Dynamical analysis and cosmological viability of varying $G$ and $\Lambda$ cosmology

Abstract

The cosmological viability of varying $G\left(t\right)$ and $\Lambda \left(t\right)$ cosmology is discussed by determining the cosmological eras provided by the theory. Such a study is performed with the determination of the critical points while stability analysis is performed. The application of Renormalization group in the ADM formalism of General Relativity provides a modified second-order theory of gravity where varying $G\left(t\right)$ plays the role of a minimally coupled field, different from that of Scalar-tensor theories, while $\Lambda \left(t\right)=\Lambda \left(G\left(t\right)\right)$ is a potential term. We find that the theory provides two de Sitter phases and a tracking solution. In the presence of matter source, two new critical points are introduced, where the matter source contributes to the universe. One of those points describes the $\Lambda$CDM cosmology and in order for the solution at the point to be cosmologically viable, it has to be unstable. Moreover, the second point, where matter exists, describes a universe where the dark energy parameter for the equation of state has a different value from that of the cosmological constant.

13 pages, 4 figures, discussion improved, to appear in EPJC

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• Dynamics of Einstein-Aether Scalar field Cosmology