https://doi.org/10.1140/epjc/s10052-018-6165-6
Regular Article - Theoretical Physics
Dynamical analysis and cosmological viability of varying G and 
cosmology
1
Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile, Valdivia, Chile
2
Department of Mathematics and Natural Sciences, Core Curriculum Program, Prince Mohammad Bin Fahd University, Al Khobar, 31952, Kingdom of Saudi Arabia
3
Institute of Systems Science, Durban University of Technology, PO Box 1334, Durban, 4000, Republic of South Africa
* e-mail: anpaliat@phys.uoa.gr
Received:
13
June
2018
Accepted:
17
August
2018
Published online:
27
August
2018
The cosmological viability of varying 
and 
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 plays the role of a minimally coupled field, different from that of scalar–tensor theories, while 
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 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.
© The Author(s), 2018
