On The Stability Of $H_0$ And The Inverse Distance Ladder

TL;DR

This study evaluates the inverse distance ladder method using SNe Ia and BAO data, concluding it cannot reconcile the Hubble Tension due to the minimal impact of systematics and the implausibility of required redshift evolution.

Contribution

The paper demonstrates that the inverse distance ladder cannot resolve the Hubble Tension, highlighting the limitations of SNe Ia measurements and the necessity of unphysical redshift-dependent effects.

Findings

Inverse distance ladder anchored to CMB yields H0 = 67.4 ± 0.5 km/s/Mpc.

Systematics in SNe Ia only shift H0 by less than 0.1 km/s/Mpc.

A redshift-dependent magnitude change of 0.2 mag per unit redshift is needed to match local H0 values.

Abstract

The `Inverse Distance Ladder' uses relative-distance measurements with type Ia supernovae (SNe Ia), anchored to an absolute distance scale from Baryon Acoustic Oscillations (BAO) and the cosmic microwave background (CMB), to provide an alternative measurement technique for the local expansion rate $H_0$. Using SNe Ia from the Dark Energy Survey and BAO measurements from the Dark Energy Spectroscopic Instrument, we show that the inverse distance ladder is unable to explain the Hubble Tension, anchored as it is to the CMB and its value of $H_0 = 67.4 \pm 0.5$ kms$^{-1}$ Mpc$^{-1}$. To do so, we first show that the suite of systematics considered in cosmology analyses with SNe Ia only move the inferred $H_0$ by $<0.1$kms$^{-1}$ Mpc$^{-1}$, and second, we investigate the scale of redshift-dependent magnitude changes necessary to change the inferred inverse distance ladder $H_0$ from $67$ to the local network of distance measurements value of $73$, and the impact that this would have on other cosmological inferences with SNe Ia. We find that a change of $d\mu/dz = 0.2$ mag would be necessary to infer an $H_0$ in concordance with local distance measurements, and that this $d\mu/dz$ value would result in a Flat $\Lambda$CDM $\Omega_M = 0.23$, $10\sigma$ discrepant with other cosmological probes, {indicating that the precision of SNe Ia measurements preclude the necessary redshift evolution for an $H_0$ of 74 kms$^{-1}$ Mpc$^{-1}$}. Therefore, we conclude that current SN Ia cosmology leaves little freedom for the inverse distance ladder to yield $H_0$ values significantly different from $67$ kms$^{-1}$ Mpc$^{-1}$.