f(R,T) Cosmological Models in Phase Space

We investigate cosmological solutions of f(R,T) modified theories of gravity for perfect fluid in spatially FLRW metric through phase space analysis, where R is Ricci scalar and T denotes the trace of energy-momentum tensor of matter content. We explore and analyze three general theories with Lagrangians of minimal $g(R)+h(T)$, pure non--minimal g(R)h(T) and non-minimal $g(R)(1+h(T))$ couplings through dynamical systems approach. We introduce a few variables and dimensionless parameters to simplify the equations in more concise forms. The conservation of energy-momentum tensor leads to a constraint equation that, in the minimal gravity, confines functionality of h(T) to a particular form, hence, relates the dynamical variables. In this case, acceptable cosmological solutions that contain a long enough matter dominated era followed by a late-time accelerated expansion are found. To support theoretical results, we also obtain numerical solutions for a few functions of g(R), and results of the corresponding models confirm the predictions. We classify 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 late-time acceleration. We draw different diagrams of the matter densities (consistent with the present values), the related scale factors and effective equation of state. The corresponding diagrams of parameters illustrate that there is a saddle acceleration era which is a middle era before final stable acceleration de Sitter era for some models. All presented diagrams determine radiation, matter and late-time acceleration eras very well.