Palatini formulation of f(R, T) gravity theory, and its cosmological implications

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 nonconservation 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 − α 2 /R + g(T ) and f = R + α 2 R 2 + g(T ) are investigated. These models lead to evolution equations whose solutions describe accelerating Universes at late times.

Stellar structure models in modified theories of gravity: Lessons and challenges

“…On the other hand, analogously to the case of f (R) gravity which can be considered either in metric or metricaffine formalism, the f (R, T ) gravity originally proposed in [416] can be also extended to the metric-affine formulation [417,418]. The action is thus…”

Exact solution of the fiels equation of the generalized cosmological F(R,T) model

“…here =-Hubble parameter, and by A and B we mean the following expressions: This equation cannot be solved analytically. However, we can take F in the form of a generalized Starobinsky model, for which = + 2 + + 2 , found by us in this form earlier [16].…”

“…So, already taking into account the presence of the functions u, v -describing the connection between the curvature scalar and the torsion scalar, which should help to give in the limit, respectively, the general theory of relativity or teleparallelgravity [12][13][14][15] is already so difficult to compute that researchers often try to describe the solution without taking into account these functions [16]. As a first approximation, it is possible to take into account these components as functions of the scale factor and its first time derivative.…”

Identification of non‐random sequence properties in groups of signature peptides obtained in random sequence peptide microarray experiments

“…Since the peptides are fairly long 17-mers, such shifts are likely to occur and putting patterns in the same register requires alignment-based approaches. 3,30 Another possible reason for the failure is that multi-group classification itself represents a very non-trivial problem, 31,32 especially when the number of groups is as large as 14 in trial 2. The issue with the presence of multiple groups is further aggravated by the fact that the number of peptides within each group is small (24 or 20) and may not provide a sufficiently large number of training examples necessary to obtain a wellperforming prediction model and avoid over-fitting.…”