fields are shown to admit a class of nonsingular isotropic homogeneous solutions that correspond to a picture of the Universe being initially in the most symmetric (de Sitter) state.
We use a new and statistically powerful Planck likelihood to show that the Planck temperature and polarization spectra are consistent with a spatially flat Universe, in contrast to recent claims in the literature. When combined with other astrophysical data, particularly geometrical measurements of baryon acoustic oscillations, our likelihood constrains the Universe to be spatially flat to extremely high precision. We deduce a curvature density parameter ΩK = 0.0004 ± 0.0018 in good agreement with the 2018 results of the Planck team. In the context of inflationary cosmology, the observations offer strong support for models of inflation with a large number of e-foldings and disfavour models of incomplete inflation.
Phantom dark energy (w<−1) can produce amplified cosmic acceleration at late times, thus increasing the value of H0 favored by CMB data and releasing the tension with local measurements of H0. We show that the best fit value of H0 in the context of the CMB power spectrum is degenerate with a constant equation-of-state parameter w, in accordance with the approximate effective linear equation H0+30.93w−36.47=0 (H0 in km sec−1 Mpc−1). This equation is derived by assuming that both Ω0mh2 and dA=∫0zrecdzH(z) remain constant (for an invariant CMB spectrum) and equal to their best fit Planck/ΛCDM values as H0, Ω0m, and w vary. For w=−1, this linear degeneracy equation leads to the best fit H0=67.4 km sec−1 Mpc−1 as expected. For w=−1.22, the corresponding predicted CMB best fit Hubble constant is H0=74 km sec−1 Mpc−1, which is identical with the value obtained by local-distance ladder measurements, while the best fit matter density parameter is predicted to decrease, since Ω0mh2 is fixed. We verify the above H0−w degeneracy equation by fitting a wCDM model with fixed values of w to the Planck TT spectrum, showing also that the quality of fit (χ2) is similar to that of ΛCDM. However, when including SnIa, baryon acoustic oscillation, or growth data, the quality of fit becomes worse than ΛCDM when w<−1. Finally, we generalize the H0−w(z) degeneracy equation for the parametrization w(z)=w0+w1z/(1+z) and identify analytically the full w0−w1 parameter region (straight line) that leads to a best fit H0=74 km sec−1 Mpc−1 in the context of the Planck CMB spectrum. This exploitation of H0−w(z) degeneracy can lead to immediate identification of all parameter values of a given w(z) parametrization that can potentially resolve the H0 tension.
We present a measurement of the Hubble constant (H0) and other cosmological parameters from a joint analysis of six gravitationally lensed quasars with measured time delays. All lenses except the first are analyzed blindly with respect to the cosmological parameters. In a flat ΛCDM cosmology, we find $H_{0} = 73.3_{-1.8}^{+1.7}~\mathrm{km~s^{-1}~Mpc^{-1}}$, a $2.4{{\ \rm per\ cent}}$ precision measurement, in agreement with local measurements of H0 from type Ia supernovae calibrated by the distance ladder, but in 3.1σ tension with Planck observations of the cosmic microwave background (CMB). This method is completely independent of both the supernovae and CMB analyses. A combination of time-delay cosmography and the distance ladder results is in 5.3σ tension with Planck CMB determinations of H0 in flat ΛCDM. We compute Bayes factors to verify that all lenses give statistically consistent results, showing that we are not underestimating our uncertainties and are able to control our systematics. We explore extensions to flat ΛCDM using constraints from time-delay cosmography alone, as well as combinations with other cosmological probes, including CMB observations from Planck, baryon acoustic oscillations, and type Ia supernovae. Time-delay cosmography improves the precision of the other probes, demonstrating the strong complementarity. Allowing for spatial curvature does not resolve the tension with Planck. Using the distance constraints from time-delay cosmography to anchor the type Ia supernova distance scale, we reduce the sensitivity of our H0 inference to cosmological model assumptions. For six different cosmological models, our combined inference on H0 ranges from ∼73–78 km s−1 Mpc−1, which is consistent with the local distance ladder constraints.
We determine the Hubble constant H 0 precisely (2.3% uncertainty) in a manner independent of the cosmological model through Gaussian process regression, using strong lensing and supernova data. Strong gravitational lensing of a variable source can provide a time-delay distance D Δ t and angular diameter distance to the lens D d . These absolute distances can anchor Type Ia supernovae, which give an excellent constraint on the shape of the distance–redshift relation. Updating our previous results to use the H0LiCOW program’s milestone data set consisting of six lenses, four of which have both D Δ t and D d measurements, we obtain for a flat universe and for a non-flat universe. We carry out several consistency checks on the data and find no statistically significant tensions, though a noticeable redshift dependence persists in a particular systematic manner that we investigate. Speculating on the possibility that this trend of derived Hubble constant with lens distance is physical, we show how this can arise through modified gravity light propagation, which would also impact the weak lensing σ 8 tension.
Late times dark energy transitions at redshifts z≪0.1 can raise the predicted value of the Hubble constant to the SH0ES value, 74.03±1.42 (km s−1 Mpc−1) or more, while providing an equally good fit as ΛCDM at 67.73±0.41 to higher redshift data, in particular from the cosmic microwave background and baryon acoustic oscillations. These models however do not fully resolve the true source of tension between the distance ladder and high redshift observations: the local calibration of supernovae luminosities well out into the Hubble flow. When tested in this manner by transferring the SH0ES calibration to the Pantheon supernovae dataset, the ability of such transitions to raise the Hubble constant is reduced to 69.17±1.09. Such an analysis should also be used when testing any dynamical dark energy model which can produce similarly fine features in redshift or local void models.
The inconsistent Hubble constant values derived from cosmic microwave background (CMB) observations and from local distance-ladder measurements may suggest new physics beyond the standard ACDM paradigm. It has been found in earlier studies that, at least phenomenologically, non-standard recombination histories can reduce the ≳ 4δ Hubble tension to ∼ 2δ. Following this path, we vary physical and phenomenological parameters in RECFAST, the standard code to compute ionization history of the universe, to explore possible physics beyond standard recombination. We find that the CMB constraint on the Hubble constant is sensitive to the hydrogen ionization energy and 2s → 1s two-photon decay rate, both of which are atomic constants, and is insensitive to other details of recombination. Thus, the Hubble tension is very robust against perturbations of recombination history, unless exotic physics modifies the atomic constants during the recombination epoch.
We present a detailed investigation of a subdominant oscillating scalar field [“early dark energy” (EDE)] in the context of resolving the Hubble tension. Consistent with earlier work, but without relying on fluid approximations, we find that a scalar field frozen due to Hubble friction until log10(zc)∼3.5, reaching ρEDE(zc)/ρtot∼10% and diluting faster than matter afterwards, can bring cosmic microwave background (CMB), baryonic acoustic oscillations, supernovae luminosity distances, and the late-time estimate of the Hubble constant from the SH0ES Collaboration into agreement. A scalar field potential that scales as V(ϕ)∝ϕ2n with 2≲n≲3.4 around the minimum is preferred at the 68% confidence level, and the Planck polarization places additional constraints on the dynamics of perturbations in the scalar field. In particular, the data prefer a potential that flattens at large field displacements. A Markov-chain Monte Carlo analysis of mock data shows that the next-generation CMB observations (i.e., CMB-S4) can unambiguously detect the presence of the EDE at a very high significance. This projected sensitivity to the EDE dynamics is mainly driven by improved measurements of the E-mode polarization. We also explore new observational signatures of EDE scalar field dynamics: (i) We find that depending on the strength of the tensor-to-scalar ratio, the presence of the EDE might imply the existence of isocurvature perturbations in the CMB. (ii) We show that a strikingly rapid, scale-dependent growth of EDE field perturbations can result from parametric resonance driven by the anharmonic oscillating field for n≈2. This instability and ensuing potentially nonlinear, spatially inhomogeneous, dynamics may provide unique signatures of this scenario.
Measurements of the Hubble constant and, more generally, measurements of the expansion rate and distances over the interval 0<z<1 appear to be inconsistent with the predictions of the standard cosmological model (ΛCDM) given observations of cosmic microwave background temperature and polarization anisotropies. Here we consider a variety of types of departures from ΛCDM that could, in principle, restore concordance among these datasets, and we explain why we find almost all of them unlikely to be successful. We single out the set of solutions that increases the expansion rate in the decade of scale factor expansion just prior to recombination as the least unlikely. These solutions are themselves tightly constrained by their impact on photon diffusion and on the gravitational driving of acoustic oscillations of the modes that begin oscillating during this epoch—modes that project on to angular scales that are very well measured. We point out that a general feature of such solutions is a residual to fits to ΛCDM, like the one observed in Planck power spectra. This residual drives the modestly significant inferences of angular-scale dependence to the matter density and anomalously high lensing power, puzzling aspects of a dataset that is otherwise extremely well fit by ΛCDM.
Consistency between cosmological datasets is essential for ongoing and future cosmological analyses. We first investigate the questions of stability and applicability of some moment-based inconsistency measures to multiple datasets. We show that the recently introduced index of inconsistency (IOI) is numerically stable while it can be applied to multiple datasets. We use an illustrative construction of constraints as well as an example with real datasets (i.e., WMAP versus Planck) to show some limitations of the application of the Karhunen-Loeve decomposition to discordance measures. Second, we perform various consistency analyses using IOI between multiple current datasets while working with the entire common parameter spaces. We find current large-scale-structure (LSS) datasets [Planck cosmic microwave background lensing, Dark Energy Survey (DES) lensing clustering, and sloan digital sky survey, redshift space distorsions] all to be consistent with one another. This is found to not be the case for Planck temperature (temperature auto correlation, TT) versus polarization [temperature and E-mode polarization cross correlation (TE), E-mode polarization auto correlation (EE)] data, where moderate inconsistencies are present. Noteworthy, we find a strong inconsistency between joint LSS probes and Planck with IOI=5.27, and a moderate tension between DES and Planck with IOI=3.14. Next, using the IOI metric, we compare the Hubble constant from five independent probes. We confirm previous strong tensions between local measurement (Supernovae, HO, for the equation of state of dark energy, SH0ES) and Planck as well as between H0 lenses in COSMOGRAIL’s wellspring and Planck, but also find new strong tensions between SH0ES measurement and the joint LSS probes with IOI=6.73 (i.e., 3.7−σ in one dimension) as well as between joint LSS and combined probes SH0ES+H0LiCOW with IOI=8.59 (i.e., 4.1−σ in one dimension). Whether because of systematic effects in the datasets or problems with the underlying model, sources of these old and new tensions need to be identified and dealt with.
We discuss the ability of a dark fluid becoming relevant around the time of matter-radiation equality to significantly relieve the tension between local measurements of the Hubble constant and cosmic microwave background (CMB) inference, within the ΛCDM model. We show that the gravitational impact of acoustic oscillations in the dark fluid balance the effects on the CMB and result in an improved fit to CMB measurements themselves while simultaneously raising the Hubble constant. The required balance favors a model where the fluid is a scalar field that converts its potential to kinetic energy around matter-radiation equality, which then quickly redshifts away. We derive the requirements on the potential for this conversion mechanism and find that a simple canonical scalar with two free parameters for its local slope and amplitude robustly improves the fit to the combined data by Δχ2≈12.7 over ΛCDM. We uncover the CMB polarization signatures that can definitively test this scenario with future data.
Motivated by the current status of cosmological observations and significant tensions in the estimated values of some key parameters assuming the standard ΛCDM model, we propose a simple but radical phenomenological emergent dark energy model where dark energy has no effective presence in the past and emerges at later times. Theoretically, in this phenomenological dark energy model with zero degrees of freedom (similar to a ΛCDM model), one can derive that the equation of state of dark energy increases from in the past to −1 in the future. We show that by setting a hard-cut 2 σ lower bound prior for H 0 associated with a 97.72% probability from recent local observations, this model can satisfy different combinations of cosmological observations at low and high redshifts (SNe Ia, baryon acoustic oscillation (BAO), Ly α BAO, and cosmic microwave background (CMB)) substantially better than the concordance ΛCDM model with and Δ DIC ∼ −35.38. If there are no substantial systematics in SN Ia, BAO, or Planck CMB data, and assuming the reliability of current local H 0 measurements, there is a very high probability that with more precise measurements of the Hubble constant our proposed phenomenological model rules out the cosmological constant with decisive statistical significance and is a strong alternative to explain the combination of different cosmological observations. This simple phenomenologically emergent dark energy model can guide theoretically motivated dark energy model building activities.
Early dark energy (EDE) that behaves like a cosmological constant at early times (redshifts z≳3000) and then dilutes away like radiation or faster at later times can solve the Hubble tension. In these models, the sound horizon at decoupling is reduced resulting in a larger value of the Hubble parameter H0 inferred from the cosmic microwave background (CMB). We consider two physical models for this EDE, one involving an oscillating scalar field and another a slowly rolling field. We perform a detailed calculation of the evolution of perturbations in these models. A Markov Chain Monte Carlo search of the parameter space for the EDE parameters, in conjunction with the standard cosmological parameters, identifies regions in which H0 inferred from Planck CMB data agrees with the SH0ES local measurement. In these cosmologies, current baryon acoustic oscillation and supernova data are described as successfully as in the cold dark matter model with a cosmological constant, while the fit to Planck data is slightly improved. Future CMB and large-scale-structure surveys will further probe this scenario.
We propose a cosmological model, üΛCDM, based on “über gravity,” which is a canonical ensemble average of many theories of gravity. In this model, we have a sharp transition from (a purely) ΛCDM era to a phase in which the Ricci scalar is a constant. This transition occurs when the Ricci scalar reaches a critical scale or alternatively a transition redshift, z⊕. We use the observations of baryonic acoustic oscillations and supernovae Ia, as well as the cosmic microwave background data to constrain üΛCDM. This yields H0=70.6−1.3+1.1 km/s/Mpc, Ωm=0.2861±0.0092, and z⊕=0.537−0.375+0.277, providing a marginally better fit with a Akaike information criterion of 0.8. Therefore, üΛCDM can ease the H0 tension, albeit marginally, with one additional free parameter. We also provide a preliminary study of the linear perturbation theory in üΛCDM that points to interesting potential smoking guns in the observations of large scale structure at z<z⊕.
The Gibbs sampler, the algorithm of Metropolis and similar iterative simulation methods are potentially very helpful for summarizing multivariate distributions. Used naively, however, iterative simulation can give misleading answers. Our methods are simple and generally applicable to the output of any iterative simulation; they are designed for researchers primarily interested in the science underlying the data and models they are analyzing, rather than for researchers interested in the probability theory underlying the iterative simulations themselves. Our recommended strategy is to use several independent sequences, with starting points sampled from an overdispersed distribution. At each step of the iterative simulation, we obtain, for each univariate estimand of interest, a distributional estimate and an estimate of how much sharper the distributional estimate might become if the simulations were continued indefinitely. Because our focus is on applied inference for Bayesian posterior distributions in real problems, which often tend toward normality after transformations and marginalization, we derive our results as normal-theory approximations to exact Bayesian inference, conditional on the observed simulations. The methods are illustrated on a random-effects mixture model applied to experimental measurements of reaction times of normal and schizophrenic patients.
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