Beyond Einstein’s General Relativity: Hybrid metricPalatini gravity and curvaturematter couplings
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, at least for weak gravitational fields. Its predictions range from the existence of black holes and gravitational radiation (now confirmed) to the cosmological models. Indeed, a central theme in modern Cosmology is the perplexing fact that the Universe is undergoing an accelerating expansion, which represents a new imbalance in the governing gravitational equations. The cause of the latetime cosmic acceleration remains an open and tantalizing question, and has forced theorists and experimentalists to question whether GR is the correct relativistic theory of gravitation. This has spurred much research in modified theories of gravity, where extensions of the HilbertEinstein action describe the gravitational field, in particular, f(R) gravity, where R is the curvature scalar. In this review, we perform a detailed theoretical and phenomenological analysis of specific modified theories of gravity and investigate their astrophysical and cosmological applications. We present essentially two largely explored extensions of f(R) gravity, namely: (i) the hybrid metricPalatini theory; (ii) and modified gravity with curvaturematter 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 curvaturematter 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 nonvanishing covariant derivative of the energymomentum tensor, which implies nongeodesic motion and consequently leads to the appearance of an extra force. We extensively explore both theories in a plethora of applications, namely, the weakfield limit, galactic and extragalactic dynamics, cosmology, stellartype compact objects, irreversible matter creation processes and the quantum cosmology of a specific curvaturematter coupling theory.
 Publication:

International Journal of Modern Physics D
 Pub Date:
 2020
 DOI:
 10.1142/S0218271820300086
 arXiv:
 arXiv:2007.15345
 Bibcode:
 2020IJMPD..2930008H
 Keywords:

 Modified gravity;
 curvaturematter couplings;
 hybrid metricPalatini gravity;
 General Relativity and Quantum Cosmology;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 High Energy Physics  Theory
 EPrint:
 68 pages