A note on the equivalence of a barotropic perfect fluid with a K-essence scalar field

TL;DR

This paper establishes the precise conditions under which certain non-canonical scalar field models are equivalent to barotropic perfect fluids, revealing implications for perturbation behavior and model redefinition.

Contribution

It provides the necessary and sufficient criteria for scalar fields to be equivalent to barotropic fluids, including the impact on non-adiabatic perturbations and model reformulation.

Findings

Non-adiabatic pressure perturbation vanishes at all orders.

Scalar field models can be redefined as purely kinetic K-essence.

Exact equivalence conditions are derived for specific scalar field classes.

Abstract

In this short note, we obtain the necessary and sufficient condition for a class of non-canonical single scalar field models to be exactly equivalent to barotropic perfect fluids, under the assumption of an irrotational fluid flow. An immediate consequence of this result is that the non-adiabatic pressure perturbation in this class of scalar field systems vanishes exactly at all orders in perturbation theory and on all scales. The Lagrangian for this general class of scalar field models depends on both the kinetic term and the value of the field. However, after a field redefinition, it can be effectively cast in the form of a purely kinetic K-essence model.