On the uniqueness of $\Lambda$CDM-like evolution for homogeneous and isotropic cosmology in General Relativity

TL;DR

This paper investigates whether alternative cosmological models with interactions in the dark sector can produce the same expansion history as the standard flat $\\Lambda$CDM model, concluding that only models with phantom fluids can do so.

Contribution

It demonstrates that in General Relativity, only phantom fluid models with dark sector interactions can replicate the \\Lambda$CDM expansion history under kinematic degeneracy conditions.

Findings

Only phantom fluid models can be kinematically degenerate with \\Lambda$CDM.

Physically viable coupled quintessence models are of measure zero in reproducing \\Lambda$CDM.

Models with non-phantom fluids cannot mimic \\Lambda$CDM evolution.

Abstract

We address the question of the uniqueness of spatially flat $\Lambda$CDM-like evolution for FLRW cosmologies in General Relativity, i.e. whether any model other than the spatially flat $\Lambda$CDM can give rise to the same type of scale factor evolution. Firstly, we elaborate on what we exactly imply by a $\Lambda$CDM-like evolution or kinematic/cosmographic degeneracy with the $\Lambda$CDM model, using the lessons from the statefinder diagnostic. Then, we consider two models with interaction in the dark sector: coupled fluid-fluid model and coupled quintessence model. We enforce the \emph{kinematic} degeneracy with the spatially flat $\Lambda$CDM model via the cosmographic condition $j=1$ ($j$ being the jerk parameter), which in turn fixes the function of the interaction term that is a priori unspecified. We argue that in General Relativity this cosmographic condition is consistent only with spatial flatness. Employing a dynamical system approach, we show that the spatially flat coupled fluid-fluid interacting models kinematically degenerate with $\Lambda$CDM must necessarily be based on a phantom fluid, whereas the set of physically viable spatially flat coupled quintessence models with power law or exponential potential kinematically degenerate to $\Lambda$CDM is of measure zero. Our analysis establishes that coupled fluid-fluid models with non-phantom fluids or coupled quintessence models with power law and exponential potential can never reproduce a cosmological evolution similar to that of the $\Lambda$CDM. The astrophysical consequences of our findings are qualitatively discussed in light of observational cosmological tensions.