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

TL;DR

This study tests whether the inverse distance ladder, which uses BAO anchored to the CMB sound horizon to calibrate SN Ia distances, can yield $H_0$ values as high as the local measurements. By employing a cosmographic expansion up to fifth order and combining DESI BAO with DES-Dovekie SN Ia data (with cross-checks from Pantheon+ and Union), the authors find $H_0$ remains tightly clustered around the CMB value ($\sim 66$–$67$ km s$^{-1}$ Mpc$^{-1}$) and cannot accommodate $H_0 \approx 73$ km s$^{-1}$ Mpc$^{-1}$ without invoking implausible redshift-dependent SN Ia systematics. They show SN Ia systematics shift $H_0$ by $<0.1$ km s$^{-1}$ Mpc$^{-1}$, and a hypothetical $d\mu/dz \sim 0.2$ mag is required to reach the local $H_0$, which would conflict with other cosmological constraints. The results support the view that, within current SN Ia data quality and BAO anchoring to the CMB, the inverse distance ladder cannot independently resolve the Hubble tension, though future independent probes may help cross-check the absolute distance scale.

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$^{-1}$.

Figures (5)

• Figure 1: The $c\ln(1+z)/D_M(z)$ v redshift relationship, demonstrating the inverse distance ladder method. In black are the $D_M(z)/r_d$ measurements from DESI; individual SNe Ia are shown in light pink points and the binned averages in dark pink. Overplotted are the 4th (pink line) and 5th (blue line) order polynomial fits to the combined data. The y-intercept of this plot gives $H_0 \sim 67$, varying slightly with the choice of polynomial.
• Figure 2: The SN Ia systematic effects tested in DES-Dovekie and their associated $H_0$ values from this work are shown in pink points with errors. The CMB value of $H_0 = 67.4 \pm 0.5$ is plotted in pink, and for reference the local distance network value of $H_0 = 73.04 \pm 1.04$ km s$^{-1}$ Mpc$^{-1}$H0DN25 is plotted in grey. The scatter of $H_0$ values across all systematics is $0.1$ km s$^{-1}$Mpc$^{-1}$. For an explanation of the systematic names, see tables 6 and 7 in Popovic26.
• Figure 3: As in Fig. \ref{['fig:systematics']}, but presenting the $q_0$ parameter. A $q_0 \sim 0.1$ corresponds to a universe without dark energy; $q_0 \sim -0.5$ signals a dark-energy dominant universe.
• Figure 4: The inferred $H_0$ and $M_0$ values as a function of the change in SN Ia magnitudes below $z=0.1$. The $H_0$ values are shown in purple points, with the nominal value in pink fill, and the local distance network value H0DN25 provided in grey. Alongside we provide the equivalent $M_0$ values for the fit in blue points, and the nominal $M_0$ value in blue fill.
• Figure 5: A $d\mu/dz = -0.20$ mag shift is applied to the SN Ia data in pink, such that $H_0 = 71$ km s$^{-1}$ Mpc$^{-1}$. The nominal cosmographic expansion is shown in blue, for contrast against the $d\mu/dz = -0.20$ mag slope in pink. A better cosmographic fit may be acquired with the addition of even higher-order terms, but would not change the resulting $w$CDM inference.