Exploring late-time cosmic evolution through dynamical systems in non-minimally coupled scalar-tensor models

Abstract

This dissertation explores late-time cosmic evolution through the lens of scalartensor theories using a dynamical systems approach. Although the Λ Cold Dark Matter (ΛCDM) model has been successful in accounting for the accelerated expansion of the Universe, it faces persistent theoretical challenges such as the cosmological constant problem and observational tensions like the Hubble constant (H0) discrepancy. Scalar fields central to early-universe inflation and now considered candidates for dark energy offer a promising extension to standard cosmology. We construct dynamical systems by introducing non-minimal scalar field couplings into the cosmological equations, focussing on exponential and power-law potentials. The resulting systems are analysed using critical points, stability theory, and phase portraits to reveal attractor solutions and asymptotic behaviours. Our study demonstrates that certain scalar-field models can replicate the late-time acceleration of the Universe while offering richer dynamics than the cosmological constant alone. Many of the models explored exhibit the key critical points found in ΛCDM and, in some cases, additional points that reflect a more nuanced evolution profile. These results underscore the utility of dynamical systems in probing beyond-ΛCDM scenarios and provide a pathway for future observational tests of scalar-tensor cosmologies.