Focus Issue on the Hubble Constant Tension

 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, H₀, made by the early time probes in concert with the ‘vanilla’ ΛCDM cosmological model, and a number of late time, model-independent determinations of H₀ 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 (H₀ = 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 H₀ 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.

The cosmological principle (CP)—the notion that the Universe is spatially isotropic and homogeneous on large scales—underlies a century of progress in cosmology. It is conventionally formulated through the Friedmann-Lemaître-Robertson-Walker (FLRW) cosmologies as the spacetime metric, and culminates in the successful and highly predictive Λ-Cold-Dark-Matter (ΛCDM) model. Yet, tensions have emerged within the ΛCDM model, most notably a statistically significant discrepancy in the value of the Hubble constant, H₀. Since the notion of cosmic expansion determined by a single parameter is intimately tied to the CP, implications of the H₀ tension may extend beyond ΛCDM to the CP itself. This review surveys current observational hints for deviations from the expectations of the CP, highlighting synergies and disagreements that warrant further study. Setting aside the debate about individual large structures, potential deviations from the CP include variations of cosmological parameters on the sky, discrepancies in the cosmic dipoles, and mysterious alignments in quasar polarizations and galaxy spins. While it is possible that a host of observational systematics are impacting results, it is equally plausible that precision cosmology may have outgrown the FLRW paradigm, an extremely pragmatic but non-fundamental symmetry assumption.

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 ΛCDM model poses a possible crisis for the Friedmann–Lemaître–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 Ω_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 5σ. 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 Ω_k0 equal to that preferred from the Planck power spectra resolves the Hubble tension within our dark energy-free model.

In this letter we construct the Hubble diagram for a universe where dark matter is universally charged under a dark non-linear electromagnetic force which features a screening mechanism of the K-mouflage type for repulsive forces. By resorting to the Newtonian approximation, we explicitly show that the cosmological evolution generates an inhomogeneous Hubble diagram that corresponds to a curvature dominated expansion at short distances and converges to the cosmological one of ΛCDM. We discuss the potential impact of this inhomogeneous profile on the Hubble tension. For completeness, we explicitly show how the Newtonian approximation can be derived from an inhomogeneous relativistic Lemaître model.

The heliocentric redshifts (z_hel) reported for 150 type Ia supernovae in the Pantheon compilation are significantly discrepant from their corresponding values in the JLA compilation. Both catalogues include corrections to the redshifts and magnitudes of the supernovae to account for the motion of the heliocentric frame relative to the ‘CMB rest frame’, as well as corrections for the directionally coherent bulk motion of local galaxies with respect to this frame. The latter is done employing modelling of peculiar velocities which assume the ΛCDM cosmological model but nevertheless provide evidence for residual bulk flows which are discordant with this model (implying that the observed Universe is in fact anisotropic). Until recently such peculiar velocity corrections in the Pantheon catalogue were made at redshifts exceeding 0.2 although there is no data on which to base such corrections. We study the impact of these vexed issues on the 4.4σ discrepancy between the Hubble constant of H₀ = 67.4 ± 0.5 km s⁻¹ Mpc⁻¹ inferred from observations of CMB anisotropies by Planck assuming ΛCDM, and the measurement of H₀ = 73.5 ± 1.4 km s⁻¹ Mpc⁻¹ by the SH0ES project which extended the local distance ladder using type Ia supernovae. Using the same methodology as the latter study we find that for supernovae whose redshifts are discrepant between Pantheon and JLA with Δz_hel > 0.0025, the Pantheon redshifts favour H₀ ≃ 72 km s⁻¹ Mpc⁻¹, while the JLA redshifts favour H₀ ≃ 68 km s⁻¹ Mpc⁻¹. Thus the discrepancies between SNe Ia datasets are sufficient to undermine the claimed ‘Hubble tension’. We further note the systematic variation of H₀ by ∼6–9 km s⁻¹ Mpc⁻¹ across the sky seen in multiple datasets, implying that it cannot be measured locally to better than ∼10% in a model-independent manner.

The tension between early and late Universe probes of the Hubble constant has motivated various new FLRW cosmologies. Here, we reanalyse the Hubble tension with a recent age of the Universe constraint. This allows us to restrict attention to matter and a dark energy sector that we treat without assuming a specific model. Assuming analyticity of the Hubble parameter H(z), and a generic low redshift modification to flat ΛCDM, we find that low redshift data (z ≲ 2.5) and well-motivated priors only permit a dark energy sector close to the cosmological constant Λ. This restriction rules out late Universe modifications within FLRW. We show that early Universe physics that alters the sound horizon can yield an upper limit of H₀ ∼ 71 ± 1 km s⁻¹ Mpc⁻¹. Since various local determinations may be converging to H₀ ∼ 73 km s⁻¹ Mpc⁻¹, a breakdown of the FLRW framework is a plausible resolution. We outline how future data, in particular strongly lensed quasar data, could also provide further confirmations of such a resolution.

The Universe may feature large-scale inhomogeneities beyond the standard paradigm, implying that statistical homogeneity and isotropy may be reached only on much larger scales than the usually assumed ∼100 Mpc. This means that we are not necessarily typical observers and that the Copernican principle could be recovered only on super-Hubble scales. Here, we do not assume the validity of the Copernican principle and let cosmic microwave background, baryon acoustic oscillations, type Ia supernovae, local H₀, cosmic chronometers, Compton y-distortion and kinetic Sunyaev–Zeldovich observations constrain the geometrical degrees of freedom of the local structure, which we parametrize via the ΛLTB model—basically a non-linear radial perturbation of a FLRW metric. In order to quantify if a non-Copernican structure could explain away the Hubble tension, we pay careful attention to computing the Hubble constant in an inhomogeneous Universe, and we adopt model selection via both the Bayes factor and the Akaike information criterion. Our results show that, while the ΛLTB model can successfully explain away the H₀ tension, it is favored with respect to the ΛCDM model only if one solely considers supernovae in the redshift range that is used to fit the Hubble constant, that is, 0.023 < z < 0.15. If one considers all the supernova sample, then the H₀ tension is not solved and the support for the ΛLTB model vanishes. Combined with other data sets, this solution to the Hubble tension barely helps. Finally, we have reconstructed our local spacetime. We have found that data are best fit by a shallow void with δ_L ≈ −0.04 and ${r}_{\mathrm{L}}^{\text{out}}\approx 300$ Mpc, which, interestingly, lies on the border of the 95% credible region relative to the standard model expectation.