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Curvature–matter couplings in modified gravity: From linear models to conformally invariant theories

F. S. N. Lobo, T. Harko

In this paper, we review modified theories of gravity with a curvature–matter coupling between an arbitrary function of the scalar curvature and the Lagrangian density of matter. This explicit nonminimal coupling induces a nonvanishing covariant derivative of the energy–momentum tensor, that implies nongeodesic motion and consequently leads to the appearance of an extra force. Here, we explore the physical and cosmological implications of the nonconservation of the energy–momentum tensor by using the formalism of irreversible thermodynamics of open systems in the presence of matter creation/annihilation. The particle creation rates, pressure, and the expression of the comoving entropy are obtained in a covariant formulation and discussed in detail. Applied together with the gravitational field equations, the thermodynamics of open systems lead to a generalization of the standard ΛCDM cosmological paradigm, in which the particle creation rates and pressures are effectively considered as components of the cosmological fluid energy–momentum tensor. Furthermore, we also briefly present the coupling of curvature to geometry in conformal quadratic Weyl gravity, by assuming a coupling term of the form LmR˜2, where Lm is the ordinary matter Lagrangian, and R˜ is the Weyl scalar. The coupling explicitly satisfies the requirement of the conformal invariance of the theory. Expressing R˜2 with the use of an auxiliary scalar field and of the Weyl scalar, the gravitational action can be linearized in the Ricci scalar, leading in the Riemann space to a conformally invariant f(R,Lm)-type theory, with the matter Lagrangian nonminimally coupled to geometry.

Curvature–matter couplings; modified gravity; irreversible thermodynamics of open systems; matter creation; conformal quadratic Weyl gravity

International Journal of Modern Physics D
Volume 31, Number 11
2022 April

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Faculdade de Ciências da Universidade de Lisboa Universidade do Porto Faculdade de Ciências e Tecnologia da Universidade de Coimbra
Fundação para a Ciência e a Tecnologia COMPETE 2020 PORTUGAL 2020 União Europeia