Absence of solid angle deficit singularities in beyond-generalized Proca theories

TL;DR

This paper demonstrates that beyond-generalized Proca theories avoid solid angle deficit singularities present in some scalar-tensor theories, due to the temporal vector component, and confirms the Vainshtein mechanism remains effective.

Contribution

It shows that solid angle deficit singularities are absent in beyond-generalized Proca theories up to quartic order, extending the understanding of their regularity and screening mechanisms.

Findings

Solid angle deficit singularities are absent in these theories.

The vector-field profiles around compact objects are derived.

The Vainshtein mechanism remains effective in these theories.

Abstract

In Gleyzes-Langlois-Piazza-Vernizzi (GLPV) scalar-tensor theories, which are outside the domain of second-order Horndeski theories, it is known that there exists a solid angle deficit singularity in the case where the parameter $\alpha_{\rm H}$ characterizing the deviation from Horndeski theories approaches a non-vanishing constant at the center of a spherically symmetric body. Meanwhile, it was recently shown that second-order generalized Proca theories with a massive vector field $A^{\mu}$ can be consistently extended to beyond-generalized Proca theories, which recover shift-symmetric GLPV theories in the scalar limit $A^{\mu} \to \nabla^{\mu} \chi$. In beyond-generalized Proca theories up to quartic-order Lagrangians, we show that solid angle deficit singularities are generally absent due to the existence of a temporal vector component. We also derive the vector-field profiles around a compact object and show that the success of the Vainshtein mechanism operated by vector Galileons is not prevented by new interactions in beyond generalized Proca theories.