Nonminimally Coupled Boltzmann Equation I: Foundations

Abstract

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.

arXiv comment9 pages

References in corpus (26)

• f(R) Theories Of Gravity
• The Confrontation between General Relativity and Experiment
• f(R) theories
• Extra force in $f(R)$ modified theories of gravity
• Action functionals for relativistic perfect fluids
• Nonminimal coupling of perfect fluids to curvature
• Dark energy and dark matter as curvature effects
• The (pseudo)issue of the conformal frame revisited
• Energy Conditions and Stability in $f(R)$ theories of gravity with non-minimal coupling to matter
• Einstein and Jordan frames reconciled: a frame-invariant approach to scalar-tensor cosmology
• Accelerated expansion from a non-minimal gravitational coupling to matter
• Generalized virial theorem in f(R) gravity
• Reheating via a generalized non-minimal coupling of curvature to matter
• Mimicking dark matter in galaxy clusters through a non-minimal gravitational coupling with matter
• Mimicking dark matter through a non-minimal gravitational coupling with matter
• On the dynamics of perfect fluids in non-minimally coupled gravity
• Gravitational waves in theories with a non-minimal curvature-matter coupling
• Modified Friedmann Equation from Nonminimally Coupled Theories of Gravity
• Early formation of supermassive black holes via dark matter self-interactions
• Baryogenesis in Nonminimally Coupled $f(R)$ Theories
• Inflation in non-minimal matter-curvature coupling theories
• Relativistic Kinetic Theory: An Introduction
• The cosmological constant problem: a user's guide
• The Layzer-Irvine equation in theories with non-minimal coupling between matter and curvature
• Viability of nonminimally coupled f (R) gravity
• The Boltzmann equation in special and general relativity

Cited by in corpus (13)

• The CosmoVerse White Paper: Addressing observational tensions in cosmology with systematics and fundamental physics
• Generalizing the coupling between geometry and matter: $f(R,L_m,T)$ gravity
• Non-minimal geometry-matter couplings in Weyl-Cartan space-times: $f(R,T,Q,T_m)$ gravity
• Jeans Instability in Non-Minimal Matter-Curvature Coupling Gravity
• Quantum kinetic theory of Jeans instability in non-minimal matter-curvature coupling gravity
• Constrained transit cosmological models in $f(R,L_m,T)$-gravity
• Pressureless stationary solutions in a Newton-Yukawa gravity model
• Modified Gravity with Nonminimal Curvature-Matter Couplings: A Framework for Gravitationally Induced Particle Creation
• Black Hole Solutions in Non-Minimally Coupled Weyl Connection Gravity
• Testing the Dark Universe through the Layzer-Irvine Equation
• Cosmological implications and causality in $f(R,L_m,T)$ gravity theory with observational constraints
• Weak Field Limit of the Nonminimally Coupled Weyl Connection Gravity
• A note on the comments of arXiv:2003.10154 [gr-qc] to our paper Nonminimally Coupled Boltzmann Equation I: Foundations (arXiv:2002.08184 [gr-qc])