The Imperfect Fluid behind Kinetic Gravity Braiding

TL;DR

This paper develops a hydrodynamical framework for non-canonical scalar fields with kinetic gravity braiding, revealing their imperfect fluid nature with unique charge and diffusion properties, and analyzing their thermodynamic equilibrium conditions.

Contribution

It introduces a hydrodynamical description for kinetic gravity braiding theories, clarifying their physical interpretation and simplifying their analysis.

Findings

Fluid carries shift charges with diffusion behavior.

Incompressible limit yields standard diffusion equation.

Fluid is imperfect but non-dissipative with zero vorticity.

Abstract

We present a standard hydrodynamical description for non-canonical scalar field theories with kinetic gravity braiding. In particular, this picture applies to the simplest galileons and k-essence. The fluid variables not only have a clear physical meaning but also drastically simplify the analysis of the system. The fluid carries charges corresponding to shifts in field space. This shift-charge current contains a spatial part responsible for diffusion of the charges. Moreover, in the incompressible limit, the equation of motion becomes the standard diffusion equation. The fluid is indeed imperfect because the energy flows neither along the field gradient nor along the shift current. The fluid has zero vorticity and is not dissipative: there is no entropy production, the energy-momentum is exactly conserved, the temperature vanishes and there is no shear viscosity. Still, in an expansion around a perfect fluid one can identify terms which correct the pressure in the manner of bulk viscosity. We close by formulating the non-trivial conditions for the thermodynamic equilibrium of this imperfect fluid.