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]

https://iopscience.iop.org/article/10.1088/1361-6382/ac086d/pdf

In the realm of the Hubble tension - a review of solutions

Cosmology Intertwined: A Review of the Particle Physics, Astrophysics, and Cosmology Associated with the Cosmological Tensions and Anomalies

Dynamical horizons are considered in full, nonlinear general relativity. Expressions of fluxes of energy and angular momentum carried by gravitational waves across these horizons are obtained. Fluxes are local, the energy flux is positive, and change in the horizon area is related to these fluxes. The flux formulas also give rise to balance laws analogous to the ones obtained by Bondi and Sachs at null infinity and provide generalizations of the first and second laws of black-hole mechanics.

Dynamical Horizons: Energy, Angular Momentum, Fluxes and Balance Laws

Recently it has been noted by Di Valentino, Melchiorri and Silk (2019) that the enhanced lensing signal relative to that expected in the spatially flat $\Lambda$CDM model poses a possible crisis for the Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) class of models usually used to interpret cosmological data. The `crisis' amounts to inconsistencies between cosmological datasets arising when the FLRW curvature parameter $\Omega_{k0}$ is determined from the data rather than constrained to be zero a priori. Moreover, the already substantial discrepancy between the Hubble parameter as determined by Planck and local observations increases to the level of $5\sigma$. While such inconsistencies might arise from systematic effects of astrophysical origin affecting the Planck Cosmic Microwave Background (CMB) power spectra at small angular scales, it is an option that the inconsistencies are due to the failure of the FLRW assumption. In this paper we recall how the FLRW curvature ansatz is expected to be violated for generic relativistic spacetimes. We explain how the FLRW conservation equation for volume-averaged spatial curvature is modified through structure formation, and we illustrate in a simple framework how the curvature tension in a FLRW spacetime can be resolved---and is even expected to occur---from the point of view of general relativity. Requiring early-time convergence towards a Friedmannian model with a spatial curvature parameter $\Omega_{k0}$ equal to that preferred from the Planck power spectra resolves the Hubble tension within our dark energy-free model.

Solving the curvature and Hubble parameter inconsistencies through structure formation-induced curvature

We analyze GW150914 postmerger data to understand if ringdown overtone detection claims are robust. We find no evidence in favor of an overtone in the data after the waveform peak. Around the peak, the Bayes factor does not indicate the presence of an overtone, while the support for a nonzero amplitude is sensitive to changes in the starting time much smaller than the overtone damping time. This suggests that claims of an overtone detection are noise dominated. We perform GW150914-like injections in neighboring segments of the real detector noise, and we show that noise can indeed induce artificial evidence for an overtone. 

/pdf/analysis-of-ringdown-overtones-in-gw150914-25by910u.pdf

Analysis of Ringdown Overtones in GW150914

We investigate effective equations governing the volume expansion of spatially averaged portions of inhomogeneous cosmologies in spacetimes filled with an arbitrary fluid. This work is a follow-up to previous studies focused on irrotational dust models (Paper I) and irrotational perfect fluids (Paper II) in flow-orthogonal foliations of spacetime. It complements them by considering arbitrary foliations, arbitrary lapse and shift, and by allowing for a tilted fluid flow with vorticity. As for the first studies, the propagation of the spatial averaging domain is chosen to follow the congruence of the fluid, which avoids unphysical dependencies in the averaged system that is obtained. We present two different averaging schemes and corresponding systems of averaged evolution equations providing generalizations of Papers I and II. The first one retains the averaging operator used in several other generalizations found in the literature. We extensively discuss relations to these formalisms and pinpoint limitations, in particular regarding rest mass conservation on the averaging domain. The alternative averaging scheme that we subsequently introduce follows the spirit of Papers I and II and focuses on the fluid flow and the associated $$1+3$$ threading congruence, used jointly with the $$3+1$$ foliation that builds the surfaces of averaging. This results in compact averaged equations with a minimal number of cosmological backreaction terms. We highlight that this system becomes especially transparent when applied to a natural class of foliations which have constant fluid proper time slices.

/pdf/on-average-properties-of-inhomogeneous-fluids-in-general-1ei54bsm1x.pdf

On Average Properties of Inhomogeneous Fluids in General Relativity III: General Fluid Cosmologies

It is expected that all astrophysical black holes in equilibrium are well described by the Kerr solution. Moreover, any black hole far away from equilibrium, such as one initially formed in a compact binary merger or by the collapse of a massive star, will eventually reach a final equilibrium Kerr state. At sufficiently late times in this process of reaching equilibrium, we expect that the black hole is modeled as a perturbation around the final state. The emitted gravitational waves will then be damped sinusoids with frequencies and damping times given by the quasinormal mode spectrum of the final Kerr black hole. An observational test of this scenario, often referred to as black hole spectroscopy, is one of the major goals of gravitational wave astronomy. It was recently suggested that the quasinormal mode description including the higher overtones might hold even right after the remnant black hole is first formed. At these times, the black hole is expected to be highly dynamical and nonlinear effects are likely to be important. In this paper we investigate this remarkable scenario in terms of the horizon dynamics. Working with high accuracy simulations of a simple configuration, namely the head-on collision of two nonspinning black holes with unequal masses, we study the dynamics of the final common horizon in terms of its shear and its multipole moments. We show that they are indeed well described by a superposition of ringdown modes as long as a sufficiently large number of higher overtones are included. This description holds even for the highly dynamical final black hole shortly after its formation. We discuss the implications and caveats of this result for black hole spectroscopy and for our understanding of the approach to equilibrium.

/pdf/quasinormal-modes-and-their-overtones-at-the-common-horizon-3cfrr7hesa.pdf

Pierre Mourier

Papers

On Average Properties of Inhomogeneous Fluids in General Relativity III: General Fluid Cosmologies

Quasinormal modes and their overtones at the common horizon in a binary black hole merger