Cosmology with a successful Vainshtein screening in theories beyond Horndeski

Understand

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.