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We forecast the main cosmological parameter constraints achievable with the CORE space mission which is dedicated to mapping the polarisation of the Cosmic Microwave Background (CMB). CORE was recently submitted in response to ESA's fifth call for medium-sized mission proposals (M5). Here we report the results from our pre-submission study of the i...

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... We will first study the simple ΛCDM spatially-flat cosmological model with free sum of neutrino masses, the ΛCDM+ m ν model. We assume for simplicity the three neutrinos to have the same mass, since it has been shown that current experiments are sensitive only to the sum of neutrino masses, irrespective of how are they distributed [13]. ...
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The recent DESI 2024 Baryon Acoustic Oscillations (BAO) measurements combined with the CMB data from the Planck 18 PR3 dataset and the Planck PR4+ACT DR6 lensing data, with a prior on the sum of the neutrino masses $\sum m_\nu>0$, leads to a strong constraint, $\sum m_\nu<0.072$ eV, which would exclude the inverted neutrino hierarchy and put some tension on even the standard hierarchy. We show that actually this bound gets significantly relaxed when combining the new DESI measurements with the HiLLiPoP+LoLLiPoP likelihoods, based on the Planck 2020 PR4 dataset, and with supernovae datasets. We note that the fact that neutrino masses are pushed towards zero, and even towards negative values, is known to be correlated with the so-called $A_L$ tension, a mismatch between lensing and power spectrum measurements in the Planck PR3 data, which is reduced by HiLLiPoP+LoLLiPoP to less than 1$\sigma$. We find $\sum m_\nu<0.1$ eV and $\sum m_\nu<0.12$ eV, with the supernovae Pantheon+ and DES-SN5YR datasets respectively. The shift caused by these datasets is more compatible with the expectations from neutrino oscillation experiments, and both the normal and inverted hierarchy scenarios remain now viable, even with the $\sum m_\nu>0$ prior. Finally, we analyze neutrino mass bounds in an extension of $\Lambda$CDM that addresses the $H_0$ tension, with extra fluid Dark Radiation, finding that in such models bounds are further relaxed and the posterior probability for $\sum m_\nu$ begins to exhibit a peak at positive values.
... This degenerate mass model does not exactly correspond to either of the physically expected NH or IH scenarios; however, it produces a very good approximation of the observable effects of both [234]. In the event that a positive detection of non-zero neutrino mass is possible, an analysis using the degenerate mass model with a prior m ν > 0 will recover the correct value of m ν for both NH and IH scenarios with little reconstruction bias [235]. On the other hand, when a positive detection is not possible, using the degenerate model with appropriately modified priors on m ν as above will also recover the correct upper bounds for both the NH and IH scenarios [236]. ...
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... Here, we assume that the angle θ is allowed to vary in the range ½0; π=2, and the phases η, ϕ c , α 21 , and α 31 are randomly varied in the range ½0; 2π while the parameters a, b, and c are varied in the range ½−1; 1. The predicted upper bound value of P m i is close to the result of the Planck Collaboration [42], while the lower bound (∼0.06 eV) requires further studies in future cosmological data and may be tested in the future by experiments such as CORE þ BAO aiming to reach a 0.062 eV sensitivity [43]. For m β , the obtained values are far from the forthcoming β-decay experiment sensitivities [44][45][46][47], and thus require experiments with improved sensitivities around 0.02 eV. ...
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... For instance, the effective relativistic neutrino species, N eff , has been precisely measured to be N eff = 2.99 ± 0.17 [1], exhibiting good agreement with the prediction of the standard model (SM), N SM eff ≈ 3.045 [2][3][4][5][6]. Looking ahead, future precision measurements of N eff at CMB-S4 [7,8], SPT-3G [9], Simons Observatory [10,11], PICO [12], CORE [13] and CMB-HD [14] are anticipated to reach the percent level, providing an excellent opportunity to thoroughly probe the SM prediction, including the small deviation from three. ...
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A bstract We investigate the impact of new light particles, carrying significant energy in the early universe after neutrino decoupling, on the cosmological effective relativistic neutrino species, N eff . If the light particles are produced from decoupled neutrinos, N eff is predominantly modified through the dilution-resistant effect. This effect arises because the energy stored in the mass of new particles is less diluted than the photon and neutrino energy as the universe expands. Our study comprehensively explores this effect, deriving N eff constraints on the couplings of light mediators with neutrinos, encompassing both scalar and vector mediators. We find that the dilution-resistant effect can increase N eff by 0.118 and 0.242 for scalar and vector mediators, respectively. These values can be readily reached by forthcoming CMB experiments. Upon reaching these levels, future N eff constraints on the couplings will be improved by many orders of magnitude.
... If the ultimate resolution of the Hubble tension involves a slightly larger value of N CMB eff ≃ 3.27, consistent with Eq. (28c), then the orange region is favored. Future observatories, including SPT-3G [129], CORE [130], Simons Observatory [131], PICO [132], CMB-S4 [67], CMB-HD [133], are anticipated to reach much smaller values, for example CMB-S4 is anticipated to ultimately obtain ∆N eff ≃ 0.06 at 95% C.L. [67]. Here we see these future experiments are capable of probing a significantly larger fraction of the (m X , g X ) parameter space in both the Majorana and Dirac neutrino cases. ...
... In the SM, applying this procedure yields Y p | Eq. 41 SM = 0.248 in agreement with Y p | PDG = 0.245 ± 0.006 at 95% C.L. [28]. We define the BSM deviation of helium abundance as [67,[129][130][131][132][133], have the opportunity to gain sensitivity to a very weakly coupled U (1) B−L gauge boson in certain mass and coupling ranges that is not accessible by any other method. ...
... For the Dirac case shown in Fig. 8, however, there is a nontrivial region of parameter space (approximately 0.1 MeV ≲ m X ≲ 1 MeV, g X ≲ 4 × 10 −9 ), where the BBN constraints are stronger than the constraints from ∆N eff from Planck data. However, future CMB observatories [67,[129][130][131][132][133], will be able to fully cover this region, and probe considerably smaller couplings, once they achieve ∆N eff ≲ 0.15 sensitivity. ...
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We calculate the effects of a light, very weakly-coupled boson $X$ arising from a spontaneously broken $U(1)_{B-L}$ symmetry on $\Delta N_{\rm eff}$ as measured by the CMB and $Y_p$ from BBN. Our focus is the mass range $1 \; {\rm eV} \lesssim m_X \lesssim 100 \; {\rm MeV}$; masses lighter than about an ${\rm eV}$ have strong constraints from fifth-force law constraints, while masses heavier than about $100$~MeV are constrained by other probes. We do not assume $X$ began in thermal equilibrium with the SM; instead, we allow $X$ to freeze-in from its very weak interactions with the SM. We find $U(1)_{B-L}$ is more strongly constrained by $\Delta N_{\rm eff}$ than previously considered. The bounds arise from the energy density in electrons and neutrinos slowly siphoned off into $X$ bosons, which become nonrelativistic, redshift as matter, and then decay, dumping their slightly larger energy density back into the SM bath causing $\Delta N_{\rm eff} > 0$. While some of the parameter space has complementary constraints from stellar cooling, supernova emission, and terrestrial experiments, we find future CMB observatories can access regions of mass and coupling space not probed by any other method. In gauging $U(1)_{B-L}$, we assume the $[U(1)_{B-L}]^3$ anomaly is canceled by right-handed neutrinos, and so our $\Delta N_{\rm eff}$ calculations have been carried out in two scenarios: neutrinos have Dirac masses, or, right-handed neutrinos acquire Majorana masses. In the latter scenario, we comment on the additional implications of thermalized right-handed neutrinos decaying during BBN. We also briefly consider the possibility that $X$ decays into dark sector states. If these states behave as radiation, we find weaker constraints, whereas if they are massive, there are stronger constraints, though now from $\Delta N_{\rm eff} < 0$.
... Currently the leading ΔN eff constraint is set by measuring the damping tail and the phase shift in the CMB anisotropy spectrum (Hou et al. 2013;Follin et al. 2015;Ade et al. 2016;Wallisch 2018;Aich et al. 2020), which reads ΔN eff < 0.3 at 95% confidence level (C.L.) from the latest Planck CMB data (Planck Collaboration et al. 2020). Future CMB missions are expected to provide significant improvements on ΔN eff (Abazajian et al. 2016;Di Valentino et al. 2018;Hanany et al. 2019). For example, the CMB Stage IV (S4) experiment is aiming to constrain ΔN eff < 0.027 at 2σ C.L. (Abazajian et al. 2016;Baumann et al. 2016aBaumann et al. , 2016bWallisch 2018). ...
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Sufficiently large scalar perturbations in the early universe can create overdense regions that collapse into primordial black holes (PBHs). This process is accompanied by the emission of scalar-induced gravitational waves that behave like an extra radiation component, thus contributing to the relativistic degrees of freedom ( N eff ). We show that the cosmological constraints on N eff can be used to pose stringent limits on PBHs created from this particular scenario as well as the relevant small-scale curvature perturbation (   ( k ) ). We show that the combination of cosmic microwave background (CMB), baryon acoustic oscillation, and Big Bang nucleosynthesis data sets can exclude supermassive PBHs with peak mass M • ∈ [5 × 10 ⁵ , 5 × 10 ¹⁰ ] M ⊙ as the major component of dark matter, while the detailed constraints depend on the shape of the PBHs’ mass distribution. A future CMB mission such as CMB-S4 can greatly broaden this constraint window to M • ∈ [8 × 10 ⁻⁵ , 5 × 10 ¹⁰ ] M ⊙ , covering substellar masses. These limits on PBHs correspond to a tightened constraint on   on scales of k ∈ [10, 10 ²² ] Mpc ⁻¹ , much smaller than those probed by direct CMB and large-scale structure power spectra.
... Since our lensing results originate from low redshifts, minimal extrapolation to z = 0 (where S CMBL 8 is evaluated) is required, which makes our constraints comparatively insensitive to neutrino mass. In constrast, for 37 Following the arguments in Lesgourgues & Pastor (2006) and Di Valentino et al. (2018), here we consider a degenerate combination of three equally massive neutrinos. CMB power spectrum constraints, extrapolation over a wide redshift range from z ∼ 1100 to z = 0 is required, which implies that the constraints have significant sensitivity to neutrino mass. ...
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We present new measurements of cosmic microwave background (CMB) lensing over $9400$ sq. deg. of the sky. These lensing measurements are derived from the Atacama Cosmology Telescope (ACT) Data Release 6 (DR6) CMB dataset, which consists of five seasons of ACT CMB temperature and polarization observations. We determine the amplitude of the CMB lensing power spectrum at $2.3\%$ precision ($43\sigma$ significance) using a novel pipeline that minimizes sensitivity to foregrounds and to noise properties. To ensure our results are robust, we analyze an extensive set of null tests, consistency tests, and systematic error estimates and employ a blinded analysis framework. The baseline spectrum is well fit by a lensing amplitude of $A_{\mathrm{lens}}=1.013\pm0.023$ relative to the Planck 2018 CMB power spectra best-fit $\Lambda$CDM model and $A_{\mathrm{lens}}=1.005\pm0.023$ relative to the $\text{ACT DR4} + \text{WMAP}$ best-fit model. From our lensing power spectrum measurement, we derive constraints on the parameter combination $S^{\mathrm{CMBL}}_8 \equiv \sigma_8 \left({\Omega_m}/{0.3}\right)^{0.25}$ of $S^{\mathrm{CMBL}}_8= 0.818\pm0.022$ from ACT DR6 CMB lensing alone and $S^{\mathrm{CMBL}}_8= 0.813\pm0.018$ when combining ACT DR6 and Planck NPIPE CMB lensing power spectra. These results are in excellent agreement with $\Lambda$CDM model constraints from Planck or $\text{ACT DR4} + \text{WMAP}$ CMB power spectrum measurements. Our lensing measurements from redshifts $z\sim0.5$--$5$ are thus fully consistent with $\Lambda$CDM structure growth predictions based on CMB anisotropies probing primarily $z\sim1100$. We find no evidence for a suppression of the amplitude of cosmic structure at low redshifts
... Our baseline constraint uses ACT lensing with Planck CMB anisotropies (and optical depth information from the SRoll2 re-analysis of the 16 This suppression is however degenerate with the physical matter density Ωmh 2 and hence it is crucial to incorporate BAO data that helps break this degeneracy (Pan & Knox 2015). 17 Following the arguments in Lesgourgues & Pastor (2006) and Di Valentino et al. (2018), we consider a degenerate combination of three equally massive neutrinos when varying mν . ...
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We present cosmological constraints from a gravitational lensing mass map covering 9400 sq. deg. reconstructed from CMB measurements made by the Atacama Cosmology Telescope (ACT) from 2017 to 2021. In combination with BAO measurements (from SDSS and 6dF), we obtain the amplitude of matter fluctuations $\sigma_8 = 0.819 \pm 0.015$ at 1.8% precision, $S_8\equiv\sigma_8({\Omega_{\rm m}}/0.3)^{0.5}=0.840\pm0.028$ and the Hubble constant $H_0= (68.3 \pm 1.1)\, \text{km}\,\text{s}^{-1}\,\text{Mpc}^{-1}$ at 1.6% precision. A joint constraint with CMB lensing measured by the Planck satellite yields even more precise values: $\sigma_8 = 0.812 \pm 0.013$, $S_8\equiv\sigma_8({\Omega_{\rm m}}/0.3)^{0.5}=0.831\pm0.023$ and $H_0= (68.1 \pm 1.0)\, \text{km}\,\text{s}^{-1}\,\text{Mpc}^{-1}$. These measurements agree well with $\Lambda$CDM-model extrapolations from the CMB anisotropies measured by Planck. To compare these constraints to those from the KiDS, DES, and HSC galaxy surveys, we revisit those data sets with a uniform set of assumptions, and find $S_8$ from all three surveys are lower than that from ACT+Planck lensing by varying levels ranging from 1.7-2.1$\sigma$. These results motivate further measurements and comparison, not just between the CMB anisotropies and galaxy lensing, but also between CMB lensing probing $z\sim 0.5-5$ on mostly-linear scales and galaxy lensing at $z\sim 0.5$ on smaller scales. We combine our CMB lensing measurements with CMB anisotropies to constrain extensions of $\Lambda$CDM, limiting the sum of the neutrino masses to $\sum m_{\nu} < 0.12$ eV (95% c.l.), for example. Our results provide independent confirmation that the universe is spatially flat, conforms with general relativity, and is described remarkably well by the $\Lambda$CDM model, while paving a promising path for neutrino physics with gravitational lensing from upcoming ground-based CMB surveys.
... The upper value for ∑ m i aligns with the upper limit reported by the Planck collaboration [28]. However, the lower value ∼0.063 eV requires additional investigations, and may be tested in future experiments, such as CORE+BAO which aim to achieve a sensitivity of 0.062 eV [29]. There are two additional avenues for exploring the absolute mass scale of neutrinos. ...
... The upper value for ∑ m i aligns with the upper limit reported by the Planck collaboration [28]. However, the lower value ∼ 0.063 eV requires additional investigations, and may be tested in future experiments, such as CORE+BAO which aim to achieve a sensitivity of 0.062 eV [29]. There are two additional avenues for exploring the absolute mass scale of neutrinos. ...