A non-parametric test of variability of Type Ia supernovae luminosity and CDDR

TL;DR

This study tests the constancy of Type Ia supernova luminosity and the cosmic distance duality relation, finding no significant evolution of supernova brightness and supporting a flat universe within current confidence levels.

Contribution

It provides a non-parametric test of supernova luminosity variability and the validity of the CDDR, incorporating multiple parametrizations and priors, which enhances understanding of cosmic acceleration evidence.

Findings

CDDR is consistent within 2σ for various parametrizations

No significant evolution of supernova absolute magnitude detected

Results favor a flat universe but allow mild non-flatness

Abstract

The first observational evidence for cosmic acceleration appeared from Type Ia supernovae (SNe Type Ia) Hubble diagram from two different groups. However, the empirical treatment of SNe Type Ia and their ability to show cosmic acceleration have been the subject of some debate in the literature. In this work we probe the assumption of redshift-independent absolute magnitude $(M_{\mathrm{B}})$ of SNe along with its correlation with spatial curvature ($\Omega_{k0}$) and cosmic distance duality relation (CDDR) parameter ($\eta(z)$). This work is divided into two parts. Firstly, we check the validity of CDDR which relates the luminosity distance ($d_L$) and angular diameter distance ($d_A$) via redshift. We use the Pantheon SNe Ia dataset combined with the $H(z)$ measurements derived from the cosmic chronometers. Further, four different redshift-dependent parametrizations of the distance duality parameter $(\eta(z))$ are used. The CDDR is fairly consistent for almost every parametrization within a $2\sigma$ confidence level in both flat and a non-flat universe. In the second part, we assume the validity of CDDR and emphasize on the variability of $M_{\mathrm{B}}$ and its correlation with $\Omega_{k0}$. We choose four different redshift-dependent parametrizations of $M_{\mathrm{B}}$. The results indicate no evolution of $M_{\mathrm{B}}$ within $2\sigma$ confidence level. For all parametrizations, the best fit value of $\Omega_{k0}$ indicates a flat universe at $2\sigma$ confidence level. However a mild inclination towards a non flat universe is also observed. We have also examined the dependence of the results on the choice of different priors for $H_0$.