Cosmic curvature on large-scale structures with homogeneous dark energy

TL;DR

This paper investigates how cosmic curvature influences large-scale structure formation using relativistic perturbation theory and observational data, revealing nuanced effects on dark energy behavior and constraints on cosmological parameters.

Contribution

It introduces a relativistic framework incorporating cosmic curvature into structure formation analysis and provides observational constraints on curvature and dark energy models.

Findings

Constraints on some parameters remain consistent with previous studies.

Inclusion of cosmic curvature weakens constraints on matter density and fluctuation amplitude.

Evidence suggests non-zero curvature in ΛCDM but not in dynamical dark energy models.

Abstract

This study explores the impact of cosmic curvature on structure formation through general relativistic first-order perturbation theory. We analyze continuity and Euler equations, incorporating cosmic curvature into Einstein equations. Emphasizing late-time dynamics, we investigate matter density contrast evolution in the presence of cosmic curvature, with a specific focus on sub-hubble scales. Solving the evolution equation, we conduct data analysis using cosmic chronometers, baryon acoustic oscillations from Dark Energy Spectroscopic Instrument Data Release 2 (DESI DR2) (including $r_d$ constraint from CMB), type Ia supernova observations from Pantheon+ sample, logarithmic growth rate $f$ data and $f\sigma_8$ data. While constraints on some parameters remain consistent, inclusion of cosmic curvature losens constraints on $\Omega_{\rm m0}$ and $\sigma_{\rm 8,0}$ in $\Lambda$CDM and $w_0$CDM models. The non-phantom behavior of dark energy proves more favorable in $w_0$CDM model, whereas in CPL model, there is certain evidence for non-phantom behaviour at lower redshift and phantom behaviour at higher redshift. Interestingly, we find certain evidence for non-zero cosmic curvature in $\Lambda$CDM model, but no evidence for it in both $w_0$CDM and CPL models, which indirectly proves the non-degeneracy between dynamical dark energy and cosmic curvature.