Relativistic Hydrodynamics With Sources for Cosmological K-Fluids

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 symmetry" ϕ → ϕ + const leading to the conserved number of fluid particles in conventional hydrodynamics is globally broken and, as a result, the non-conservation of particle number appears as a source term in the continuity equation. The non-conservation of particle number is balanced by the entropy change, with both the entropy and the source term expressed 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.