A reciprocal Wald theorem for varying gravitational function

TL;DR

This paper investigates conditions under which a varying gravitational function in Hyperextended Scalar Tensor theories leads to a cosmological constant-like behavior, providing a reciprocal Wald theorem for Bianchi models.

Contribution

It introduces a reciprocal Wald theorem that characterizes when the potential approaches a constant, vanishes, or diverges in models with varying gravitational functions.

Findings

Conditions for potential to tend to a non-zero constant

Criteria for potential to vanish or diverge

Application to Bianchi type I and V cosmological models

Abstract

We study when a cosmological constant is a natural issue if it is mimicked by the potential of a massive Hyperextended Scalar Tensor theory with a perfect fluid for Bianchi type I and V models. We then deduce a reciprocal Wald theorem giving the conditions such that the potential tends to a non vanishing constant when the gravitational function varies. We also get the conditions allowing the potentiel to vanish or diverge.