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

68 pages; invited review paper to appear in IJMPD (abstract in metadata shortened)

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Cited by in corpus (48)

• Generalizing the coupling between geometry and matter: $f(R,L_m,T)$ gravity
• Geodesic deviation, Raychaudhuri equation, Newtonian limit, and tidal forces in Weyl-type $f(Q,T)$ gravity
• Cosmology in scalar-tensor $f(R,T)$ gravity
• Quasinormal modes of Schwarzschild black holes in projective invariant Chern-Simons modified gravity
• Dark matter as a Weyl geometric effect
• Cosmological evolution and dark energy in osculating Barthel-Randers geometry
• Observational Constraints and Cosmological Implications of Scalar-Tensor $f(R,T)$ Gravity
• Palatini formulation of the conformally invariant $f\left(R,L_m\right)$ gravity theory
• Dynamic wormhole geometries in hybrid metric-Palatini gravity
• Non-minimal geometry-matter couplings in Weyl-Cartan space-times: $f(R,T,Q,T_m)$ gravity
• Landau damping for gravitational waves in parity-violating theories
• Dark energy and accelerating cosmological evolution from osculating Barthel-Kropina geometry
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• Torsional birefringence in metric-affine Chern-Simons gravity: gravitational waves in late-time cosmology
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• Curvature-matter couplings in modified gravity: from linear models to conformally invariant theories
• Weak-field regime of the generalized hybrid metric-Palatini gravity
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