Self-similar cosmological solutions in f(R,T) gravity theory

We study the [Formula: see text] cosmological models under the self-similarity hypothesis. We determine the exact form that each physical and geometrical quantity may take in order that the field equations (FE) admit exact self-similar (SS) solutions through the matter collineation approach. We study two models: the case[Formula: see text] and the case [Formula: see text]. In each case, we state general theorems which determine completely the form of the unknown functions [Formula: see text] such that the FE admit SS solutions. We also state some corollaries as limiting cases. These results are quite general and valid for any homogeneous SS metric[Formula: see text] In this way, we are able to generate new cosmological scenarios. As examples, we study two cases by finding exact solutions to these particular models.

A comparative study of some cosmological models with time varying G and Λ: A symmetry approach

We study how the constants G and Λ may vary in four different theoretical models: general relativity with time-varying constants (Y.-K. Lau. Aust. J. Phys. 38, 547 (1985). doi: 10.1071/PH850547 ), the model proposed by Lu et al. (Phys Rev D, 89, 063526 (2014). doi: 10.1103/PhysRevD.89.063526 ), the model proposed by Bonanno et al. (Class. Quant. Grav. 24, 1443 (2007). doi: 10.1088/0264-9381/24/6/005 ), and the Brans–Dicke model with Λ([Formula: see text]) [ 25 ]. To carry out this study, we work under the self-similar hypothesis and we assume the same metric, a flat Friedmann–Robertson–Walker metric, and the same matter source, a perfect fluid. We put special emphasis on mathematical and formal aspects, which allows us to calculate exact power-law solutions through symmetry methods, matter collineation, and Noether symmetries. This enables us to compare the solutions of each model and in the same way to contrast the results with some observational data.

Exact solutions for a scalar-tensor theory through symmetries

In this paper, we study how to determine the unknown functions for the scalar tensor model [Formula: see text] where the Ricci scalar is allowed to appear in a nonlinear way. The methods followed to determine these functions are: the matter collineation approach, the Lie group method and the Lagrangian collineation approach. We find several exact analytical solutions for a cosmological model with a FRW metric. We determine that some of the results are also valid for some anisotropic metric (e.g. the self-similar ones).