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

Abstract

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() [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.