Model independent $H(z)$ reconstruction using the cosmic inverse distance ladder

TL;DR

This work develops a model-independent reconstruction of the expansion history by fitting a flexible $H(z)$ to BAO and Pantheon SN data, calibrated with priors on the sound horizon $r_d$ from Planck/WMAP or BBN-informed analyses. By using the inverse distance ladder under the FRW metric and GR, it obtains $H_0$ values around $68$ km s$^{-1}$ Mpc$^{-1}$, aligning with Planck/LCDM and remaining in tension with the SH0ES value. The results show that the low-redshift gradient of $H(z)$ is tightly constrained by SNe data, while BAO anchors the high-redshift evolution; no evidence for new low-redshift physics is found. Consistency checks with high-redshift physics indicate that reconciling the $H_0$ discrepancy would require early-Universe modifications that reduce $r_d$ without spoiling CMB/BBN observations, a challenging prospect for new physics.

Abstract

Recent distance ladder determinations of the Hubble constant $H_0$ disagree at about the $3.5σ$ level with the value determined from Planck measurements of the cosmic microwave background (CMB) assuming a $Λ$CDM cosmology. This discrepancy has prompted speculation that new physics might be required beyond that assumed in the $Λ$CDM model. In this paper, we apply the inverse distance ladder to fit a parametric form of $H(z)$ to baryon acoustic oscillation (BAO) and Type Ia supernova data together with priors on the sound horizon at the end of the radiation drag epoch, $r_d$. We apply priors on $r_d$, based on inferences from either Planck or the Wilkinson Microwave Anistropy Probe (WMAP), and demonstrate that these values are consistent with CMB-independent determinations of $r_d$ derived from measurements of the primordial deuterium abundance, BAO and supernova data assuming the $Λ$CDM cosmology. The $H(z)$ constraints that we derive are independent of detailed physics within the dark sector at low redshifts, relying only on the validity of the Friedmann-Robertson-Walker (FRW) metric of General Relativity. For each assumed prior on $r_d$, we find consistency with the inferred value of $H_0$ and the Planck $Λ$CDM value and corresponding tension with the distance ladder estimate.

Figures (5)

• Figure 1: Posterior likelihoods for the 'epsilon' (above) and 'log' (below) parameterizations of $H(z)$. Blue contours show 68% and 95% constraints using the Planck prior on $r_d$. The red contours (largely hidden by the blue contours) show the constraints using the WMAP prior on $r_d$.
• Figure 2: $H(z)$ reconstruction for the epsilon model (left hand panels) and log model (right hand panels) for the Planck and WMAP priors on $r_d$: The blue lines show the best fits, and the bands show the allowed one and two sigma ranges. The red points show the BAO estimates on $H(z)$ from Table \ref{['table:BAO']} plotted assuming the central values of the priors on $r_d$. The R18 SH0ES forward distance ladder estimate of $H_0 = 73.48 \pm 1.66 ~{\rm km} \ {\rm s}^{-1}{\rm Mpc}^{-1}$ is plotted as the green point in each panel.
• Figure 3: Posteriors for the Hubble constant $H_0$ derived from the epsilon model using the WMAP and Planck$r_d$ priors. The grey bands show the one and two sigma errors for the value obtained by R18, while the green bands show the Planck base $\Lambda$CDM value from P16.
• Figure 4: 68% and 95% constraints on the $q_0$ and $j_0$ parameters determined from the epsilon model. These constraints are set mainly by the Pantheon SNe sample and are almost independent of the prior on $r_d$. The lines give the values of $j_0$ and $q_0$ expected in the base $\Lambda$CDM model with $\Omega_m = 0.31$.
• Figure 5: The CMB constraints on the sound horizon $r_d$ from WMAP and Planck used in this paper. The black and red curves show the posteriors on $r_d$ determined by fitting to the BAO and Pantheon SNe data assuming the base $\Lambda$CDM cosmology and BBN contraints on $\Omega_b h^2$. The curve labelled BBN(M) assumes the Marcucci:2016$d(p,\gamma)^3{\rm He}$ reaction rate (labelled BBN(M)). The curve labelled BBN(A) uses the experimental rate from Adelberger:2011.