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

Abstract

A. Going beyond Einstein's General Relativity B. Motivations for hybrid metric-Palatini gravity C. Couplings between geometry and matter D. Outline of article II Hybrid metric-Palatini gravity I. General formalism A. Action and field equations B. The Newtonian limit C. The Post-Newtonian limit D. f (X) representation II. Cosmological applications A. The generalized Friedmann equations, and the deceleration parameter B. Alternative form of the generalized Friedmann equations C. Specific FLRW cosmological models 1. de Sitter type solutions 2. Marginally accelerating solutions 3. Accelerating solutions of the field equations D. Einstein's static Universe E. Gödel type solutions F. Dynamical system analysis G. Cosmological perturbations 1. Perturbations in the matter dominated cosmology 2. Perturbation propagations in the vacuum H. Constraining the cosmological evolution III. Galactic and extragalactic dynamics A. Galactic rotation curves B. Clusters of galaxies IV. Stellar type objects, black holes and wormholes 1. Stars and black holes 2. Wormhole solutions V. Thermodynamics, branes, screening, gravitational waves, strings, and further work VI. Beyond the standard linear hybrid metric-Palatini theory III Curvature-matter couplings VII. Linear nonminimal curvature-matter couplings actions and gravitational field equations A. Scalar field-geometry couplings B. Theories with standard curvature-geometry coupling C. Scalar-tensor representation D. Generalized f (R, L m) curvature-matter couplings VIII. f (R, T ) gravity A. Action and gravitational field equations B. The equations of motion of test particles C. Specific cosmological solution IX. f (R, T, R µν T µν ) gravity A. Action and field equations of the f (R, T, R µν T µν ) gravity B. Equation of motion of massive test particles C. The Dolgov-Kawasaki instability in f (R, T, R µν T µν ) gravity D. Specific cosmological application X. Irreversible matter creation processes through a nonminimal curvature-matter coupling A. Thermodynamic open systems B. Thermodynamic interpretation in curvature-matter couplings XI. Quantum cosmology of f (R, T ) curvature-matter couplings A. The Wheeler-de Witt equation in f (R, T ) gravity 1. The effective cosmological Lagrangian and the potential 2. The cosmological Hamiltonian 3. The Wheeler-de Witt equation B. Specific cosmological application: f (R, T ) = F 0 (R) + θRT 1. The Hamiltonian and the Wheeler-de Witt equation 2. The Hamiltonian form of the field equations C. The problem of time D. The physical interpretation of the effective Hamiltonian IV Conclusions

Static spherically symmetric three-form stars

“…The equilibrium equations for a spherically symmetric configuration (mass continuity and Tolman-Oppenheimer-Volkoff) were derived, and their solutions were obtained numerically for different equations of state of neutron and quark matter. The internal structure and the physical properties of specific classes of neutron, quark and Bose-Einstein Condensate stars in the hybrid metric-Palatini gravity theory [17][18][19][20][21], which is a combination of the metric and Palatini f (R) formalisms, was considered in [22]. As a general result it was found that for all the considered equations of state, hybrid metric-Palatini gravity stars are more massive than their general relativistic counterparts.…”

Spherically symmetric space-times in generalized hybrid metric-Palatini gravity

“…The same authors [23] found the conditions under which vacuum solutions of GR with R µν = 0, such as the Schwarzschild and Kerr solutions, are also solutions of GHT, and investigated the stability conditions for the Kerr solution in this theory. A review encompassing both the original HMPG and its generalized version can be found in [25].…”

Geodesic deviation, Raychaudhuri equation, Newtonian limit, and tidal forces in Weyl-type $f(Q,T)$ gravity

“…To fix the theoretical imperfections of standard General Relativity, two important physical components, the dark matter and the dark energy, are introduced in the cosmological scenario in a rather ad hoc way, with the major goal of explaining and adapting the standard gravity model to describe realistic physical situations, related to the motion of massive particles around galaxies, and to solve the problem of the accelerated expansionary state of Universe. We may call the approach based on the introduction of two new physical components in the overall matter/energy balance of the Universe as the dark components model [14].…”

“…However, a second approach to gravitational phenomena is also possible, and it is called the dark gravity approach [14]. In this approach one assumes that both dark matter and dark energy can be explained by changing the nature of the gravitational force.…”

“…In these classes of theories the covariant derivative of the energy-momentum tensor is always non-zero, which implies a non-geodesic motion of test particles, and the appearance of an extra force. For a recent review of some modified gravity theories in Riemann geometry one can refer to [14] and [49], respectively.…”