Nonminimally Coupled Boltzmann Equation I: Foundations

Understand

We derive the Boltzmann equation in the context of a gravity theory with non-minimal coupling between matter and curvature.

• We show that as the energy-momentum tensor is not conserved in these theories, it follows a condition on the normalisation of an homogeneous distribution function.
• The Boltzmann H-theorem is preserved such that the entropy vector flux is still a non-decreasing function in these theories.
• The case of an homogeneous and isotropic Universe is analysed.