General Scalar-Tensor cosmology: Analytical solutions via Noether symmetry

TL;DR

This paper employs Noether symmetry to derive exact solutions in a broad class of Scalar-Tensor cosmological models, revealing conditions for cosmic acceleration, stability, and transitions between different universe phases.

Contribution

It introduces a symmetry-based method to determine functional forms in Scalar-Tensor theories, enabling exact solutions and stability analysis without phenomenological assumptions.

Findings

Identifies models allowing transition from matter-dominated to dark energy-dominated phases.

Derives conditions for the stability of de Sitter solutions as attractors.

Classifies models into phantom or quintessence dark energy regimes.

Abstract

We analyze the cosmology of a general Scalar-Tensor theory which encompasses generalized Brans-Dicke theory, Gauss-Bonnet gravity, non-minimal derivative gravity, generalized Galileon gravity and also the general k-essence type models. Instead of taking into account phenomenological considerations we adopt a Noether symmetry approach, as a physical criterion, to single out the form of undetermined functions in the action. These specified functions symmetrize equations of motion in the simplest possible form which result in exact solutions. Demanding de Sitter, power-law and bouncing universe solutions in the absence and presence of matter density leads to exploring new as well as well-investigated models. We show that there are models for which dynamics of the system allow transition from a decelerating phase (matter dominated era) to an accelerating phase (dark energy epoch) and could also lead to general Brans-Dicke with string correction without a self-interaction potential. Furthermore, we classify the models based on phantom or quintessence dark energy point of view. Finally, we obtain the condition for stability of a de Sitter solution for which the solution is an attractor of the system.