Beyond Einstein's General Relativity: Hybrid metric-Palatini gravity and curvature-matter couplings

TL;DR

This paper reviews and analyzes two extensions of $f(R)$ gravity—hybrid metric-Palatini gravity and curvature-matter couplings—highlighting their theoretical features, advantages, and applications in cosmology, astrophysics, and quantum cosmology.

Contribution

It provides a comprehensive theoretical and phenomenological analysis of hybrid metric-Palatini gravity and curvature-matter couplings, emphasizing their potential to address cosmological and astrophysical phenomena.

Findings

Hybrid metric-Palatini gravity successfully explains observed cosmological phenomena.

Curvature-matter couplings induce non-conservation of energy-momentum, offering new insights into matter dynamics.

Both theories have broad applications in astrophysics and quantum cosmology.

Abstract

Einstein's General Relativity (GR) is possibly one of the greatest intellectual achievements ever conceived by the human mind. In fact, over the last century, GR has proven to be an extremely successful theory, with a well established experimental footing. However, the discovery of the late-time cosmic acceleration, which represents a new imbalance in the governing gravitational field equations, has forced theorists and experimentalists to question whether GR is the correct relativistic theory of gravitation, and has spurred much research in modified gravity, where extensions of the Hilbert-Einstein action describe the gravitational field. In this review, we perform a detailed theoretical and phenomenological analysis of two largely explored extensions of $f(R)$ gravity, namely: (i) the hybrid metric-Palatini theory; (ii) and modified gravity with curvature-matter couplings. Relative to the former, it has been established that both metric and Palatini versions of $f(R)$ gravity possess interesting features but also manifest severe drawbacks. A hybrid combination, containing elements from both of these formalisms, turns out to be very successful in accounting for the observed phenomenology and avoids some drawbacks of the original approaches. Relative to the curvature-matter coupling theories, these offer interesting extensions of $f(R)$ gravity, where the explicit nonminimal couplings between an arbitrary function of the scalar curvature $R$ and the Lagrangian density of matter, induces a non-vanishing covariant derivative of the energy-momentum tensor. We extensively explore both theories in a plethora of applications, namely, the weak-field limit, galactic and extragalactic dynamics, cosmology, stellar-type compact objects, irreversible matter creation processes and the quantum cosmology of a specific curvature-matter coupling theory.