Abstract
We consider the Palatini formulation of f(R, T) gravity theory, in which a non-minimal coupling between the Ricci scalar and the trace of the energy-momentum tensor is introduced, by considering the metric and the affine connection as independent field variables. The field equations and the equations of motion for massive test particles are derived, and we show that the independent connection can be expressed as the Levi-Civita connection of an auxiliary, energy-momentum trace dependent metric, related to the physical metric by a conformal transformation. Similar to the metric case, the field equations impose the non-conservation of the energy-momentum tensor. We obtain the explicit form of the equations of motion for massive test particles in the case of a perfect fluid, and the expression of the extra force, which is identical to the one obtained in the metric case. The thermodynamic interpretation of the theory is also briefly discussed. We investigate in detail the cosmological implications of the theory, and we obtain the generalized Friedmann equations of the f(R, T) gravity in the Palatini formulation. Cosmological models with Lagrangians of the type f=R-alpha ^2/R+g(T) and f=R+alpha ^2R^2+g(T) are investigated. These models lead to evolution equations whose solutions describe accelerating Universes at late times.
Highlights
The observational discovery of the recent acceleration of the Universe [1,2,3,4,5] has raised the fundamental theoretical problem if general relativity, in its standard formulation, can fully account for all the observed phenomena at both galactic and extra-galactic scales
The simplest theoretical explanation for the observed cosmological dynamics consists in slightly modifying the Einstein field equations, by adding to it a cosmological constant [6]
The CDM model can fit the observational data at a high level of precision, it is a very simple theoretical approach, it is easy to use in practice, but up to now no fundamental theory can explain it
Summary
The observational discovery of the recent acceleration of the Universe [1,2,3,4,5] has raised the fundamental theoretical problem if general relativity, in its standard formulation, can fully account for all the observed phenomena at both galactic and extra-galactic scales. The first possibility for such a coupling is to replace the gravitational action by an arbitrary function of the Ricci scalar and the matter Lagrangian Lm, obtaining the so-called f (R, Lm) class of modified gravity theories [26] This class of theories has the potential of explaining the recent acceleration of the Universe without the need of the cosmological constant, and can give some new insights into the dark matter problem, and on the nature of the gravitational motion. After a brief review of the metric formulation of f (R, T ) gravity theory, we derive the field equations of the theory by using the Palatini formalism
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