CMB Anomalies and the Hubble Tension

The standard $\Lambda$CDM model of cosmology is largely successful in describing many observations, including precise measurements of the Cosmic Microwave Background (CMB) radiation. However, some intriguing anomalies remain currently unexplained within this theoretical framework. Such discrepancies can be broadly categorized into two groups: those involving CMB-independent probes and those within different CMB experiments. Examples of the former category include the $H_0$-tension between the value of the present-day expansion rate of the Universe inferred by CMB observations and local distance ladder measurements. The latter category involves anomalies between the values of cosmological parameters obtained by different CMB experiments, as well as their consistency with the predictions of $\Lambda$CDM. In this chapter, we primarily focus on this second category and study the agreement among the most recent CMB measurements to acquire a better understanding of the limitations and uncertainties underlying both the current data and the cosmological model. Finally, we discuss the implications for the $H_0$-tension.Comment: Invited chapter for the edited book "Hubble Constant Tension" (Eds. E. Di Valentino and D. Brout, Springer Singapore, expected in 2024

Propagating speed of primordial gravitational waves

Primordial gravitational waves, i.e., a background of metric perturbations sourced by the quantum inflationary fluctuations, if measured, could both provide substantial evidence for primordial inflation and shed light on physics at extremely high energy scales. In this work we focus on their propagating speed. Using an effective field theory approach we introduce a time-dependent propagating speed cT(t) showing that also small deviations from the general relativity (GR) prediction cT(t)=c can lead to testable consequences. We derive a set of equations that relate the propagating speed and its time dependence to the inflationary parameters and that generalize the usual slow roll consistency relations. Imposing the new generalized consistency relations and combining small and large scales data, we derive model-independent constraints on inflation with nontrivial primordial tensor speed. In particular, we constrain its scale dependence to be dlogcT/dlogk=0.082-0.11+0.047 at 68% C.L. while we only derive the lower bound cT>0.22c at 95% C.L. We also constrain the tensor-to-scalar ratio at the pivot scale k∗=0.05 Mpc-1 to be r<0.0599 at 95% C.L. in agreement with the result provided by the Planck Collaboration. Thanks to a proper small scale parametrization of the tensor spectrum we derive stringent constraints on the tensor tilt nT=-0.084-0.047+0.10 at 68% C.L. and on its runnings αT=dnT/dlogk=0.0141-0.021+0.0035 and βT=dαT/dlogk=-0.0061-0.0014+0.010 both at 68% C.L. Our results show a remarkable agreement with the standard slow roll predictions and prove that current data can significantly constrain deviations from GR on the inflationary energy scales

Probing the inflationary background of gravitational waves from large to small scales

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 versio

Higher-Curvature Corrections and Tensor Modes

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 figure

Is the Harrison-Zel'dovich spectrum coming back? ACT preference for ns∼1n_s \sim 1 and its discordance with Planck

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 MNRA

Exploring the H0H_0 tension and the evidence of dark sector interaction from 2D BAO measurements

We explore observational constraints on a cosmological model with an interaction between dark energy (DE) and dark matter (DM), using a compilation of 15 measurements of the 2D BAO (i.e., transversal) scale in combination with Planck-CMB data, to explore the parametric space of a class of interacting DE models. We find that 2D BAO measurements can generate different observational constraints compared to the traditional approach of studying the matter clustering in the 3D BAO measurements. Contrary to the observations for the $\Lambda$CDM and IDE models when analyzed with Planck-CMB + 3D BAO data, we note that Planck-CMB + 2D BAO data favor high values of the Hubble constant $H_0$. From the joint analysis with Planck-CMB + 2D BAO + Gaussian prior on $H_0$, we find $H_0 = 73.4 \pm 0.88$ km/s/Mpc. We conclude that the $H_0$ tension is solved in the IDE model with strong statistical evidence (more than 3$\sigma$) for the IDE cosmologies.Comment: 7 Pages, 2 Figures, 2 Tables. Matches the version published in PR

Hints of Neutrino Dark Matter scattering in the CMB? Constraints from the Marginalized and Profile Distributions

We study scatter-like interactions between neutrinos and dark matter in light of different combinations of temperature, polarization and lensing data released by three independent CMB experiments - the Planck satellite, the Atacama Cosmology Telescope (ACT), and the South Pole Telescope (SPT) - in conjunction with Baryon Acoustic Oscillation (BAO) measurements. We apply two different statistical methodologies. Alongside the usual marginalization technique, we cross-check all the results through a Profile Likelihood analysis. As a first step, working under the assumption of massless neutrinos, we perform a comprehensive (re-)analysis aimed at assessing the validity of some recent results hinting at a mild preference for non-vanishing interactions from small-scale CMB data. We find compelling resilience in the results already documented in the literature, confirming that interactions with a strength $u_{\nu\rm{DM}} \sim 10^{-5} - 10^{-4}$ appear to be globally favored by ACT (both alone and in combination with Planck). This result is corroborated by the inclusion of additional data, such as the recent ACT-DR6 lensing likelihood, as well as by the Profile Likelihood analysis. Interestingly, a fully consistent preference for interactions emerges from SPT, as well, although it is weaker than the one obtained from ACT. As a second step, we repeat the same analysis considering neutrinos as massive particles. Despite the larger parameter space, all the hints pointing towards interactions are confirmed also in this more realistic case. In addition, we report a very mild preference for interactions in Planck+BAO alone (not found in the massless case) which aligns with small-scale data. While this latter result is not fully confirmed by the Profile Likelihood analysis, the profile distribution does confirm that interactions are not disfavoured by Planck.Comment: 35 pages, 16 figures, 5 table

The state of the dark energy equation of state circa 2023

We critically examine the state of current constraints on the dark energy (DE) equation of state (EoS) $w$. Our study is partially motivated by the observation that, while broadly consistent with the cosmological constant value $w=-1$, several independent probes appear to point towards a slightly phantom EoS ($w \sim -1.03$). We pay attention to the apparent preference for phantom DE from Planck Cosmic Microwave Background (CMB) data alone, whose origin we study in detail and attribute to a wide range of (physical and geometrical) effects. We deem the combination of Planck CMB, Baryon Acoustic Oscillations, Type Ia Supernovae, and Cosmic Chronometers data to be particularly trustworthy, inferring from this final consensus dataset $w=-1.013^{+0.038}_{-0.043}$, in excellent agreement with the cosmological constant value. Overall, despite a few scattered hints, we find no compelling evidence forcing us away from the cosmological constant (yet).Comment: 21 pages, 10 figures, 3 table

Revealing the effects of curvature on the cosmological models

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.