Power-law solutions and accelerated expansion in scalar-tensor theories

TL;DR

This paper derives exact power-law solutions in scalar-tensor theories, clarifies conditions for accelerated cosmic expansion, and distinguishes these solutions from f(R) theories, linking them to dark energy with a time-dependent equation of state.

Contribution

It provides new exact solutions for scalar-tensor theories, analyzes their conditions for acceleration, and compares them with f(R) theories, enhancing understanding of dark energy models.

Findings

Power-law solutions can explain accelerated expansion in scalar-tensor theories.

Signs of Hubble rate and deceleration parameter differ between frames.

Power-law solutions are not possible in f(R) theories.

Abstract

We find exact power-law solutions for scalar-tensor theories and clarify the conditions under which they can account for an accelerated expansion of the Universe. These solutions have the property that the signs of both the Hubble rate and the deceleration parameter in the Jordan frame may be different from the signs of their Einstein-frame counterparts. For special parameter combinations we identify these solutions with asymptotic attractors that have been obtained in the literature through dynamical-system analysis. We establish an effective general-relativistic description for which the geometrical equivalent of dark energy is associated with a time dependent equation of state. The present value of the latter is consistent with the observed cosmological ``constant". We demonstrate that this type of power-law solutions for accelerated expansion cannot be realized in f(R) theories.