Hamiltonian study of the Generalized scalar-tensor theory with potential in a Bianchi type I model

TL;DR

This paper investigates the dynamics of a generalized scalar-tensor theory with potential in a Bianchi type I universe, analyzing conditions for expansion, isotropy, and late-time behavior in different frames using the ADM formalism.

Contribution

It provides a detailed analysis of the asymptotic behavior of the universe in this theory, focusing on power-law and exponential solutions in the Einstein frame.

Findings

Conditions for late-time expansion and isotropy are identified.

Power-law and exponential asymptotic behaviors are characterized.

Positive potential leads to accelerated expansion in certain cases.

Abstract

We study the generalized scalar tensor theory with a potential in the Bianchi type I model by using the ADM formalism. We examine the conditions for the Universe to be in expansion, isotropic and with a positive potential at late time in the Brans-Dicke and Einstein frames. In particular, we analyse the two important cases where metric functions tend, in an asymptotic way, toward power or exponential laws in the Einstein frame.