Relativistic hydrodynamics with sources for cosmological K-fluids

TL;DR

This paper develops a framework for relativistic hydrodynamics with non-conserved particle number using effective fluid Lagrangians, exploring implications for cosmological K-fluids and entropy dynamics.

Contribution

It introduces a novel Lagrangian formulation for hydrodynamics with sources, breaking shift symmetry and linking particle non-conservation to entropy change in cosmological models.

Findings

Derived hydrodynamic equations with source terms using a modified Schutz's variational principle.

Demonstrated applications to fluids like tachyon condensate and k-essence in cosmology.

Showed how non-conservation of particles affects entropy and fluid dynamics in the universe.

Abstract

We consider hydrodynamics with non conserved number of particles and show that it can be modeled with effective fluid Lagrangians which explicitly depend on the velocity potentials. For such theories, the {}``shift symetry'' $\phi\to\phi+$const. leading to the conserved number of fluid particles in conventional hydrodynamics is globaly broken and, as a result, the non conservation of particle number appears as a source term in the continuity equation. The particle number non-conservation is balanced by the entropy change, with both the entropy and the source term expresed in terms of the fluid velocity potential. Equations of hydrodynamics are derived using a modified version of Schutz's variational principle method. Examples of fluids described by such Lagrangians (tachyon condensate, k-essence) in spatially flat isotropic universe are briefly discussed.