Linear Growth of Matter Perturbations Probed by Redshift-Space Distortions in Interacting $Λ(t)$CDM Cosmologies

TL;DR

The paper addresses the $S8$ and $H0$ tensions by testing a minimal IDE extension within a spatially flat Λ(t)CDM framework, introducing two couplings $Q_I$ and $Q_{II}$ that describe energy transfer between vacuum dark energy and dark matter. It develops a sub-horizon, quasi-static perturbation formalism for IDE and constrains the model parameters using a Bayesian analysis of a comprehensive data set that includes RSD, CCs, BAO, SNe Ia, and CMB distance priors. The main finding is that a small positive coupling $\varepsilon \sim 0.02$ yields $S8 \approx 0.87$ and $H0 \approx 68.5$ km s$^{-1}$ Mpc$^{-1}$, with Model I and Model II being nearly degenerate. This demonstrates that IDE can accommodate current growth and expansion data with minimal deviations from ΛCDM, while highlighting the need for relativistic Boltzmann treatments and future surveys (Euclid, LSST, DESI) to tighten constraints on the coupling and robustly test the viability of IDE as a resolution to cosmological tensions.

Abstract

In the context of a spatially flat $Λ(t)$CDM cosmology, we investigate interacting dark energy (IDE) scenarios characterized by phenomenological interaction terms proportional to the Hubble expansion rate and the dark energy density. Our analysis is performed at both the background and linear perturbation levels, with particular emphasis on the evolution of dark matter density fluctuations. Cosmological constraints are derived from a joint analysis of CMB distance priors, Baryon Acoustic Oscillations (BAO), Type Ia supernovae (SNe Ia) from Pantheon+, Redshift-Space Distortions (RSD), and $H(z)$ data from Cosmic Chronometers (CC). Using the linear growth of matter perturbations, we estimate the clustering parameter $S_8$ within IDE extensions of the flat $Λ(t)$CDM framework. At the perturbative level, we consider interaction terms of the form $Q_{\text{I}}=\varepsilon a H\barρ_{Λ(t)}$ (Model I) and $Q_{\text{II}}=\varepsilon H\barρ_{Λ(t)}$ (Model II). From the combined dataset, we obtain the constraints $S_8 = 0.870 \pm 0.026$ for Model I and $S_8 = 0.872 \pm 0.026$ for Model II. Finally, we discuss the implications for the coupling parameter $\varepsilon$, taking into account the semi-analytical approximations and observational data employed in this study.

Figures (2)

• Figure 1: Marginalized posterior distributions and 68% and 95% confidence level (CL) contours for the main cosmological parameters $H_0$, $\Omega_{\rm DM0}$, $\varepsilon$, and $S_8$. The results are shown for different combinations of datasets, as indicated in the legend. Left panel: Constraints from individual datasets. Right panel: Constraints from the joint analysis of datasets.
• Figure 2: Marginalized posterior distributions and 68% and 95% C.L. contours for the main cosmological parameters $H_0$, $\Omega_{\rm DM0}$, $\varepsilon$, and $S_8$. The results are shown for different combinations of datasets, as indicated in the legend. Left panel: Constraints from individual datasets. Right panel: Constraints from the joint analysis of datasets.