  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.
