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Register a new userThe Hubble Tension Revisited: Additional Local Distance Ladder Uncertainties
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In a recent paper, we argued that systematic uncertainties related to the choice of Cepheid color-luminosity calibration may have a large influence on the tension between the Hubble constant as inferred from distances to Type Ia supernovae and the cosmic microwave background as measured with the Planck satellite. Here, we investigate the impact of other sources of uncertainty in the supernova distance ladder, including Cepheid temperature and metallicity variations, supernova magnitudes and GAIA parallax distances. Excluding Milky Way Cepheids based on parallax calibration uncertainties, for the color excess calibration we obtain $H_0 = 70.8pm 2.1$ km/s/Mpc, in $1.6,sigma$ tension with the Planck value.
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Estimates of the Hubble constant, $H_0$, from the distance ladder and the cosmic microwave background (CMB) differ at the $sim$3-$sigma$ level, indicating a potential issue with the standard $Lambda$CDM cosmology. Interpreting this tension correctly requires a model comparison calculation depending on not only the traditional `$n$-$sigma$ mismatch but also the tails of the likelihoods. Determining the form of the tails of the local $H_0$ likelihood is impossible with the standard Gaussian least-squares approximation, as it requires using non-Gaussian distributions to faithfully represent anchor likelihoods and model outliers in the Cepheid and supernova (SN) populations, and simultaneous fitting of the full distance-ladder dataset to correctly propagate uncertainties. We have developed a Bayesian hierarchical model that describes the full distance ladder, from nearby geometric anchors through Cepheids to Hubble-Flow SNe. This model does not rely on any distributions being Gaussian, allowing outliers to be modeled and obviating the need for arbitrary data cuts. Sampling from the $sim$3000-parameter joint posterior using Hamiltonian Monte Carlo, we find $H_0$ = (72.72 $pm$ 1.67) ${rm km,s^{-1},Mpc^{-1}}$ when applied to the outlier-cleaned Riess et al. (2016) data, and ($73.15 pm 1.78$) ${rm km,s^{-1},Mpc^{-1}}$ with SN outliers reintroduced. Our high-fidelity sampling of the low-$H_0$ tail of the distance-ladder likelihood allows us to apply Bayesian model comparison to assess the evidence for deviation from $Lambda$CDM. We set up this comparison to yield a lower limit on the odds of the underlying model being $Lambda$CDM given the distance-ladder and Planck XIII (2016) CMB data. The odds against $Lambda$CDM are at worst 10:1 or 7:1, depending on whether the SNe outliers are cut or modeled, or 60:1 if an approximation to the Planck Int. XLVI (2016) likelihood is used.
We propose that stellar-mass binary black holes like GW150914 will become a tool to explore the local Universe within ~100Mpc in the era of the Laser Interferometer Space Antenna (LISA). High calibration accuracy and annual motion of LISA could enable us to localize up to ~60 binaries more accurately than the error volume of ~100Mpc^3 without electromagnetic counterparts under moderately optimistic assumptions. This accuracy will give us a fair chance to determine the host object solely by gravitational waves. By combining the luminosity distance extracted from gravitational waves with the cosmological redshift determined from the host, the local value of the Hubble parameter will be determined up to a few % without relying on the empirically constructed distance ladder. Gravitational-wave cosmography would pave the way for resolution of the disputed Hubble tension, where the local and global measurements disagree in the value of the Hubble parameter at 3.4sigma level, which amounts to ~9%.
Motivated by the large observed diversity in the properties of extra-galactic extinction by dust, we re-analyse the Cepheid calibration used to infer the local value of the Hubble constant, $H_0$, from Type Ia supernovae. Unlike the SH0ES team, we do not enforce a universal color-luminosity relation to correct the near-IR Cepheid magnitudes. Instead, we focus on a data driven method, where the measured colors of the Cepheids are used to derive a color-luminosity relation for each galaxy individually. We present two different analyses, one based on Wesenheit magnitudes, a common practice in the field that attempts to combine corrections from both extinction and variations in intrinsic colors, resulting in $H_0=66.9pm 2.5$ km/s/Mpc, in agreement with the Planck value. In the second approach, we calibrate using color excesses with respect to derived average intrinsic colors, yielding $H_0=71.8pm 1.6$ km/s/Mpc, a $2.7,sigma$ tension with the value inferred from the cosmic microwave background. Hence, we argue that systematic uncertainties related to the choice of Cepheid color-luminosity calibration method currently inhibits us from measuring $H_0$ to the precision required to claim a substantial tension with Planck data.
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 $4-6sigma$ 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 $1-2sigma$ 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]
It is shown, from the two independent approaches of McCrea-Milne and of Zeldovich, that one can fully recover the set equations corresponding to the relativistic equations of the expanding universe of Friedmann-Lemaitre-Robertson-Walker geometry. Although similar, the Newtonian and relativistic set of equations have a principal difference in the content and hence define two flows, local and global ones, thus naturally exposing the Hubble tension at the presence of the cosmological constant Lambda. From this, we obtain absolute constraints on the lower and upper values for the local Hubble parameter, sqrt{Lambda c^2/3} simeq 56.2$ and sqrt{Lambda c^2} simeq 97.3 (km/sec Mpc^{-1}), respectively. The link to the so-called maximum force--tension issue in cosmological models is revealed.
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