Gauge invariant fluid lagrangian and its application to cosmology

TL;DR

This paper develops a gauge-invariant Lagrangian for relativistic fluids, deriving new equations of motion that connect to classical fluid dynamics and applying the model to cosmological homogeneous universe scenarios.

Contribution

It introduces a novel gauge-invariant fluid Lagrangian and derives a relativistic fluid equation that reduces to classical Euler equations in the non-relativistic limit.

Findings

Derived a new relativistic fluid equation of motion.

Applied the model to a homogeneous universe scenario.

Analyzed free energy density behavior near Hubble distance.

Abstract

A lagrangian for relativistic fluid systems with matters inside is developed using gauge principle. In the model, the gauge boson represents the fluid field in a form $A_\mu \equiv \epsilon_\mu \phi$, where $\epsilon_\mu$ contains the fluid kinematics and $\phi$ is an auxiliary field representing the fluid distribution. This leads to a new relativistic equation of motion for fluid, but which further coincides to the classical Euler equation at non-relativistic limit. The lagrangian is applied to model homogeneous universe as a bulk pure fluid system. Taking the simplest case of fluid with radial velocity and uniform distribution, the free energy density is calculated and its behaviour around Hubble distance is discussed.