Saturation Mechanisms in the Interacting Dark Sector

TL;DR

This paper introduces cosmological models with an interacting dark sector modulated by a sparseness scale, which influences late-time universe acceleration and is supported by observational data.

Contribution

It proposes a novel saturation mechanism inspired by ecology, incorporating a sparseness scale to bound dark sector interactions and analyze their cosmological effects.

Findings

The sparseness scale affects the dynamical behavior of the universe's expansion.

Observational data disfavor zero sparseness, supporting a nonzero interaction scale.

Phase-space analysis reveals stability properties of the models' stationary points.

Abstract

We introduce a family of phenomenological cosmological models featuring an interacting dark sector modulated by a sparseness scale parameter, in order to describe the late-time accelerated expansion of the universe. The sparseness scale, inspired by well-established saturation mechanisms in ecology and biology, is introduced in the interaction as a half-saturation constant that bounds the energy exchange between dark matter and dark energy, controls the dynamical behaviour of the physical variables and can prevent the phantom crossing. We consider three nonlinear interacting models, where two of them recover the linear interacting scenarios when the sparsity parameter vanishes. We examine the phase-space of the cosmological field equations by using the Hubble normalization approach. We determine the stationary points and their stability properties in order to reconstruct the asymptotics behaviour of the field equations. Such an analysis allows us to demonstrate the effects of the sparseness scale on the background dynamics. We test the interacting models with observational data. Specifically, we employ Supernovae catalogues, cosmic chronometers, Baryon Acoustic Oscillation measurements from DESI DR2, and redshift-space distortion measurements of the growth of large-scale structure through the $f$ and $f\sigma_8$ observables. The Bayesian analysis suggests that, for two of the three models, a vanishing sparsity parameter is disfavoured at more than the 95\% confidence interval, providing observational support for a nonzero sparseness scale in the dark sector interaction.