Effects of time-varying $\beta$ in SNLS3 on constraining interacting dark energy models

TL;DR

This study investigates how the redshift evolution of the color-luminosity parameter $eta$ affects cosmological parameter estimation in interacting dark energy models using SNLS3, CMB, galaxy clustering, and Hubble constant data.

Contribution

It demonstrates that accounting for $eta$'s evolution significantly improves model fits and alters key cosmological parameters, highlighting the importance of including $eta$'s evolution in analyses.

Findings

Varying $eta$ reduces $ ilde{ ext{chi}}^2$ by about 34.

$eta$ evolution rules out $eta_1=0$ at 5.8$\sigma$ CL.

Varying $eta$ increases $\Omega_{c0}$ and $w$, and decreases $h$ in the $w$CDM model.

Abstract

It has been found that, for the Supernova Legacy Survey three-year (SNLS3) data, there is strong evidence for the redshift-evolution of color-luminosity parameter $\beta$. In this paper, adopting the $w$-cold-dark-matter ($w$CDM) model and considering its interacting extensions (with three kinds of interaction between dark sectors), we explore the evolution of $\beta$ and its effects on parameter estimation. In addition to the SNLS3 data, we also take into account the Planck distance priors data of the cosmic microwave background (CMB), the galaxy clustering (GC) data extracted from SDSS DR7 and BOSS, as well as the direct measurement of Hubble constant from the Hubble Space Telescope (HST) observation. We find that, for all the interacting dark energy (IDE) models, adding a parameter of $\beta$ can reduce $\chi^2$ by $\sim$ 34, indicating that $\beta_1 = 0$ is ruled out at 5.8$\sigma$ confidence level (CL). Furthermore, it is found that varying $\beta$ can significantly change the fitting results of various cosmological parameters: for all the dark energy models considered in this paper, varying $\beta$ yields a larger $\Omega_{c0}$ and a larger $w$; on the other side, varying $\beta$ yields a smaller $h$ for the $w$CDM model, but has no impact on $h$ for the three IDE models. This implies that there is a degeneracy between $h$ and $\gamma$. Our work shows that the evolution of $\beta$ is insensitive to the interaction between dark sectors, and then highlights the importance of considering $\beta$'s evolution in the cosmology fits.