The correspondence between a scalar field and an effective perfect fluid

TL;DR

This paper explores the formal equivalence and differences between a minimally coupled scalar field and an effective perfect fluid, highlighting the nuances in their Lagrangian descriptions and the implications for scalar field models.

Contribution

It clarifies the incomplete correspondence between scalar fields and perfect fluids, especially regarding their Lagrangian densities and the role of phantom fields.

Findings

The Lagrangian densities P and -rho are not equivalent for scalar fields.

Exchanging these densities corresponds to switching between canonical and phantom scalar fields.

The formal equivalence between scalar fields and perfect fluids has limitations in Lagrangian descriptions.

Abstract

It is widely acknowledged that, for formal purposes, a minimally coupled scalar field is equivalent to an effective perfect fluid with equation of state determined by the scalar potential. This correspondence is not complete because the Lagrangian densities P and -rho, which are equivalent for a perfect fluid, are not equivalent for a minimally coupled scalar field. The exchange between these two Lagrangian densities amounts to exchanging a canonical scalar field with a phantom scalar field.