Cosmological model insensitivity of local $H_0$ from the Cepheid distance ladder

TL;DR

This study assesses whether the local $H_0$ inferred from the Cepheid-calibrated SN Ia distance ladder is sensitive to the assumed expansion history of the universe. By jointly analyzing calibrator SNe Ia and Pantheon high-z SNe Ia under multiple dark energy models and a cosmographic, model-independent expansion, and by propagating a full systematics covariance, the authors quantify shifts in $H_0$. They find the maximum model-induced shift in $H_0$ to be only $0.6\%$ (up to $0.47\ \mathrm{km\,s^{-1}\,Mpc^{-1}}$), with most models yielding values near the fiducial ΛCDM result, and the cosmographic approach yielding $q_0=-0.59\pm0.14$. The SN Ia systematics dominate the uncertainty budget (≈0.8\%), and including calibrator–Hubble-flow covariance can shift $H_0$ by up to ~0.75, underscoring the need for careful covariance treatment in future precision work. Overall, the local $H_0$ estimate is robust against a wide range of expansion-history models within the explored parameter space.

Abstract

The observed tension ($\sim 9\%$ difference) between the local distance ladder measurement of the Hubble constant, $H_0$, and its value inferred from the cosmic microwave background (CMB) could hint at new, exotic, cosmological physics. We test the impact of the assumption about the expansion history of the universe ($0.01<z<2.3$) on the local distance ladder estimate of $H_0$. In the fiducial analysis, the Hubble flow Type Ia supernova (SN~Ia) sample is truncated to $z < 0.15$ and the deceleration parameter ($q_0$) fixed to -0.55. We create realistic simulations of the calibrator and Pantheon samples and account for a full systematics covariance between these two sets. We fit several physically motivated dark energy models and derive combined constraints from calibrator and Pantheon SNe~Ia and simultaneously infer $H_0$ and dark energy properties. We find that the assumption on the dark energy model does not significantly change the local distance ladder value of $H_0$, with a maximum difference ($ΔH_0$) between the inferred value for different models of 0.47 km$^{-1}$ s$^{-1}$ Mpc $^{-1}$, i.e. a 0.6$\%$ shift in $H_0$, significantly smaller than the observed tension. Additional freedom in the dark energy models does not increase the error in the inferred value of $H_0$. Including systematics covariance between the calibrators, low redshift SNe, and high redshift SNe can induce small shifts in the inferred value for $H_0$. The SN~Ia systematics in this study contribute $\lesssim 0.8 \%$ to the total uncertainty on $H_0$.

Figures (3)

• Figure 1: The Hubble residuals as a function of redshift for each dark energy model relative to the best fit $\Lambda$CDM model. The residuals for the data are plotted relative to the best fit $\Lambda$CDM model.
• Figure 2: The probability density of $H_0$ for the different cosmological models describing the SN magnitude-redshift relation. The solid lines show the marginalised distribution for $H_0$ for each assumed model and the dotted blue line is the case for the standard $\Lambda$CDM scenario with only statistical uncertainties. The median value and the 1-D marginalised posterior distribution for the different models are very similar (see text for more details). The SN Ia absolute magnitude is chosen to reproduce the fiducial analysis in 2019ApJ...876...85R.
• Figure 3: The joint posterior distribution on $H_0$ and $q_0$ for the cosmographic expansion of the dimensionless Hubble parameter as a function of redshift (Equation \ref{['eq:cosmograph']}) for the case with the complete systematics covariance matrix (green), only $z < 0.15$ SNe Ia having systematic uncertainties (magenta) and the case with only statistical uncertainties (red).