$R^2$ Dark Energy in the Laboratory

TL;DR

This paper explores how curvature squared gravity terms relate to dark energy, showing that in certain models the scalar field associated with these terms could be detectable through fifth force experiments, linking cosmology and laboratory tests.

Contribution

It demonstrates a natural relationship between curvature squared coefficients and dark energy scale, and connects low-energy gravity theories with string-inspired models predicting testable fifth forces.

Findings

The scalar field is ultralocal on cosmological scales, producing no large-scale effects.

The scalar field mass is constrained by fifth force experiments, making it potentially detectable.

The relationship $c_0\lambda^2 \\simeq 1$ is supported by string-inspired supergravity models.

Abstract

We analyse the role, on large cosmological scales and laboratory experiments, of the leading curvature squared contributions to the low energy effective action of gravity. We argue for a natural relationship $c_0\lambda^2\simeq 1$ at low-energy between the ${\cal R}^2$ coefficients $c_0$ of the Ricci scalar squared term in this expansion and the dark energy scale $\Lambda=(\lambda M_{\rm Pl})^4$ in four dimensional Planck mass units. We show how the compatibility between the acceleration of the expansion rate of the Universe, local tests of gravity and the quantum stability of the model all converge to select such a relationship up to a coefficient which should be determined experimentally. When embedding this low energy theory of gravity into candidates for its ultraviolet completion, we find that the proposed relationship is guaranteed in string-inspired supergravity models with modulus stabilisation and supersymmetry breaking leading to de Sitter compactifications. In this case, the scalar degree of freedom of ${\cal R}^2$ gravity is associated to a volume modulus. Once written in terms of a scalar-tensor theory, the effective theory corresponds to a massive scalar field coupled with the universal strength $\beta=1/\sqrt{6}$ to the matter stress-energy tensor. When the relationship $c_0\lambda^2\simeq 1$ is realised we find that on astrophysical scales and in cosmology the scalar field is ultralocal and therefore no effect arises on such large scales. On the other hand, the scalar field mass is tightly constrained by the non-observation of fifth forces in torsion pendulum experiments such as E\"ot-Wash. It turns out that the observation of the dark energy scale in cosmology implies that the scalar field could be detectable by fifth force experiments in the near future.