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 4σ to 6σ 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 1–2σ 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 3σ 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.

NOTE: First draft. We welcome comments, corrections, suggestions. For missing references we kindly ask to specify in relation to which topic and at which point of the review it would be appropriate to include a citation. We will not be able to address unspecifed requests.

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Axion stars are hypothetical objects formed of axions, obtained as localized and coherently oscillating solutions to their classical equation of motion. Depending on the value of the field amplitude at the core $|\theta_0| \equiv |\theta(r=0)|$, the equilibrium of the system arises from the balance of the kinetic pressure and either self-gravity or axion self-interactions. Starting from a general relativistic framework, we obtain the set of equations describing the configuration of the axion star, which we solve as a function of $|\theta_0|$. For small $|\theta_0| \lesssim 1$, we reproduce results previously obtained in the literature, and we provide arguments for the stability of such configurations in terms of first principles. We compare qualitative analytical results with a numerical calculation. For large amplitudes $|\theta_0| \gtrsim 1$, the axion field probes the full non-harmonic QCD chiral potential and the axion star enters the {\it dense} branch. Our numerical solutions show that in this latter regime the axions are relativistic, and that one should not use a single frequency approximation, as previously applied in the literature. We employ a multi-harmonic expansion to solve the relativistic equation for the axion field in the star, and demonstrate that higher modes cannot be neglected in the dense regime. We interpret the solutions in the dense regime as pseudo-breathers, and show that the life-time of such configurations is much smaller than any cosmological time scale.Comment: 11 pages, 4 figures. v2: added references, matches published versio

We study for what specific values of the theoretical parameters the axion can form the totality of cold dark matter. We examine the allowed axion parameter region in the light of recent data collected by the WMAP5 mission plus baryon acoustic oscillations and supernovae, and assume an inflationary scenario and standard cosmology. We also upgrade the treatment of anharmonicities in the axion potential, which we find important in certain cases. If the Peccei-Quinn symmetry is restored after inflation, we recover the usual relation between axion mass and density, so that an axion mass m a = (85 ± 3) µeV makes the axion 100% of the cold dark matter.If the Peccei-Quinn symmetry is broken during inflation, the axion can instead be 100% of the cold dark matter for m a < 15 meV provided a specific value of the initial misalignment angle θ i is chosen in correspondence to a given value of its mass m a . Large values of the Peccei-Quinn symmetry breaking scale correspond to small, perhaps uncomfortably small, values of the initial misalignment angle θ i .

The Event Horizon Telescope (EHT) collaboration has recently released the first image of a black hole (BH), opening a new window onto tests of general relativity in the strong field regime. In this paper, we derive constraints on the nature of M87* (the supermassive object at the centre of the galaxy M87), exploiting the fact that its shadow appears to be highly circular, and using measurements of its angular size. We first consider the simple case where M87* is assumed to be a Kerr BH. We find that the inferred circularity of M87* excludes Kerr BHs with observation angle θ obs 45 • for dimensionless rotational parameter 0.95 a * ≤ 1 whereas the observation angle is unbounded for a * 0.9. We then consider the possibility that M87* might be a superspinar, i.e. an object described by the Kerr solution and spinning so fast that it violates the Kerr bound by having |a * | > 1. We find that, within certain regions of parameter space, the inferred circularity and size of the shadow of M87* do not exclude the possibility that this object might be a superspinar.

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We derive constraints on mixed dark-matter scenarios consisting of primordial black holes (PBHs) and weakly interacting massive particles (WIMPs). In these scenarios, we expect a density spike of the WIMPs that are gravitationally bound to the PBHs, which results in an enhanced annihilation rate and increased indirect detection prospects. We show that such scenarios provide strong constraints on the allowed fraction of PBHs that constitutes the dark matter, depending on the WIMP mass m χ and the velocity-averaged annihilation cross-section σv . For the standard scenario with m χ = 100 GeV and σv = 3 × 10 −26 cm 3 /s, we derive bounds that are stronger than all existing bounds for PBHs with masses 10 −12 M M BH 10 4 M , where M is the solar mass, and mostly so by several orders of magnitude.