Cosmological perturbations in the interacting dark sector: Mapping fields and fluids

TL;DR

This paper establishes a unique field theory form for dark sector interactions, demonstrating a one-to-one correspondence with fluid models, and analyzes the stability and timing of dark energy dominance in these models.

Contribution

It derives a unique interaction form consistent with field theory, linking fluid and field descriptions, and introduces a stability analysis for the interacting dark sector.

Findings

Unique interaction form derived from field theory.

One-to-one mapping between fields and fluids exists only for this form.

Dark-energy dominated epoch occurs earlier in interacting models.

Abstract

There is no unique way to describe the dark energy-dark matter interaction, as we have little information about the nature and dynamics of the dark sector. Hence, in many of the phenomenological dark matter fluid interaction models in the literature, the interaction strength $Q_{\nu}$ in the dark sector is introduced by hand. Demanding that the interaction strength $Q_{\nu}$ in the dark sector must have a field theory description, we obtain a unique form of interaction strength. We show the equivalence between the fields and fluids for the $f(R,\chi)$ model where $f$ is an arbitrary, smooth function of $R$ and classical scalar field $\chi$, which represents dark matter. Up to first order in perturbations, we show that the one-to-one mapping between the \emph{classical} field theory description and the phenomenological fluid description of interacting dark energy and dark matter exists \emph{only} for this unique form of interaction. We then classify the interacting dark energy models considered in the literature into two categories based on the field-theoretic description. We introduce a novel autonomous system and its stability analysis for the general interacting dark sector. We show that the dark-energy dominated epoch occurs earlier than the non-interacting systems for a specific scalar field potential and a range of coupling strengths.