Equivalence between Horndeski and beyond Horndeski theories and imperfect fluids

TL;DR

This paper demonstrates a formal equivalence between Horndeski and beyond Horndeski theories and general relativity with effective imperfect fluids, clarifying their cosmological implications and differences.

Contribution

It establishes a formal link between these modified gravity theories and effective fluid descriptions, highlighting differences in their stress-energy tensor properties.

Findings

Horndeski theories are equivalent to imperfect fluids with anisotropic stresses.

Beyond Horndeski theories correspond to perfect fluids.

Effective stress-energy tensors differ between the theories.

Abstract

In this paper we show that an equivalence between Horndeski and beyond Horndeski theories and general relativity with an effective imperfect fluid can be formally established. The formal equivalence is discussed for several particular cases of interest. Working in the cosmological framework, it is shown that, while the effective stress-energy tensor of viable Horndeski theories is formally equivalent to that of an imperfect fluid with anisotropic stresses and vanishing heat flux vector, the effective stress-energy tensor of beyond Horndeski theories is equivalent to the one of a perfect fluid instead.