Cosmology with a successful Vainshtein screening in theories beyond Horndeski

TL;DR

This paper introduces a beyond Horndeski dark energy model with scalar self-interactions that successfully implement Vainshtein screening, ensuring compatibility with solar system tests and maintaining stable cosmological perturbations.

Contribution

It develops a new class of scalar-tensor theories beyond Horndeski with specific conditions for stability and screening, expanding the landscape of viable dark energy models.

Findings

Scalar sound speed squared remains positive from radiation to today.

Deviations from Horndeski do not cause heavy oscillations in gravitational potentials.

The model can satisfy solar system constraints while remaining cosmologically viable.

Abstract

We propose a dark energy model where a scalar field $\phi$ has nonlinear self-interactions in the presence of a dilatonic coupling with the Ricci scalar. This belongs to a sub-class of theories beyond Horndeski, which accommodates covariant Galileons and Brans-Dicke theories as specific cases. We derive conditions under which the scalar sound speed squared $c_{\rm s}^2$ is positive from the radiation era to today. Since $c_{\rm s}^2$ remains to be smaller than the order of 1, the deviation from Horndeski theories does not cause heavy oscillations of gauge-invariant gravitational potentials. In this case, the evolution of matter perturbations at low redshifts is similar to that in the coupled dark energy scenario with an enhanced gravitational interaction. On the spherically symmetric background with a matter source, the existence of field self-interactions suppresses the propagation of fifth force inside a Vainshtein radius. We estimate an allowed parameter space in which the model can be compatible with solar system constraints while satisfying conditions for the cosmological viability of background and perturbations.