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 [21], the model proposed by J. Lu, L. Xu, H.Tan and S. Gao [23], the model proposed by A. Bonanno, G. Esposito, C. Rubano, and P. Scudellaro [24] and the Brans-Dicke model with Λ(φ) [25]. In order to carry out such study, we will work under the self-similar hypothesis and we assume the same metric, a flat FRW, and the same matter source, a perfect fluid. We put special emphasis in mathematical and formal aspects which allow 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.