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

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 $dμ/dz = 0.2$ mag would be necessary to infer an $H_0$ in concordance with local distance measurements, and that this $dμ/dz$ value would result in a Flat $Λ$CDM $Ω_M = 0.23$, $10σ$ 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$^{-1}$.