COSMOLOGICAL DYNAMICS OF MODIFIED GRAVITY WITH A NONMINIMAL CURVATURE-MATTER COUPLING

摘要

We perform a phase space analysis of a nonminimally coupled modified gravity theory with the Lagrangian density of the form 1/2 f_1(R) + [1 + λf_2(R)]L_m, where f_1(R) and f_2(R) are arbitrary functions of the curvature scalar R and L_m is the matter Lagrangian density. We apply the dynamical system approach to this scenario in two particular models. In the first model we assume f_1(R) = 2R with a general form for f_2(R) and set favorable values for effective equation of state parameter which is related to the several epochs of the cosmic evolution and study the critical points and their stability in each cosmic eras. In the second case, we allow the f_1 (R) to be an arbitrary function of R and set f_2(R) = 2R. We find the late-time attractor solution for the model and show that this model has a late-time accelerating epoch and an acceptable matter era.