https://doi.org/10.1140/epjc/s10052-018-5923-9
Regular Article - Theoretical Physics
Palatini formulation of f(R, T) gravity theory, and its cosmological implications
1
School of Physics, Sun Yat-Sen University, Guangzhou, 510275, People’s Republic of China
2
Department of Physics, Babes-Bolyai University, Kogalniceanu Street, 400084, Cluj-Napoca, Romania
3
Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, UK
4
State Key Laboratory of Optoelectronic Material and Technology, Guangdong Province Key Laboratory of Display Material and Technology, Guangzhou, People’s Republic of China
* e-mail: t.harko@ucl.ac.uk
Received:
9
April
2018
Accepted:
18
May
2018
Published online:
29
May
2018
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 
and 
are investigated. These models lead to evolution equations whose solutions describe accelerating Universes at late times.
© The Author(s), 2018
