f(R,T)cosmological models in phase space

Abstract

We investigate the cosmological solutions of f (R, T ) modified theories of gravity for a perfect fluid in a spatially FLRW metric through the phase space analysis, where R is the Ricci scalar and T denotes the trace of the energy-momentum tensor of the matter content. We explore and analyze the three general theories with the Lagrangians of minimal g(R) + h(T ), pure non-minimal g(R)h(T ) and non-minimal g(R) (1 + h(T )) couplings through the dynamical systems approach. We introduce a few variables and dimensionless parameters to simplify the equations in more concise forms. The conservation of the energy-momentum tensor leads to a constraint equation that, in the minimal gravity, confines the functionality of h(T ) to a particular form, hence, relates the dynamical variables. In this case, the acceptable cosmological solutions that contain a long enough matter dominated era followed by a late-time accelerated expansion are found. To support the theoretical results, we also obtain the numerical solutions for a few functions of g(R), and the results of the corresponding models confirm the predictions. We classify the solutions into six classes which demonstrate more acceptable solutions and there is more freedom to have the matter dominated era than in the f (R) gravity. In particular, there is a new fixed point which can represent the late-time acceleration. We draw different diagrams of the matter densities (consistent with the present values), the related scale factors and the effective equation of state. The corresponding diagrams of the parameters illustrate that there is a saddle acceleration era which is a middle era before the final stable acceleration de Sitter era for some models. All presented diagrams determine radiation, matter and late-time acceleration eras very well. The pure non-minimal theory suffers from the absence of a standard matter era, though we illustrate that the non-minimal theory can have acceptable cosmological solutions.2 development of a general phenomenological framework, i.e. the PPN-formalism, determine that it is the best known metric theory of gravity [46].Among the extended theories of gravity, there are at least two main motivations 3 for employing the higher-order gravities, i.e., those in which the Einstein-Hilbert action is modified by higher-order curvature invariants with respect to the Ricci scalar. The first motivation has a theoretical background and is related to the non-renormalizability of GR [49,50] and to the fact that GR cannot be quantized conventionally. Regarding this issue, some authors have shown that the inclusion of higher-order terms can solve this problem [51,52]. The other motivation is related to the recently achieved data in astrophysics and cosmology. Two contemporary evidences, which are referred to as dark matter and dark energy, have challenged our knowledge about the universe and have accounted for the first signals of GR breakdown. It is also worth mentioning that the concordance or ΛCDM model [53], the simplest model which adequately fits the...

f(T,𝒯) gravity and cosmology

“…However, since there is no theoretical reason against couplings between the gravitational sector and the standard matter one, one can consider modified theories where the matter Lagrangian is coupled to functions of the Ricci scalar [74][75][76][77], and extend the theory to arbitrary functions (R, L m ) [78][79][80][81][82]. Alternatively, one can consider models where the Ricci scalar is coupled with the trace of the energy momentum tensor T and extend to arbitrary functions, such as in f (R, T ) theory [83][84][85][86][87], or even consider terms of the form R µν T µν [88,89]. We stress that the above modifications, in which one handles the gravitational and matter sectors on equal footing, do not present any problem at the theoretical level, and one would only obtain observational constraints due to non-geodesic motion.…”

Static spherically symmetric wormholes in f(R, T) gravity

“…Till the present time, different cosmological aspects have been addressed in f (R, T ) gravity including reconstruction schemes, anisotropic solutions, energy conditions, thermodynamics, viscous solutions, phase space perturbations and stability, etc. [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32].…”

A dynamical system analysis of f(R,T) gravity

“…Also energy conditions [16], cosmological solutions [17], scalar perturbations [13] are investigated. In [18] solar system consequences of the model is argued. Further generalization of this theory to f (R, T, R µν T µν ) is proposed in [19].…”

“…The method of autonomous dynamical systems is a use- * b.mirza@cc.iut.ac.ir † f.oboudiat@ph.iut.ac.ir ful tool for investigating the modified theories of gravity such as f (R) and some other theories [20][21][22][23]. In [24] the method is investigated for f (R, T ) theory assuming conservation of energy. In this paper we study the method by no limiting condition on energy.…”