Convergence of Scalar-Tensor theories toward General Relativity and Primordial Nucleosynthesis

TL;DR

This paper investigates the conditions under which scalar-tensor gravity theories evolve towards General Relativity, highlighting how boundary conditions and the form of the coupling function influence convergence and nucleosynthesis constraints.

Contribution

It provides a detailed analysis of the mechanisms driving scalar-tensor theories toward Einstein's theory and how different coupling functions affect nucleosynthesis bounds.

Findings

Attraction mechanism dominates in recent universe epochs under certain boundary conditions.

Nucleosynthesis bounds on coupling vary significantly with the form of the coupling function.

Analytical estimates show very stringent bounds for some scalar-tensor theories.

Abstract

In this paper, we analyze the conditions for convergence toward General Relativity of scalar-tensor gravity theories defined by an arbitrary coupling function $\alpha$ (in the Einstein frame). We show that, in general, the evolution of the scalar field $(\phi)$ is governed by two opposite mechanisms: an attraction mechanism which tends to drive scalar-tensor models toward Einstein's theory, and a repulsion mechanism which has the contrary effect. The attraction mechanism dominates the recent epochs of the universe evolution if, and only if, the scalar field and its derivative satisfy certain boundary conditions. Since these conditions for convergence toward general relativity depend on the particular scalar-tensor theory used to describe the universe evolution, the nucleosynthesis bounds on the present value of the coupling function, $\alpha_0$, strongly differ from some theories to others. For example, in theories defined by $\alpha \propto \mid\phi\mid$ analytical estimates lead to very stringent nucleosynthesis bounds on $\alpha_0$ ($\lesssim 10^{-19}$). By contrast, in scalar-tensor theories defined by $\alpha \propto \phi$ much larger limits on $\alpha_0$ ($\lesssim 10^{-7}$) are found.