Gauge invariant fluid lagrangian and its application to cosmology

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.