Evolution of Dynamical Coupling in Scalar Tensor Theory from Noether Symmetry

TL;DR

This paper derives the gravitational coupling function in scalar-tensor theory using Noether symmetry and finds cosmological solutions showing the theory approaches Einstein gravity asymptotically.

Contribution

It introduces a method to determine the coupling function via Noether symmetry and analyzes the evolution of scalar-tensor cosmologies.

Findings

The coupling function $\omega(\phi)$ is derived from symmetry considerations.

Cosmological solutions indicate the theory approaches Einstein gravity asymptotically.

The attractor mechanism is not sufficient to reduce the theory to Einstein gravity.

Abstract

We present the gravitational coupling function $\omega(\phi)$ in the vacuum scalar-tensor theory as allowed by the Noether symmetry. We also obtain some exact cosmological solutions in the spatially homogeneous and isotropic background thereby showing that the attractor mechanism is not effective enough to reduce the theory to Einstein theory. It is observed that, asymptotically, the scalar tensor theory goes over to Einstein theory with finite value of $\omega$. This work thus supports earlier works in this direction.