Covariantizing the interaction between dark energy and dark matter

TL;DR

This paper develops a covariant framework for modeling interactions between dark energy and dark matter as imperfect fluids, addressing the challenge of formulating a Lagrangian for such interactions.

Contribution

It introduces a covariant, effective metric approach to describe dark sector interactions, advancing beyond traditional comoving coordinate methods.

Findings

Provides a formal solution for a single fluid interaction

Establishes a covariant description of dark sector coupling

Highlights the difficulty in constructing a Lagrangian for interacting fluids

Abstract

Coupling dark energy and dark matter through an effective fluid description is a very common procedure in cosmology, however it always remains in comoving coordinates in the special FLRW space. We construct a consistent, general, and covariant formulation, where the interaction is a natural implication of the imperfectness of the fluids. This imperfectness makes difficult the final step towards a robust formulation of interacting fluids, namely the construction of a Lagrangian whose variation would give rise to the interacting equations. Nevertheless, we present a formal solution to this problem for a single fluid, through the introduction of an effective metric.