Cosmology-Independent Constraints on the Etherington Relation and SNeIa Absolute Magnitude Evolution from DESI-DR2

Abstract

We carry out a test of the fundamental Etherington relation (cosmic distance duality relation) which relates the luminosity distance $D_{\rm L}$ and angular diameter distance $D_{\rm A}$ in metric theories of gravity. We use the latest measurements of the angular diameter distance as a function of redshift from the Dark Energy Spectroscopic Instrument Data Release 2 (DESI-DR2) and the luminosity distance from a variety of compilations of Supernovae of Type Ia (SNeIa). Our results indicate that these measurements are statistically consistent with the Etherington relation. In addition to providing a confirmation of the underlying assumptions of the Etherington relation, i.e., the metric nature of gravity, Lorentz invariance and photon number conservation, our results are also a stringent test of any residual systematic effects. We interpret the absence of evidence of any deviation from this relation to constrain the evolution of the absolute magnitude of SNeIa to $dM/dz = 0.07 \pm 0.07$ over and above the systematics that are already accounted for in the SNeIa analyses. We discuss how the Etherington relation can be used to constrain systematic parameters in the analyses of dynamical dark energy using geometric probes, to make it more robust against systematic effects.

Figures (5)

• Figure 1: The data points with errorbars in different panels show the distance modulus corresponding to SNeIa compiled by (a) JLA, (b) Pantheon+, (c) Union3, and (d) DESY5 as indicated at the top of each panel. In each panel, top subpanel shows the distance modulus $\mu - 5\log{h}$ obtained from SNeIa, bottom subpanel shows the corresponding residuals which are fit with a quadratic function. The 68 and 95 credible regions for the residuals are shown with the shaded region.
• Figure 2: The validity of the Etherington relation as seen using the quantity ${\cal R}(z, z_{\rm ref})$, with $z_{\rm ref}=0.706$ using $D_{\rm L}$ measurements from a variety of SNeIa compilations and $D_{\rm A}$ measurements from DESI DR 2.
• Figure 3: Cross-correlation matrix for ${\cal R}(z, z_{\rm ref})$ for various SNeIa samples. Note that the different samples should not be combined as they may contain data from same SNeIa analyzed under differing assumptions. We caution the reader that the block diagonal form of the cross-correlation matrix that appears here is for the economy of representation of all cross-correlation matrices in a single figure. Our analysis treats each one separately.
• Figure 4: Same as Figure \ref{['fig:eth_combined_plot']}, but extended to lower redshifts to include the DESI Bright Galaxy Survey (BGS) measurement at $z=0.295$. Since the BGS data only provides the volume-averaged distance $D_V/r_s$, we extract the angular diameter distance by adopting a fiducial Planck 2018 $\Lambda$CDM cosmology for $D_H/r_s$. This introduces a mild model dependence to the lowest redshift data point, breaking the strict model independence maintained in the rest of the analysis.
• Figure 5: Deviations from the Etherington relation from the combination of DESI-DR2 with Pantheon+ (top panel) and Union3 (bottom panel) compilations, respectively. The 68 percent credible interval for this deviation with a power law model is shown as the blue shaded region, while the deviation with a model including evolution of the SNeIa absolute magnitude is shown as the red shaded region in each of the panels.