Abstract
We propose general f(R,T,RμνTμν) theory as generalization of covariant Hořava-like gravity with dynamical Lorentz symmetry breaking. FRLW cosmological dynamics for several versions of such theory is considered. The reconstruction of the above action is explicitly done, including the numerical reconstruction for the occurrence of ΛCDM universe. De Sitter universe solutions in the presence of non-constant fluid are also presented. The problem of matter instability in f(R,T,RμνTμν) gravity is discussed.
Highlights
Much attention has been paid on modified gravities, and on their possible role in the accelerated expansion of the universe, a fact widely accepted by a major part of the scientific community, and strongly supported by the observations
The reconstruction of f (R) theories that are capable of reproducing the dark energy epoch, and even the inflationary phase, is generally straightforward in comparison with other modifications of gravity. f (R) gravity is able of reproducing ΛCDM epoch, or mimicking a cosmological constant at the current era, and even unifying the entire cosmological history [4]
As well viable f (R) gravity may pass the matter instability [6], a large perturbation that may occur in the study of celestial body solution
Summary
Much attention has been paid on modified gravities, and on their possible role in the accelerated expansion of the universe, a fact widely accepted by a major part of the scientific community, and strongly supported by the observations. P = Rμν T μν has been defined for convenience and in order to simplify the expressions that are coming below, whereas the subscript means variation with respect to P , R and T Those terms corresponding to the variations of the metric determinant, the Ricci scalar and the trace of the energy-momentum tensor have been already found in the literature In the case of f (R, T, RμνT μν) gravity, where terms proportional to Rμν T μν appear in the action, an explicit form of the gravitational Lagrangian that satisfies the continuity equation can not be obtained in general, since the equation involves very complex expressions that does not allow to get an explicit form of the action f (R, T, RμνT μν), as pointed out in Ref. By exploring some particular cosmological solutions, the dynamics of the matter sector may lead to similar behaviors as in GR
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