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arXiv · 1812.10983

Kinetic equation for Lifshitz scalar

Shinji Mukohyama·Yota Watanabe
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Abstract

Employing the method of Wigner functions on curved spaces, we study classical kinetic (Boltzmann-like) equations of distribution functions for a real scalar field with the Lifshitz scaling. In particular, we derive the kinetic equation for $z=2$ on general curved spaces and for $z=3$ on spatially flat spaces under the projectability condition $N=N(t)$, where $z$ is the dynamical critical exponent and $N$ is the lapse function. We then conjecture a form of the kinetic equation for a real scalar field with a general dispersion relation in general curved geometries satisfying the projectability condition, in which all the information about the non-trivial dispersion relation is included in the group velocity and which correctly reproduces the equations for the $z=2$ and $z=3$ cases as well as the relativistic case. The method and equations developed in the present paper are expected to be useful for developments of cosmology in the context of Ho\v{r}ava-Lifshitz gravity.

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Shinji Mukohyama, Yota Watanabe. 2018-12-28. Kinetic equation for Lifshitz scalar. https://doi.org/10.1103/physrevd.99.065003

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