Abstract: The simplest ΛCDM model provides a good fit to a large span of cosmological data but harbors large areas of phenomenology and ignorance. With the improvement of the number and the accuracy of observations, discrepancies among key cosmological parameters of the model have emerged. The most statistically significant tension is the 4 sigma to 6 sigma disagreement between predictions of the Hubble constant, H (0), made by the early time probes in concert with the 'vanilla' ΛCDM cosmological model, and a number of late time, model-independent determinations of H (0) from local measurements of distances and redshifts. The high precision and consistency of the data at both ends present strong challenges to the possible solution space and demands a hypothesis with enough rigor to explain multiple observations-whether these invoke new physics, unexpected large-scale structures or multiple, unrelated errors. A thorough review of the problem including a discussion of recent Hubble constant estimates and a summary of the proposed theoretical solutions is presented here. We include more than 1000 references, indicating that the interest in this area has grown considerably just during the last few years. We classify the many proposals to resolve the tension in these categories: early dark energy, late dark energy, dark energy models with 6 degrees of freedom and their extensions, models with extra relativistic degrees of freedom, models with extra interactions, unified cosmologies, modified gravity, inflationary models, modified recombination history, physics of the critical phenomena, and alternative proposals. Some are formally successful, improving the fit to the data in light of their additional degrees of freedom, restoring agreement within 1-2 sigma between Planck 2018, using the cosmic microwave background power spectra data, baryon acoustic oscillations, Pantheon SN data, and R20, the latest SH0ES Team Riess, et al (2021 Astrophys. J. 908 L6) measurement of the Hubble constant (H (0) = 73.2 +/- 1.3 km s(-1) Mpc(-1) at 68% confidence level). However, there are many more unsuccessful models which leave the discrepancy well above the 3 sigma disagreement level. In many cases, reduced tension comes not simply from a change in the value of H (0) but also due to an increase in its uncertainty due to degeneracy with additional physics, complicating the picture and pointing to the need for additional probes. While no specific proposal makes a strong case for being highly likely or far better than all others, solutions involving early or dynamical dark energy, neutrino interactions, interacting cosmologies, primordial magnetic fields, and modified gravity provide the best options until a better alternative comes along.

Abstract: 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 analyse 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 Sigma m(nu) < 0.114 eV both at 95 percent 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 Sigma m(nu) < 0.105 eV, both at 95 percent 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.

Abstract: Geometrical tests such as the combination of the Hubble parameter H(z) and the angular diameter distance d(A)(z) can, in principle, break the degeneracy between the dark energy equation of state parameter w(z), and the spatial curvature Omega(k) in a direct, model-independent way. In practice, constraints on these quantities achievable from realistic experiments, such as those to be provided by Baryon Acoustic Oscillation (BAO) galaxy surveys in combination with CMB data, can resolve the cosmic confusion between the dark energy equation of state parameter and curvature only statistically and within a parameterized model for w(z). Combining measurements of both H(z) and d(A)(z) up to sufficiently high redshifts z similar to 2 and employing a parameterization of the redshift evolution of the dark energy equation of state are the keys to resolve the w(z) – Omega(k) degeneracy.

Abstract: We present a full Bayesian analysis of the combination of current neutrino oscillation, neutrinoless double beta decay and Cosmic Microwave Background observations. Our major goal is to carefully investigate the possibility to single out one neutrino mass ordering, namely Normal Ordering or Inverted Ordering, with current data. Two possible parametrizations (three neutrino masses versus the lightest neutrino mass plus the two oscillation mass splittings) and priors (linear versus logarithmic) are exhaustively examined. We find that the preference for NO is only driven by neutrino oscillation data. Moreover, the values of the Bayes factor indicate that the evidence for NO is strong only when the scan is performed over the three neutrino masses with logarithmic priors; for every other combination of parameterization and prior, the preference for NO is only weak. As a by-product of our Bayesian analyses, we are able to (a) compare the Bayesian bounds on the neutrino mixing parameters to those obtained by means of frequentist approaches, finding a very good agreement; (b) determine that the lightest neutrino mass plus the two mass splittings parametrization, motivated by the physical observables, is strongly preferred over the three neutrino mass eigenstates scan and (c) find that logarithmic priors guarantee a weakly-to-moderately more efficient sampling of the parameter space. These results establish the optimal strategy to successfully explore the neutrino parameter space, based on the use of the oscillation mass splittings and a logarithmic prior on the lightest neutrino mass, when combining neutrino oscillation data with cosmology and neutrinoless double beta decay. We also show that the limits on the total neutrino mass Sigma m(nu) can change dramatically when moving from one prior to the other. These results have profound implications for future studies on the neutrino mass ordering, as they crucially state the need for self-consistent analyses which explore the best parametrization and priors, without combining results that involve different assumptions.

Abstract: We analyse the anisotropic clustering of massive galaxies from the Sloan Digital Sky Survey III Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 9 (DR9) sample, which consists of 264-283 galaxies in the redshift range 0.43 < z < 0.7 spanning 3275 deg(2). Both peculiar velocities and errors in the assumed redshiftdistance relation (AlcockPaczynski effect) generate correlations between clustering amplitude and orientation with respect to the line of sight. Together with the sharp baryon acoustic oscillation (BAO) standard ruler, our measurements of the broad-band shape of the monopole and quadrupole correlation functions simultaneously constrain the comoving angular diameter distance (2190 +/- 61 Mpc) to z = 0.57, the Hubble expansion rate at z = 0.57 (92.4 +/- 4.5 km s(-1) Mpc(-1)) and the growth rate of structure at that same redshift (d(sigma 8)/d ln a = 0.43 +/- 0.069). Our analysis provides the best current direct determination of both DA and H in galaxy clustering data using this technique. If we further assume a cold dark matter expansion history, our growth constraint tightens to d(sigma 8)/d ln a = 0.415 +/- 0.034. In combination with the cosmic microwave background, our measurements of D-A,H and d(sigma 8)/d ln a all separately require dark energy at z > 0.57, and when combined imply Omega(A) = 0.74 +/- 0.016, independent of the Universe's evolution at z < 0.57. All of these constraints assume scale-independent linear growth, and assume general relativity to compute both O(10 per cent) non-linear model corrections and our errors. In our companion paper, Samushia et al., we explore further cosmological implications of these observations.