Required Conditions for Late Time Acceleration and Early Time Deceleration in Generalized Scalar-Tensor Theories

TL;DR

This paper explores conditions in generalized scalar-tensor theories that allow for late-time cosmic acceleration and early-time deceleration, deriving specific functional forms for the coupling and cosmological constants.

Contribution

It provides general expressions for the coupling function and cosmological constant in terms of scalar field and scale factor, analyzing conditions for realistic cosmological evolution.

Findings

Conditions for late-time acceleration and early-time deceleration are identified.

Functional forms of mbda() and mbda() consistent with observations are derived.

The model supports a decreasing cosmological constant and increasing coupling function over time.

Abstract

We consider a generalized scalar-tensor theory, where we let the coupling function $\omega(\phi)$ and the effective cosmological constants $\Lambda(\phi)$ undetermined. We obtain general expressions for $\omega(\phi)$ and $\Lambda(\phi)$ in terms of the scalar field and the scale factor, and show that $\omega(\phi)$ depends on the scalar field and the scale factor in a complicated way. In order to study the conditions for an accelerated expansion at the present time and a decelerated expansion in the past, we assume a power law evolution for the scalar field and the scale factor. We analyse the required conditions that allow our model to satisfy the weak field limits on $\omega(\phi)$, and at the same time, to obtain the correct values of cosmological parameters, as the energy density $ \Omega_{m0}$ and cosmological constant $\Lambda(t_0)$. We also study the conditions for a decelerated expansion at an early time dominated by radiation. We find values for $\omega(\phi)$ and $\Lambda(\phi)$ consistent with the expectations of a theory where the cosmological constant decreases with the time and the coupling function increases until the values accepted today.