Modified Gravity with Nonminimal Curvature-Matter Couplings: A Framework for Gravitationally Induced Particle Creation

TL;DR

The paper develops a framework in which a nonminimal curvature--matter coupling induces energy exchange between geometry and matter, enabling gravitationally induced particle creation. It advances this idea through (i) a scalar--tensor reformulation and derivation of the particle creation rate, creation pressure, and entropy production; (ii) a thermodynamic open-system treatment showing how entropy grows and can saturate in a de Sitter phase, providing thermodynamic constraints on particle production; and (iii) complementary Boltzmann and quantum-field-theoretic perspectives (Boltzmann equation with an extra gravitational source term and Klein--Gordon/Bogoliubov analysis) to connect microphysics with the macroscopic cosmological evolution. The key result is that the coupling can drive late-time acceleration via a negative creation pressure, offering an alternative to a cosmological constant while remaining compatible with a generalized second law of thermodynamics. The work also outlines observational pathways and the need to reconcile thermodynamic, kinetic, and quantum descriptions to robustly test these ideas against data from cosmic expansion, structure formation, and high-energy astrophysical phenomena.

Abstract

Modified gravity theories with a nonminimal coupling between curvature and matter offer a compelling alternative to dark energy and dark matter by introducing an explicit interaction between matter and curvature invariants. Two of the main consequences of such an interaction are the emergence of an additional force and the non-conservation of the energy--momentum tensor, which can be interpreted as an energy exchange between matter and geometry. By adopting this interpretation, one can then take advantage of many different approaches in order to investigate the phenomenon of gravitationally induced particle creation. One of these approaches relies on the so-called irreversible thermodynamics of open systems formalism. By considering the scalar--tensor formulation of one of these theories, we derive the corresponding particle creation rate, creation pressure, and entropy production, demonstrating that irreversible particle creation can drive a late-time de Sitter acceleration through a negative creation pressure, providing a natural alternative to the cosmological constant. Furthermore, we demonstrate that the generalized second law of thermodynamics holds: the total entropy, from both the apparent horizon and enclosed matter, increases monotonically and saturates in the de Sitter phase, imposing constraints on the allowed particle production dynamics. Furthermore, we present brief reviews of other theoretical descriptions of matter creation processes. Specifically, we consider approaches based on the Boltzmann equation and quantum-based aspects and discuss the generalization of the Klein--Gordon equation, as well as the problem of its quantization in time-varying gravitational fields.