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The Hubble tension, a significant discrepancy between the Hubble constant ($H_0$) values derived from early-time (Cosmic Microwave Background and Baryon Acoustic Oscillations) and late-time (Cepheid-calibrated Type Ia Supernovae) measurements, remains a major challenge in cosmology. Traditional attempts to resolve this tension have struggled to maintain consistency with dynamical and geometrical probes at redshifts $0.01 < z \lesssim 2.5$. We explore a novel model introducing new degrees of freedom in local physical laws affecting calibrators like Cepheids and Type Ia Supernovae within a distance of $d \lesssim 50$ Mpc ($z \lesssim 0.01$). Specifically, we incorporate a gravitational transition causing a change in the gravitational constant ($G$) at a specific distance, affecting the Cepheid Period-Luminosity Relation (PLR) and the absolute magnitude of SNe Ia. We verify the inverse scaling of SN luminosity $L$ with Chandrasekhar Mass $M_C$ in a changed $G$ scenario as predicted using a semi-analytical model in a recent theoretical study \cite{Wright2018}. Fixing $\Delta G/G \approx 0.04$, our model naturally resolves the Hubble tension, yielding a best-fit $H_0$ value consistent with the Planck measurement, even without using Planck data. This approach suggests a potential resolution to the Hubble tension by aligning $H_0$ with high-redshift CMB measurements., Comment: 27 pages, 5 Figures, 7 Tables. Comments are welcome!

The very first light captured by the James Webb Space Telescope (JWST) revealed a population of galaxies at very high redshifts more massive than expected in the canonical $\Lambda$CDM model of structure formation. Barring, among others, a systematic origin of the issue, in this paper, we test alternative cosmological perturbation histories. We argue that models with a larger matter component $\Omega_m$ and/or a larger scalar spectral index $n_s$ can substantially improve the fit to JWST measurements. In this regard, phenomenological extensions related to the dark energy sector of the theory are appealing alternatives, with Early Dark Energy emerging as an excellent candidate to explain (at least in part) the unexpected JWST preference for larger stellar mass densities. Conversely, Interacting Dark Energy models, despite producing higher values of matter clustering parameters such as $\sigma_8$, are generally disfavored by JWST measurements. This is due to the energy-momentum flow from the dark matter to the dark energy sector, implying a smaller matter energy density. Upcoming observations may either strengthen the evidence or falsify some of these appealing phenomenological alternatives to the simplest $\Lambda$CDM picture., Comment: 35 pages, 6 figures, 8 tables. V2: New independent JWST datasets included in the analysis; clarified some points on the analysis methodology; clarified some results; additional references added. Version accepted for publication in JCAP

We study the possibility of measuring the optical depth at reionization, $\tau$, without relying on large-scale Cosmic Microwave Background (CMB) polarization. Our analysis is driven by the need to obtain competitive measurements that can validate the state-of-the-art constraints on this parameter, widely based on E-mode polarization measurements at $\ell\le 30$. This need is partially motivated by the typical concerns regarding anomalies observed in the Planck large-scale CMB data as well as by the remarkable fact that, excluding these latter, $\tau$ consistently exhibits correlations with anomalous parameters, such as $A_{\rm lens}$ and $\Omega_k$, suggesting that slightly higher values of the optical depth at reionization could significantly alleviate or even eliminate anomalies. Within the $\Lambda$CDM model, our most constraining result is $\tau = 0.080 \pm 0.012$, obtained by combining Planck temperature and polarization data at $\ell > 30$, the Atacama Cosmology Telescope (ACT) and Planck measurements of the lensing potential, Baryon Acoustic Oscillations (BAO), and Type-Ia supernova data from the Pantheon+ catalogue. Notably, using only ACT temperature, polarization, and lensing data in combination with BAO and supernovae, we obtain $\tau = 0.076 \pm 0.015$, which is entirely independent of Planck. The relative precision of these results is approaching the constraints based on large-scale CMB polarization ($\tau = 0.054 \pm 0.008$). Despite the overall agreement, we report a slight $1.8\sigma$ shift towards larger values of $\tau$. We also test how these results change by extending the cosmological model. While in many extensions they remain robust, in general obtaining precise measurements of $\tau$ may become significantly more challenging., Comment: 24 pages, 7 Figures, 13 Tables. V2: version accepted for publication in PRD

The search for non-Gaussian signatures in the Cosmic Microwave Background (CMB) is crucial for understanding the physics of the early Universe. Given the possibility of non-Gaussian fluctuations in the CMB, a recent revision to the standard $\Lambda$-Cold Dark Matter ($\Lambda$CDM) model has been proposed, dubbed "Super-$\Lambda$CDM". This model introduces additional free parameters to account for the potential effects of a trispectrum in the primordial fluctuations. In this study, we explore the impact of the Super-$\Lambda$CDM model on current constraints on neutrino physics. In agreement with previous research, our analysis reveals that for most of the datasets, the Super-$\Lambda$CDM parameter $A_0$ significantly deviates from zero at over a $95\%$ confidence level. We then demonstrate that this signal might influence current constraints in the neutrino sector. Specifically, we find that the current constraints on neutrino masses may be relaxed by over a factor of two within the Super-$\Lambda$CDM framework, thanks to the correlation present with $A_0$. Consequently, locking $A_0=0$ might introduce a bias, leading to overly stringent constraints on the total neutrino mass., Comment: 18 pages, 10 figures, 8 tables V2: Expanded the analysis conducted considering current local trispectrum constraints and implications in the SuperLCDM predictions

The recent observations from the James Webb Space Telescope have led to a surprising discovery of a significant density of massive galaxies with masses of $M \ge 10^{10.5} M_{\odot}$ at redshifts of approximately $z\sim 10$. This corresponds to a stellar mass density of roughly $\rho_*\sim 10^6 M_{\odot} Mpc^{-3}$. Despite making conservative assumptions regarding galaxy formation, this finding may not be compatible with the standard $\Lambda$CDM cosmology that is favored by observations of CMB Anisotropies from the Planck satellite. In this paper, we confirm the substantial discrepancy with Planck's results within the $\Lambda$CDM framework. Assuming a value of $\epsilon=0.2$ for the efficiency of converting baryons into stars, we indeed find that the $\Lambda$CDM model is excluded at more than $99.7 \%$ confidence level (C.L.). An even more significant exclusion is found for $\epsilon \sim 0.1$, while a better agreement, but still in tension at more than $95 \%$, is obtained for $\epsilon =0.32$. This tension, as already discussed in the literature, could arise either from systematics in the JWST measurements or from new physics. Here, as a last-ditch effort, we point out that disregarding the large angular scale polarization obtained by Planck, which allows for significantly larger values of the matter clustering parameter $\sigma_8$, could lead to better agreement between Planck and JWST within the $\Lambda$CDM framework. Interestingly, the model compatible with Planck temperature-only data and JWST observation also favors a higher Hubble constant $H_0=69.0\pm1.1$ km/s/Mpc at $68\%$ C.L., in better agreement with observations based on SN-Ia luminosity distances., Comment: 5 pages, 2 Figures, revised

The cosmic microwave background (CMB) temperature and polarization anisotropies, as observed by independent astronomical missions such as WMAP, Planck, and most recently the Atacama Cosmology Telescope and the South Pole Telescope have played a vital role in accurately constraining cosmological theories and models, establishing cosmic inflation as the most widely accepted theory for describing the physics of the early Universe. However, the absence of a definitive detection of B-mode polarization and the emerging discrepancies among different CMB experiments present a challenge in determining which inflationary models best explain the observed data. In this work, we further explore this difficulty and conduct a case study by analyzing four well-known inflationary potentials in light of the latest CMB temperature and polarization anisotropy measurements and lensing data released by the Planck satellite and the Atacama Cosmology Telescope. Additionally, we incorporate B-modes polarization data from the BICEP/Keck Collaboration, as well as Baryon Acoustic Oscillations and Redshift Space Distortions measurements from BOSS DR12 and eBOSS DR16. We show that the most typical models such as Starobinsky and $\alpha$-attractors are in disagreement with the Atacama Cosmology Telescope small-scale CMB measurements, particularly when combined with B-modes polarization data. On the other hand, these potentials are in perfect agreement with the Planck measurements at larger angular scales. This dichotomy makes it challenging to identify a single model or a group of models that can be universally considered as the preferred choice based on all available CMB observations., Comment: 27 pages, 2 figures, 3 tables. V2: updated to match the JCAP published version

We provide an Emergent Universe picture in which the fine-tuning on the initial conditions is replaced by cut-off physics, implemented on a semiclassical level when referred to the Universe dynamics and on a purely quantum level for the quantum fluctuations of the inflaton field. The adopted cut-off physics is inspired by Polymer Quantum Mechanics but expanded in the limit of a small lattice step. On a quasi-classical level, this results in modified Poisson Brackets for the Hamiltonian Universe dynamics similar to a Generalized Uncertainty Principle algebra. The resulting Universe is indeed asymptotically Einstein-static, emerging from a finite volume configuration in the distant past and then properly reconnecting with the most relevant Universe phases. The calculation of the modifications of the primordial inflaton spectrum is then performed by treating new physics as a small correction on the standard Hamiltonian of each Fourier mode of the field. The merit of this study is to provide a new paradigm for a non-singular Emergent Universe, which is associated with a precise fingerprint on the temperature distribution of the microwave background, in principle observable by future experiments., Comment: 12 pages, 6 figures. New upload to match published version

We present model-marginalized limits on mixed hot dark matter scenarios, which consider both thermal neutrinos and thermal QCD axions. A novel aspect of our analyses is the inclusion of small-scale Cosmic Microwave Background (CMB) observations from the Atacama Cosmology Telescope (ACT) and the South Pole Telescope (SPT), together with those from the Planck satellite and Baryon Acoustic Oscillation (BAO) data. After marginalizing over a number of well-motivated non-minimal background cosmologies, the tightest $95\%$ CL upper bound we obtain is $0.21$ eV, both for $\sum m_\nu$ and $m_{\rm a}$, from the combination of ACT, Planck and BAO measurements. Restricting the analyses to the standard $\Lambda$CDM picture, we find $\sum m_\nu<0.16$ eV and $m_{\rm a}<0.18$ eV, both at $95\%$ CL. Interestingly, the best background cosmology is never found within the minimal $\Lambda$CDM plus hot relics, regardless of the data sets exploited in the analyses. The combination of Planck with either BAO, SPT or ACT prefers a universe with a non-zero value of the running in the primordial power spectrum with strong evidence. Small-scale CMB probes, both alone and combined with BAO, either prefer, with substantial evidence, non-flat universes (as in the case of SPT) or a model with a time varying dark energy component (as in the case of ACT)., Comment: 17 pages, 5 figures, 9 tables. V2:updated to match the PRD published version

Inflationary gravitational waves, behaving as additional radiation in the Early Universe, can increase the effective number of relativistic species ($N_{\rm eff}$) by a further correction that depends on the integrated energy-density in gravitational waves over all scales. This effect is typically used to constrain (blue-tilted) models of inflation in light of the bounds resulting from the Big Bang Nucleosynthesis. In this paper, we recompute this contribution, discussing some caveats of the state-of-the-art analyses. Through a parametric investigation, we first demonstrate that the calculation is dominated by the ultraviolet frequencies of the integral and therefore by the behavior of the tensor spectrum on scales corresponding to modes that cross the horizon very close to the end of inflation, when the slow-roll dynamics breaks down and the production of gravitational waves becomes strongly model dependent. Motivated by these results, we realize a theoretical Monte Carlo and, working within the framework of the Effective Field Theory of inflation, we investigate the observable predictions of a very broad class of models. For each model, we solve a system of coupled differential equations whose solution completely specifies the evolution of the spectrum up to the end of inflation. We prove the calculation of $\Delta N_{\rm eff}^{\rm GW}$ to be remarkably model-dependent and therefore conclude that accurate analyses are needed to infer reliable information on the inflationary Universe., Comment: 17 pages, 7 figures, 1 table. Updated to match the MNRAS published version

In this paper we consider the effects of adding curvature in extended cosmologies involving a free-to-vary neutrino sector and different parametrizations of Dark Energy (DE). We make use of the Planck 2018 cosmic microwave background temperature and polarization data, Baryon Acoustic Oscillations and Pantheon type Ia Supernovae data. Our main result is that a non-flat Universe cannot be discarded in light of the current astronomical data, because we find an indication for a closed Universe in most of the DE cosmologies explored in this work. On the other hand, forcing the Universe to be flat can significantly bias the constraints on the equation of state of the DE component and its dynamical nature., Comment: 40 pages, 17 tables and 22 captioned figures; accepted for publication in Phys. Rev. D

The Data Release 4 of the Atacama Cosmology Telescope (ACT) shows an agreement with an Harrison-Zel'dovich primordial spectrum ($n_s=1.009 \pm 0.015$), introducing a tension with a significance of $99.3\%$ CL with the results from the Planck satellite. The discrepancy on the value of the scalar spectral index is neither alleviated with the addition of large scale structure information nor with the low multipole polarization data. We discuss possible avenues to alleviate the tension relying on either neglecting polarization measurements from ACT or in extending different sectors of the theory., Comment: 8 pages, 5 figures, 2 tables. Accepted for publication in MNRAS

We study the global agreement between the most recent observations of the Cosmic Microwave Background temperature and polarization anisotropies angular power spectra released by the Atacama Cosmology Telescope and the Planck satellite in various cosmological models that differ by the inclusion of different combinations of additional parameters. By using the Suspiciousness statistic, we show that the global "CMB tension" between the two experiments, quantified at the Gaussian equivalent level of $\sim 2.5\,\sigma$ within the baseline $\Lambda$CDM, is reduced at the level of $1.8\sigma$ when the effective number of relativistic particles ($N_{\rm eff}$) is significantly less than the standard value, while it ranges between $2.3\,\sigma$ and $3.5\,\sigma$ in all the other extended models., Comment: 6 pages, 1 figure, 2 tables. Updated to match the MNRAS published version

We present an updated data-analysis comparison of the most recent observations of the Cosmic Microwave Background temperature anisotropies and polarization angular power spectra released by four different experiments: the Planck satellite on one side, and the Atacama Cosmology Telescope (ACTPol) and the South Pole Telescope (SPT-3G), combined with the WMAP satellite 9-years observation data in order to be "Planck-independent" on the other side. We investigate in a systematic way 8 extended cosmological models that differ from the baseline $\Lambda$CDM case by the inclusion of many different combinations of additional degrees of freedom, with the aim of finding a viable minimal extended model that can bring all the CMB experiments in agreement. Our analysis provides several hints for anomalies in the CMB angular power spectra in tension with the standard cosmological model that persist even in these multi-parameter spaces. This indicates that either significant unaccounted-for systematics in the CMB data are producing biased results or that $\Lambda$CDM is an incorrect/incomplete description of Nature. We conclude that only future independent high-precision CMB temperature and polarization measurements could provide a definitive answer., Comment: 32 pages, 18 figures, 10 tables. V2: updated to match the PRD published version

We revisit the joint constraints in the mixed hot dark matter scenario in which both thermally produced QCD axions and relic neutrinos are present. Upon recomputing the cosmological axion abundance via recent advances in the literature, we improve the state-of-the-art analyses and provide updated bounds on axion and neutrino masses. By avoiding approximate methods, such as the instantaneous decoupling approximation, and limitations due to the limited validity of the perturbative approach in QCD that forced to artificially divide the constraints from the axion-pion and the axion-gluon production channels, we find robust and self-consistent limits. We investigate the two most popular axion frameworks: KSVZ and DFSZ. From Big Bang Nucleosynthesis (BBN) light element abundances data we find for the KSVZ axion $\Delta N_{\rm eff}<0.31$ and an axion mass bound $m_a < 0.53 $ eV (i.e., a bound on the axion decay constant $f_a > 1.07 \times 10^7$ GeV) both at $95\%$ CL. These BBN bounds are improved to $\Delta N_{\rm eff}<0.14$ and $m_a< 0.16$ eV ($f_a > 3.56 \times 10^7$ GeV) if a prior on the baryon energy density from Cosmic Microwave Background (CMB) data is assumed. When instead considering cosmological observations from the CMB temperature, polarization and lensing from the Planck satellite combined with large scale structure data we find $\Delta N_{\rm eff}<0.23$, $m_a< 0.28$ eV ($f_a > 2.02 \times 10^7$ GeV) and $\sum m_\nu < 0.16$ eV at $95\%$ CL. This corresponds approximately to a factor of $5$ improvement in the axion mass bound with respect to the existing limits. Very similar results are obtained for the DFSZ axion. We also forecast upcoming observations from future CMB and galaxy surveys, showing that they could reach percent level errors for $m_a\sim 1$ eV., Comment: 22 pages, 9 figures, 5 tables. V2: updated to match the JCAP published version

The latest data release from the ACT CMB experiment (in combination with previous WMAP data) shows evidence for an Early Dark Energy component at more than $3$ standard deviations. The same conclusion has been recently shown to hold when temperature data from the Planck experiment limited to intermediate angular scales ($l \le 650$) are included while it vanishes when the full Planck dataset is considered. However, it has been shown that the full Planck dataset exhibits an anomalous lensing component and a preference for a closed universe at the level of three standard deviation. It is therefore of utmost importance to investigate if these anomalies could anti-correlate with an early dark energy component and hide its presence during the process of parameter extraction. Here we demonstrate that extended parameters choices as curvature, equation of state of dark energy and lensing amplitude $A_L$ have no impact on the Planck constraints on EDE. In practice, EDE does not solve Planck angular spectra anomalies. This indicates that current CMB evidence for an EDE component comes essentially from the ACT-DR4 dataset., Comment: 6 pages, 3 Figures

In this paper we will list a few important goals that need to be addressed in the next decade, also taking into account the current discordances between the different cosmological probes, such as the disagreement in the value of the Hubble constant $H_0$, the $\sigma_8$--$S_8$ 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 $5.0\,\sigma$ tension between the {\it Planck} CMB estimate of the Hubble constant $H_0$ and the SH0ES collaboration measurements. After showing the $H_0$ 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 {\it Planck} CMB data with weak lensing measurements and redshift surveys, about the value of the matter energy density $\Omega_m$, and the amplitude or rate of the growth of structure ($\sigma_8,f\sigma_8$). 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 $H_0$--$S_8$ 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.[Abridged], Comment: Contribution to Snowmass 2021. 224 pages, 27 figures. Accepted for publication in JHEAp

The measurements of Cosmic Microwave Background anisotropies made by the Planck satellite provide extremely tight upper bounds on the total neutrino mass scale ($\Sigma m_{\nu}<0.26 eV$ at $95\%$ C.L.). However, as recently discussed in the literature, Planck data show anomalies that could affect this result. Here we provide new constraints on neutrino masses using the recent and complementary CMB measurements from the Atacama Cosmology Telescope DR4 and the South Polar Telescope SPT-3G experiments. We found that both the ACT-DR4 and SPT-3G data, when combined with WMAP, mildly suggest a neutrino mass with $\Sigma m_{\nu}=0.68 \pm 0.31$ eV and $\Sigma m_{\nu}=0.46_{-0.36}^{+0.14}$ eV at $68 \%$ C.L, respectively. Moreover, when CMB lensing from the Planck experiment is included, the ACT-DR4 data now indicates a neutrino mass above the two standard deviations, with $\Sigma m_{\nu}=0.60_{-0.50}^{+0.44}$ eV at $95 \%$, while WMAP+SPT-3G provides a weak upper limit of $\Sigma m_{\nu}<0.37$ eV at $68 \%$ C.L.. Interestingly, these results are consistent with the Planck CMB+Lensing constraint of $\Sigma m_{\nu} = 0.41_{-0.25}^{+0.17}$ eV at $68 \%$ C.L. when variation in the $A_{\rm lens}$ parameter are considered. We also show that these indications are still present after the inclusion of BAO or SN-Ia data in extended cosmologies that are usually considered to solve the so-called Hubble tension. A combination of ACT-DR4, WMAP, BAO and constraints on the Hubble constant from the SH0ES collaboration gives $\Sigma m_{\nu}=0.39^{+0.13}_{-0.25}$ eV at $68 \%$ C.L. in extended cosmologies. We conclude that a total neutrino mass above the $0.26$ eV limit still provides an excellent fit to several cosmological data and that future data must be considered before safely ruling it out., Comment: 6 pages, 3 Figures

In light of the most recent cosmological observations, we provide new updated constraints on the slow-roll inflation in different extended scenarios beyond the $\Lambda\rm{CDM}$ cosmological model. Along with the usual six parameters, we simultaneously vary different combinations of additional parameters, including the running of the scalar spectral index $\alpha_s$, its running of running $\beta_s$, the tensor amplitude $r$ and the spatial curvature $\Omega_k$. From the Planck 2018 data, we find no evidence for a scalar running or a running of running, while analyzing the Atacama Cosmology Telescope data combined with WMAP 9-years observations data we find a preference for non-zero $\alpha_s$ and $\beta_s$ at the level of 2.9$\sigma$ and 2.7$\sigma$, respectively. Anyway, this preference is reduced when the tensor amplitude can vary in the model or $\beta_s$ is fixed to zero. The upper bound on $r$ is only slightly affected by the additional parameters while the differences in the datasets can remarkably change the compatibility among the different inflationary models, sometimes leading to discordant conclusions., Comment: 20 pages, 6 figures

One of the targets of future Cosmic Microwave Background and Baryon Acoustic Oscillation measurements is to improve the current accuracy in the neutrino sector and reach a much better sensitivity on extra dark radiation in the Early Universe. In this paper we study how these improvements can be translated into constraining power for well motivated extensions of the Standard Model of elementary particles that involve axions thermalized before the quantum chromodynamics (QCD) phase transition by scatterings with gluons. Assuming a fiducial $\Lambda$CDM cosmological model, we simulate future data for Stage-IV CMB-like and Dark Energy Spectroscopic Instrument (DESI)-like surveys and analyze a mixed scenario of axion and neutrino hot dark matter. We further account also for the effects of these QCD axions on the light element abundances predicted by Big Bang Nucleosynthesis. The most constraining forecasted limits on the hot relic masses are $m_{\rm a} \lesssim 0.92$ eV and $\sum m_\nu\lesssim 0.12$ eV at 95 per cent Confidence Level, showing that future cosmic observations can substantially improve the current bounds, supporting multi-messenger analyses of axion, neutrino and primordial light element properties., Comment: 10 pages, 5 figures. Version Published in MNRAS

The cosmological constant $\Lambda$ and cold dark matter (CDM) model ($\Lambda\text{CDM}$) is one of the pillars of modern cosmology and is widely used as the de facto theoretical model by current and forthcoming surveys. As the nature of dark energy is very elusive, in order to avoid the problem of model bias, here we present a novel null test at the perturbation level that uses the growth of matter perturbation data in order to assess the concordance model. We analyze how accurate this null test can be reconstructed by using data from forthcoming surveys creating mock catalogs based on $\Lambda\text{CDM}$ and three models that display a different evolution of the matter perturbations, namely a dark energy model with constant equation of state $w$ ($w$CDM), the Hu \& Sawicki and designer $f(R)$ models, and we reconstruct them with a machine learning technique known as the Genetic Algorithms. We show that with future LSST-like mock data our consistency test will be able to rule out these viable cosmological models at more than 5$\sigma$, help to check for tensions in the data and alleviate the existing tension of the amplitude of matter fluctuations $S_8=\sigma_8\left(\Omega_m/0.3\right)^{0.5}$., Comment: 9 pages, 4 figures. Comments welcome

In the current 3nu paradigm, flavor oscillations probe 3 mixing angles (theta_12, theta_23, theta_13), one CP phase delta, and two squared mass differences delta m^2>0 and Delta m^2, where sign(Delta m^2)=+ (-) for normal (inverted) ordering. Absolute nu masses can be probed by the effective m_beta in beta decay, by the total mass Sigma in cosmology and, if neutrinos are Majorana, by another effective m_{beta beta} in 0nu2beta decay. Within an updated global analysis of (non)oscillation data, we constrain these 3nu parameters, both separately and in selected pairs, and highlight the concordance or discordance among different constraints. Five oscillation parameters (delta m^2, Delta m^2, theta_12, theta_23, theta_13) are consistently measured, with an overall accuracy ranging from ~1% for Delta m^2 to ~6% for sin^2(theta_23) (due to its octant ambiguity). We find overall hints for normal ordering (at 2.5 sigma), as well as for theta_23

The $\Lambda$CDM model provides a good fit to a large span of cosmological data but harbors areas of phenomenology. 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 $4-6\sigma$ disagreement between predictions of the Hubble constant $H_0$ by early time probes with $\Lambda$CDM 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 demand a hypothesis with enough rigor to explain multiple observations--whether these invoke new physics, unexpected large-scale structures or multiple, unrelated errors. We present a thorough review of the problem, including a discussion of recent Hubble constant estimates and a summary of the proposed theoretical solutions. Some of the models presented are formally successful, improving the fit to the data in light of their additional degrees of freedom, restoring agreement within $1-2\sigma$ between {\it Planck} 2018, using CMB power spectra data, BAO, Pantheon SN data, and R20, the latest SH0ES Team measurement of the Hubble constant ($H_0 = 73.2 \pm 1.3{\rm\,km\,s^{-1}\,Mpc^{-1}}$ at 68\% confidence level). Reduced tension might not simply come from a change in $H_0$ but also from an increase in its uncertainty due to degeneracy with additional physics, 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.[Abridged], Comment: Invited Review of about 134 pages with many figures and tables. Accepted for publication in CQG. A sample code for producing similar whisker plots (e.g. Figs. 1, 2) associated with this Review for any choice of the data is made publicly available online at: https://github.com/lucavisinelli/H0TensionRealm

Up-to-date cosmological data analyses have shown that \textit{(a)} a closed universe is preferred by the Planck data at more than $99\%$ CL, and \textit{(b)} interacting scenarios offer a very compelling solution to the Hubble constant tension. In light of these two recent appealing scenarios, we consider here an interacting dark matter-dark energy model with a non-zero spatial curvature component and a freely varying dark energy equation of state in both the quintessential and phantom regimes. When considering Cosmic Microwave Background data only, a phantom and closed universe can perfectly alleviate the Hubble tension, without the necessity of a coupling among the dark sectors. Accounting for other possible cosmological observations compromises the viability of this very attractive scenario as a global solution to current cosmological tensions, either by spoiling its effectiveness concerning the $H_0$ problem, as in the case of Supernovae Ia data, or by introducing a strong disagreement in the preferred value of the spatial curvature, as in the case of Baryon Acoustic Oscillations., Comment: Revised version; 12 pages, 2 figures and 7 tables; published version in JCAP

Higher-curvature corrections to the effective gravitational action may leave signatures in the spectrum of primordial tensor perturbations if the inflationary energy scale is sufficiently high. In this paper we further investigate the effects of a coupling of the Inflaton field to higher-curvature tensors in models with a minimal breaking of conformal symmetry. We show that an observable violation of the tensor consistency relation from higher-curvature tensors implies also a relatively large running of the tensor tilt, enhanced even by some order of magnitude with respect to the standard slow roll case. This may leave signatures in the tensor two-point function that we could test to recognize higher-curvature effects, above all if they are translated into a blue tilted spectrum visible by future Gravitational Wave experiments. Exploiting current cosmic microwave background and gravitational wave data we also derive constraints on the inflationary parameters, inferring that large higher-curvature corrections seem to be disfavored., Comment: 11 pages, 3 figures

Axions, if realized in nature, can be copiously produced in the early universe via thermal processes, contributing to the mass-energy density of thermal hot relics. In light of the most recent cosmological observations, we analyze two different thermal processes within a realistic mixed hot-dark-matter scenario which includes also massive neutrinos. Considering the axion-gluon thermalization channel we derive our most constraining bounds on the hot relic masses $m_a < 7.46$ eV and $\sum m_\nu< 0.114$ eV both at 95 per cent CL; while studying the axion-pion scattering, without assuming any specific model for the axion-pion interactions and remaining in the range of validity of the chiral perturbation theory, our most constraining bounds are improved to $m_a<0.91$ eV and $\sum m_\nu< 0.105$ eV, both at 95 per cent CL. Interestingly, in both cases, the total neutrino mass lies very close to the inverted neutrino mass ordering prediction. If future terrestrial double beta decay and/or long baseline neutrino experiments find that the nature mass ordering is the inverted one, this could rule out a wide region in the currently allowed thermal axion window. Our results therefore strongly support multi-messenger searches of axions and neutrino properties, together with joint analyses of their expected sensitivities., Comment: 9 pages, 3 figures. Version Published on MNRAS

Recent measurements of the Cosmic Microwave Anisotropies power spectra measured by the Planck satellite show a preference for a closed universe at more than $99 \%$ Confidence Level. Such a scenario is however in disagreement with several low redshift observables, including luminosity distances of Type Ia Supernovae. Here we show that Interacting Dark Energy (IDE) models can ease the discrepancies between Planck and Supernovae Ia data in a closed Universe. Therefore IDE cosmologies remain as very appealing scenarios, as they can provide the solution to a number of observational tensions in different fiducial cosmologies. The results presented here strongly favour broader analyses of cosmological data, and suggest that relaxing the usual flatness and vacuum energy assumptions can lead to a much better agreement among theory and observations., Comment: 5 pages, 2 figures, Version accepted for publication in MNRAS letters

The concordance of the $\Lambda$CDM cosmological model in light of current observations has been the subject of an intense debate in recent months. The 2018 Planck Cosmic Microwave Background (CMB) temperature anisotropy power spectrum measurements appear at face value to favour a spatially closed Universe with curvature parameter $\Omega_K<0$. This preference disappears if Baryon Acoustic Oscillation (BAO) measurements are combined with Planck data to break the geometrical degeneracy, although the reliability of this combination has been questioned due to the strong tension present between the two datasets when assuming a curved Universe. Here, we approach this issue from yet another point of view, using measurements of the full-shape (FS) galaxy power spectrum, $P(k)$, from the Baryon Oscillation Spectroscopic Survey DR12 CMASS sample. By combining Planck data with FS measurements, we break the geometrical degeneracy and find $\Omega_K=0.0023 \pm 0.0028$. This constrains the Universe to be spatially flat to sub-percent precision, in excellent agreement with results obtained using BAO measurements. However, as with BAO, the overall increase in the best-fit $\chi^2$ suggests a similar level of tension between Planck and $P(k)$ under the assumption of a curved Universe. While the debate on spatial curvature and the concordance between cosmological datasets remains open, our results provide new perspectives on the issue, highlighting the crucial role of FS measurements in the era of precision cosmology., Comment: 36 pages, 3 figures. v3: title shortened, added discussions on addition datasets to break the geometrical degeneracy, accepted for publication in Physics of the Dark Universe

The current cosmological probes have provided a fantastic confirmation of the standard $\Lambda$ Cold Dark Matter cosmological model, that has been constrained with unprecedented accuracy. However, with the increase of the experimental sensitivity a few statistically significant tensions between different independent cosmological datasets emerged. While these tensions can be in portion the result of systematic errors, the persistence after several years of accurate analysis strongly hints at cracks in the standard cosmological scenario and the need for new physics. In this Letter of Interest we will focus on the $4.4\sigma$ tension between the Planck estimate of the Hubble constant $H_0$ and the SH0ES collaboration measurements. After showing the $H_0$ evaluations made from different teams using different methods and geometric calibrations, we will list a few interesting new physics models that could solve this tension and discuss how the next decade experiments will be crucial., Comment: Snowmass2021 - Letter of Interest

A precise measurement of the curvature of the Universe is of primeval importance for cosmology since it could not only confirm the paradigm of primordial inflation but also help in discriminating between different early Universe scenarios. The recent observations, while broadly consistent with a spatially flat standard $\Lambda$ Cold Dark Matter ($\Lambda$CDM) model, are showing tensions that still allow (and, in some cases, even suggest) a few percent deviations from a flat universe. In particular, the Planck Cosmic Microwave Background power spectra, assuming the nominal likelihood, prefer a closed universe at more than 99\% confidence level. While new physics could be in action, this anomaly may be the result of an unresolved systematic error or just a statistical fluctuation. However, since a positive curvature allows a larger age of the Universe, an accurate determination of the age of the oldest objects provides a smoking gun in confirming or falsifying the current flat $\Lambda$CDM model., Comment: Snowmass2021 - Letter of Interest

The standard $\Lambda$ Cold Dark Matter cosmological model provides a wonderful fit to current cosmological data, but a few tensions and anomalies became statistically significant with the latest data analyses. While these anomalies could be due to the presence of systematic errors in the experiments, they could also indicate the need for new physics beyond the standard model. In this Letter of Interest we focus on the tension of the Planck data with weak lensing measurements and redshift surveys, about the value of the matter energy density $\Omega_m$, and the amplitude or rate of the growth of structure ($\sigma_8,f\sigma_8$). We list a few interesting models for solving this tension, and we discuss the importance of trying to fit with a single model a full array of data and not just one parameter at a time., Comment: Snowmass2021 - Letter of Interest

The standard $\Lambda$ Cold Dark Matter cosmological model provides an amazing description of a wide range of astrophysical and astronomical data. However, there are a few big open questions, that make the standard model look like a first-order approximation to a more realistic scenario that still needs to be fully understood. In this Letter of Interest we will list a few important goals that need to be addressed in the next decade, also taking into account the current discordances present between the different cosmological probes, as the Hubble constant $H_0$ value, the $\sigma_8 - S_8$ tension, and the anomalies present in the Planck results. Finally, we will 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 questions., Comment: Snowmass2021 - Letter of Interest

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., Comment: 14 pages, 7 figures

We revisit our previous work [Phys. Rev. D 95, 096014 (2017)] where neutrino oscillation and nonoscillation data were analyzed in the standard framework with three neutrino families, in order to constrain their absolute masses and to probe their ordering (either normal, NO, or inverted, IO). We include updated oscillation results to discuss best fits and allowed ranges for the two squared mass differences $\delta m^2$ and $\Delta m^2$, the three mixing angles $\theta_{12}$, $\theta_{23}$ and $\theta_{13}$, as well as constraints on the CP-violating phase $\delta$, plus significant indications in favor of NO vs IO at the level of $\Delta\chi^2=10.0$. We then consider nonoscillation data from beta decay, from neutrinoless double beta decay (if neutrinos are Majorana), and from various cosmological input variants (in the data or the model) leading to results dubbed as default, aggressive, and conservative. In the default option, we obtain from nonoscillation data an extra contribution $\Delta\chi^2 = 2.2$ in favor of NO, and an upper bound on the sum of neutrino masses $\Sigma < 0.15$ eV at $2\sigma$; both results - dominated by cosmology - can be strengthened or weakened by using more aggressive or conservative options, respectively. Taking into account such variations, we find that the combination of all (oscillation and nonoscillation) neutrino data favors NO at the level of $3.2-3.7\sigma$, and that $\Sigma$ is constrained at the $2\sigma$ level within $\Sigma < 0.12-0.69$ eV. The upper edge of this allowed range corresponds to an effective $\beta$-decay neutrino mass $m_\beta = \Sigma/3 = 0.23$ eV, at the sensitivity frontier of the KATRIN experiment., Comment: 10 pages, including 3 tables and 5 figures. Text clarified, references added, results unchanged. To appear in PRD

We show that a combined analysis of CMB anisotropy power spectra obtained by the Planck satellite and luminosity distance data simultaneously excludes a flat universe and a cosmological constant at $99 \%$ CL. These results hold separately when combining Planck with three different datasets: the two determinations of the Hubble constant from Riess et al. 2019 and Freedman et al. 2020, and the Pantheon catalog of high redshift supernovae type-Ia. We conclude that either LCDM needs to be replaced by a different model, or else there are significant but still undetected systematics. Our result calls for new observations and stimulates the investigation of alternative theoretical models and solutions., Comment: 5 pages, 4 figures. Matches published version

The detection of Primordial Gravitational Waves (PGWs) is one of the most important goals of modern cosmology since PGWs can both provide substantial evidence for primordial inflation and shed light on its physical nature. Small scale experiments on gravitational waves such as LIGO/VIRGO and, in future, LISA and Einstein Telescope (ET), being sensitive to the stochastic background of gravitational waves, can be used together with the CMB data to constrain the inflationary parameters. In performing these analyses the primordial tensor spectrum is usually parametrized with a power law that includes only the amplitude and a scale independent tilt. In this paper, we investigate the robustness of assuming the tensor tilt as scale independent. We show that due to the huge difference in the scales probed by CMB and GWs data, even a small scale dependence can remarkably affect the shape of the primordial spectrum possibly breaking the power-law assumption. When the non-linear corrections are considered the final constraints can be significantly changed. We also study the scale dependence in two different physical models of inflation providing an example of negligible scale dependence and an example of non-negligible scale dependence., Comment: 12 Pages, 4 figures. Edited to match Phys. Lett. B published version

The recent Planck Legacy 2018 release has confirmed the presence of an enhanced lensing amplitude in CMB power spectra compared to that predicted in the standard $\Lambda$CDM model. A closed universe can provide a physical explanation for this effect, with the Planck CMB spectra now preferring a positive curvature at more than $99 \%$ C.L. 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 within the Planck data set 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 BAO. 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., Comment: 35 pages, 8 figures

We explore whether non-standard dark sector physics might be required to solve the existing cosmological tensions. The properties we consider in combination are an interaction between the dark matter and dark energy components, and a dark energy equation of state $w$ different from that of the canonical cosmological constant $w=-1$. In principle, these two parameters are independent. In practice, to avoid early-time, superhorizon instabilities, their allowed parameter spaces are correlated. We analyze three classes of extended interacting dark energy models in light of the 2019 Planck CMB results and Cepheid-calibrated local distance ladder $H_0$ measurements of Riess et al. (R19), as well as recent BAO and SNeIa distance data. We find that in quintessence coupled dark energy models, where $w > -1$, the evidence for a non-zero coupling between the two dark sectors can surpass the $5\sigma$ significance. On the other hand, in phantom coupled dark energy models, there is no such preference for a non-zero dark sector coupling. All the models we consider significantly raise the value of the Hubble constant easing the $H_0$ tension. The addition of low-redshift BAO and SNeIa measurements leaves some residual tension with R19 but at a level that could be justified by a statistical fluctuation. Bayesian evidence considerations mildly disfavour both the coupled quintessence and phantom models, while mildly favouring a coupled vacuum scenario, even when late-time datasets are considered. We conclude that non-minimal dark energy cosmologies, such as coupled quintessence, phantom, or vacuum models, are still an interesting route towards softening existing cosmological tensions, even when low-redshift datasets and Bayesian evidence considerations are taken into account. (abstract severely abridged), Comment: 19 pages, 5 figures, added Bayesian evidence computation and further discussions. Version accepted for publication in PRD

The inflationary model proposed by Starobinski in 1979 predicts an amplitude of the spectrum of primordial gravitational waves, parametrized by the tensor to scalar ratio, of $r=0.0037$ in case of a scalar spectral index of $n_S=0.965$. This amplitude is currently used as a target value in the design of future CMB experiments with the ultimate goal of measuring it at more than five standard deviations. Here we evaluate how stable are the predictions of the Starobinski model on $r$ considering the experimental uncertainties on $n_S$ and the assumption of $\Lambda$CDM. We also consider inflationary models where the $R^2$ term in Starobinsky action is generalized to a $R^{2p}$ term with index $p$ close to unity. We found that current data place a lower limit of $r>0.0013$ at $95 \%$ C.L. for the classic Starobinski model, and predict also a running of the scalar index different from zero at more than three standard deviation in the range $dn/dlnk=-0.0006_{-0.0001}^{+0.0002}$. A level of gravitational waves of $r\sim0.001$ is therefore possible in the Starobinski scenario and it will not be clearly detectable by future CMB missions as LiteBIRD and CMB-S4. When assuming a more general $R^{2p}$ inflation we found no expected lower limit on $r$, and a running consistent with zero. We found that current data are able to place a tight constraints on the index of $R^{2p}$ models at $95\%$ C.L. i.e. $p= 0.99^{+0.02}_{-0.03}$., Comment: Corrected a typo in the potential normalization

An early dark energy component consisting of a cosmic pseudo Nambu-Goldstone boson has been recently proposed to resolve the Hubble tension -- the four-sigma discrepancy between precision measurements of the expansion rate of the universe. Here we point out that such an axion-like component may be expected to couple to electromagnetism by a Chern-Simons term, and will thereby induce an anisotropic cosmic birefringence signal in the polarization of the cosmic microwave background (CMB). We show that observations of the rotation-angle power spectrum and cross-correlation with CMB temperature anisotropy can confirm the presence of this early dark energy component. Future CMB data as expected from the CMB-S4 experiment will improve sensitivity to this effect by two orders of magnitude and help in discriminating between different Hubble tension scenarios., Comment: 6 pages, 2 figures

We examine interactions between dark matter and dark energy in light of the latest cosmological observations, focusing on a specific model with coupling proportional to the dark energy density. Our data includes Cosmic Microwave Background (CMB) measurements from the Planck 2018 legacy data release, late-time measurements of the expansion history from Baryon Acoustic Oscillations (BAO) and Supernovae Type Ia (SNeIa), galaxy clustering and cosmic shear measurements from the Dark Energy Survey Year 1 results, and the 2019 local distance ladder measurement of the Hubble constant $H_0$ from the Hubble Space Telescope. Considering Planck data both in combination with BAO or SNeIa data reduces the $H_0$ tension to a level which could possibly be compatible with a statistical fluctuation. The very same model also significantly reduces the $\Omega_{\rm m}-\sigma_8$ tension between CMB and cosmic shear measurements. Interactions between the dark sectors of our Universe remain therefore a promising joint solution to these persisting cosmological tensions., Comment: 24 pages, 3 figures. v2: major revision, changed title, mildened conclusions, included late-time datasets and discussion on how these should be treated with slightly more caution when going beyond LCDM, added many references. Version accepted for publication in Physics of the Dark Universe

We present new constraints on extended cosmological scenarios using the recent data from the Planck 2018 Legacy release. In addition to the six parameters of the standard LCDM model, we also simultaneously vary the dark energy equation of state, the neutrino mass, the neutrino effective number, the running of the spectral index and the lensing amplitude $A_L$. We confirm that a resolution of the Hubble tension is given by a dark energy equation of state with w<-1, ruling out quintessence models at high statistical significance. This solution is, however, not supported by BAO and Pantheon data. We find no evidence for evolving dark energy, i.e. $w_a \neq 0$. The neutrino effective number is always in agreement with the expectations of the standard model based on three active neutrinos. The running of the spectral index also is always consistent with zero. Despite the increase in the number of parameters, the $A_L$ lensing anomaly is still present at more than two standard deviations. The $A_L$ anomaly significantly affects the bounds on the neutrino mass that can be larger by a factor four with respect to those derived under standard $\Lambda$CDM. While the lensing data reduces the evidence for $A_L>1$, the inclusion of BAO and Pantheon increase its statistical significance., Comment: 9 pages, 3 figures

Inflationary models with power-law potentials are starting to be severely constrained by the recent measurements of Cosmic Microwave Background anisotropies provided by the Planck Satellite and by the BICEP2 telescope. In particular, models with power-law potentials $V(\varphi)\propto \varphi^n$ with $n \ge 2$ are strongly disfavored by present data since they predict a sizable contribution of gravitational waves with a tensor/scalar ratio of $r\sim0.15$ that is at odds with current limits. A non-minimal coupling to gravity has been proposed as a physical mechanism to lower the predictions for $r$. In this paper we further investigate the issue, presenting constraints on non-minimal couplings from current CMB data under the assumption of power-law potentials. We found that models with $n>2$ show a statistically significant indication (above $95 \%$ C.L.) for a non minimal coupling. Non minimal coupling is also preferred by models with $n<2$ albeit just at about $68 \%$ C.L.. Interestingly, all the models considered show a non-zero running of the spectral index, $ n_{\rm run}$, consistent with the 2018 Planck release value of $-0.007 \pm 0.0068$. We point out how future accurate measurement of $ n_{\rm run}$ would be necessary to significantly constraint these models and eventually rule out some or all of them. The combination of Planck data with the Bicep/Keck dataset strengthen these considerations., Comment: 15 pages, 4 figures

Current cosmological constraints on the scalar spectral index of primordial fluctuations $n_{\rm s}$ in the $\Lambda$CDM model have excluded the minimal scale-invariant Harrison-Zel'dovich model ($n_{\rm s}=1$; hereafter HZ) at high significance, providing support for inflation. In recent years, however, some tensions have emerged between different cosmological datasets that, if not due to systematics, could indicate the presence of new physics beyond the $\Lambda$CDM model. In the light of these developments, we evaluate the Bayesian evidence against HZ in different data combinations and model extensions. Considering only the Planck temperature data, we find inconclusive evidence against HZ when including variations in the neutrino number $N_{\rm eff}$ and/or the Helium abundance $Y_{\rm He}$. Adding the Planck polarization data, on the other hand, yields strong evidence against HZ in the extensions we considered. Perhaps most interestingly, Planck temperature data combined with local measurements of the Hubble constant give as the most probable model an HZ spectrum, with additional neutrinos. However, with the inclusion of polarisation, standard $\Lambda$CDM is once again preferred, but the HZ model with extra neutrinos is not strongly disfavored. The possibility of fully ruling out the HZ spectrum is therefore ultimately connected with the solution to current tensions between cosmological datasets. If these tensions are confirmed by future data, then new physical mechanisms could be at work and an HZ spectrum could still offer a valid alternative., Comment: 14 pages, 1 figure

Gravitational-wave standard sirens present a novel approach for the determination of the Hubble constant. After the recent spectacular confirmation of the method thanks to GW170817 and its optical counterpart, additional standard siren measurements from future gravitational-wave sources are expected to constrain the Hubble constant to high accuracy. At the same time, improved constraints are expected from observations of cosmic microwave background (CMB) polarization and from baryon acoustic oscillations (BAO) surveys. We explore the role of future standard siren constraints on $H_0$ in light of expected CMB+BAO data. Considering a $10$-parameters cosmological model, in which curvature, the dark energy equation of state, and the Hubble constant are unbounded by CMB observations, we find that a combination of future CMB+BAO data will constrain the Hubble parameter to $\sim 1.5 \%$. Further extending the parameter space to a time-varying dark energy equation of state, we find that future CMB+BAO constraints on $H_0$ are relaxed to $\sim 3.0 \%$. These accuracies are within reach of future standard siren measurements from the Hanford-Livingston-Virgo and the Hanford-Livingston-Virgo-Japan-India networks of interferometers, showing the cosmological relevance of these sources. If future gravitational-wave standard siren measurements reach $1\%$ on $H_0$, as expected, they would significantly improve future CMB+BAO constraints on curvature and on the dark energy equation of state by up to a factor $\sim 3$. We also show that the inclusion of $H_0$ constraints from gravitational-wave standard sirens could result in a reduction of the dark energy figure-of-merit (i.e., the cosmological parameter volume) by up to a factor of $\sim 400$., Comment: 14 pages, 5 figures, included discussion on FoM, new references, in press on PRD

We discuss whether an unaccounted contribution to the Cosmic Microwave Background polarization $B$-mode by primordial magnetic fields (PMFs) can bias future constraints on inflationary gravitational waves. As a case-study, we consider a scale-invariant PMF spectrum with amplitude of $\approx{1}\,{\mathrm{nG}}$ on $1\,\mathrm{Mpc}$ scales, compatible with current cosmological bounds. We find a degeneracy in the $B$-mode spectra between PMFs and inflationary gravitational waves. If PMFs of this amplitude are not accounted for, future CMB experiments could claim a false detection of a tensor-to-scalar ratio $r\approx 0.007$, close to the predictions of Starobinsky and $\alpha$-attractor models. The degeneracy can be broken if $B$-modes are measured also at multipoles $\ell\gtrsim 900$: more precisely experiments like CMB-S4 or CORE-M5 would be able to discriminate PMFs from primordial GWs at high statistical significance. Experiments like LiteBIRD or PIXIE will not be able to break the degeneracy and will need complementary bounds coming, for example, from measurements of anisotropies in the Faraday rotation angle of CMB polarization. This reinforces the importance of future experimental constraints on PMFs., Comment: 16 pages, 8 figures, matches JCAP version

The precise measurements of Cosmic Microwave Background Anisotropy angular power spectra made by the Planck satellite show an anomalous value for the lensing amplitude, defined by the parameter $A_{lens}$, at more than $2$ standard deviations. In this paper, after discussing the current status of the anomaly, we quantify the potential of future CMB measurements in confirming/falsifying the $A_{lens}$ tension. We find that a space-based experiment as LiteBIRD could falsify the current $A_{lens}$ tension at the level of $5$ standard deviations. Similar constraints can be achieved by a Stage-III experiment assuming an external prior on the reionization optical depth of $\tau=0.055\pm0.010$ as already provided by the Planck satellite. A Stage-IV experiment could further test the $A_{lens}$ tension at the level of $10$ standard deviations. A comparison between temperature and polarization measurements made at different frequencies could further identify possible systematics responsible for $A_{lens}>1$. We show that, in the case of the CMB-S4 experiment, polarization data alone will have the potential of falsifying the current $A_{lens}$ anomaly at more than five standard deviation and to strongly bound its frequency dependence. We also evaluate the future constraints on a possible scale dependence for $A_{lens}$., Comment: 5 pages, 4 figures

One of the major goals of future Cosmic Microwave Background measurements is the accurate determination of the effective number of neutrinos $N_{\rm eff}$. Reaching an experimental sensitivity of $\Delta N_{\rm eff} = 0.013$ could indeed falsify the presence of any non-standard relativistic particles at $95 \%$ c.l.. In this paper, we test how this future constraint can be affected by the removal of two common assumptions: a negligible running of the inflationary spectral index $n_{\rm run}$ and a precise determination of the neutron lifetime $\tau_n$. We first show that the constraints on $N_{\rm eff}$ could be significantly biased by the unaccounted presence of a running of the spectral index. Considering the Stage-IV experiment, a negative running of ${\rm d}n/{\rm d}\ln k= - 0.002$ could mimic a positive variation of $\Delta N_{\rm eff} = 0.03$. Moreover, given the current discrepancies between experimental measurements of the neutron lifetime $\tau_n$, we show that the assumption of a conservative error of $\Delta\tau_n \sim 10$s could bring to a systematic error of $\Delta N_{\rm eff} = 0.02$. Complementary cosmological constraints on the running of the spectral index and a solution to the neutron lifetime discrepancy are therefore needed for an accurate and reliable future CMB bound of $N_{\rm eff}$ at percent level., Comment: 7 pages, 3 figures