Quintessence, scalar-tensor theories and non-Newtonian gravity

TL;DR

This paper explores scalar-tensor theories as a basis for quintessence, addressing issues like the cosmological constant problem, proposing modifications to matter coupling, and predicting potential observable effects such as variable gravitational constant.

Contribution

It introduces a modified scalar field coupling in scalar-tensor theories to better model quintessence and links it to non-Newtonian gravity effects and experimental constraints.

Findings

A static universe in the prototype model is problematic.

Modified matter coupling can resolve some issues.

Predictions include time-variability of G and possible deviations from Newtonian gravity.

Abstract

We discuss some of the issues which we encounter when we try to invoke the scalar-tensor theories of gravitation as a theoretical basis of quintessence. One of the advantages of appealing to these theories is that they allow us to implement the scenario of a ``decaying cosmological constant,'' which offers a reasonable understanding of why the observed upper bound of the cosmological constant is smaller than the theoretically natural value by as much as 120 orders of magnitude. In this context, the scalar field can be a candidate of quintessence in a broader sense. We find, however, a serious drawback in the prototype Brans-Dicke model with $\Lambda$ added; a static universe in the physical conformal frame which is chosen to have constant particle masses. We propose a remedy by modifying the matter coupling of the scalar field taking advantage of scale invariance and its breakdown through quantum anomaly. By combining this with a conjecture on another cosmological constant problem coming from the vacuum energy of matter fields, we expect a possible link between quintessence and non-Newtonian gravity featuring violation of Weak Equivalence Principle and intermediate force range, likely within the experimental constraints. A new prediction is also offered on the time-variability of the gravitational constant.