Cosmological Dynamics of a Non-Canonical Generalised Brans-Dicke Theory

TL;DR

This paper explores a generalized Brans-Dicke cosmological model with a non-canonical scalar field, analyzing its equilibrium states and stability, and finding solutions that mimic the standard Lambda-CDM model.

Contribution

It introduces a dynamical systems approach to a non-minimally coupled, non-canonical scalar field in Brans-Dicke theory, revealing viable cosmological solutions.

Findings

Viable solutions reproduce Lambda-CDM characteristics at background level.

Dynamical behavior differs from other scalar-tensor models due to non-minimal coupling.

Equilibrium states and stability analyzed for constant, power-law, and exponential potentials.

Abstract

The LCDM model has been presented with a number of cosmic tensions in the face of precision cosmological data, suggesting the presence of a dynamical dark energy component. In this context, we investigate the cosmology arising from a generalisation of Brans-Dicke theory, with a non-minimally coupled scalar field characterising deviations from standard general relativity, and having a non-canonical kinetic term. By reformulating the field equations into an autonomous set of dynamical equations, we use the methods of dynamical systems to investigate the equilibrium states of the system and their stability for a set of widely-used potentials, namely the constant, power-law, and exponential potentials, with the flow visualized using bounded phase portraits. Furthermore, we investigate the physical meaning of the critical points, and we find viable solutions that can reproduce the characteristics of the $\Lambda$CDM model at background level for each of the three potentials. Furthermore, in each case, we observe that the dynamical behaviour differs noticeably from that observed in other scalar-tensor models due to the non-minimal coupling and non-canonical field, despite using similarly defined dynamical variables.