Curvature-matter couplings in modified gravity: from linear models to conformally invariant theories

Abstract

In this proceeding, 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 non-vanishing covariant derivative of the energy-momentum tensor, that implies non-geodesic 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 $\Lambda$CDM 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 $L_m{\tilde{R}}^2$, where $L_m$ is the ordinary matter Lagrangian, and $\tilde{R}$ is the Weyl scalar. The coupling explicitly satisfies the requirement of the conformal invariance of the theory. Expressing ${\tilde{R}}^2$ 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 $f\left(R,L_m\right)$ type theory, with the matter Lagrangian nonminimally coupled to geometry.

20 pages, no figures; based on a plenary talk in the 4th PU International Conference on Gravitation and Cosmology, 22-25 Nov., 2021; accepted for published in IJMPD (proceedings)

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Cited by in corpus (11)

• Palatini formulation of the conformally invariant $f\left(R,L_m\right)$ gravity theory
• Cosmological tests of the osculating Barthel-Kropina dark energy model
• Constraining viscous dark energy equation of state in $f(R,L_m)$ gravity
• Exploring wormhole solutions in curvature-matter coupling gravity supported by noncommutative geometry and conformal symmetry
• Compact stellar structures in Weyl geometric gravity
• Dynamical reconstruction of the $\Lambda$CDM model in scalar-tensor $f(R,T)$ gravity
• Cosmological implications of the Weyl geometric gravity theory
• Dynamical reconstruction of the $\Lambda$CDM model in the scalar-tensor representation of $f\left(Q,T\right)$ gravity
• Irreversible Geometrothermodynamics of Open Systems in Modified Gravity
• Dissipative quintessence, and its cosmological implications
• Observational tests of the conformal osculating Barthel-Kropina cosmological model