Constraints on $\Lambda(t)$-cosmology with power law interacting dark sectors

TL;DR

This paper investigates a time-varying dark energy model interacting with dark matter, constrained by observational data, revealing limitations in addressing the coincidence and cosmological constant problems.

Contribution

It introduces a $ ho_{ ext{Lambda}}(t)$ model with a specific decay law and constrains it using multiple observational datasets, focusing on the case where the energy density ratio remains constant.

Findings

Strong constraints on model parameters from observational data

Exclusion of parameter regions that solve the coincidence problem

The case with $n=3/2$ maintains a constant energy density ratio

Abstract

Motivated by the cosmological constant and the coincidence problems, we consider a cosmological model where the cosmological constant $\Lambda_0$ is replaced by a cosmological term $\Lambda(t)$ which is allowed to vary in time. More specifically, we are considering that this dark energy term interacts with dark matter through the phenomenological decay law $\dot{\rho}_{\Lambda}=-Q\rho_{\Lambda}^{n}$. We have constrained the model for the range $n\in[0,10]$ using various observational data (SNeIa, GRB, CMB, BAO, OHD), emphasizing the case where $n=3/2$. This case is the only one where the late-time value for the ratio of dark energy density and matter energy density $\rho_{\Lambda}/\rho_{m}$ is constant, which could provide an interesting explanation to the coincidence problem. We obtain strong limits on the model parameters which however exclude the region where the coincidence or the cosmological constant problems are significantly ameliorated.