Existence and disappearance of conical singularities in Gleyzes-Langlois-Piazza-Vernizzi theories

TL;DR

This paper investigates conical singularities in GLPV theories, showing how they can be avoided by model design, and demonstrates compatibility with local gravity tests through Vainshtein screening.

Contribution

It introduces explicit models within GLPV theories that eliminate conical singularities and recover general relativity inside the Vainshtein radius.

Findings

Conical singularities occur if _H approaches a non-zero constant at the center.

Properly designed models can avoid conical singularities by ensuring _H vanishes as r A0 0.

Models with diatonic coupling recover GR behavior and satisfy solar system constraints.

Abstract

In a class of Gleyzes-Langlois-Piazza-Vernizzi (GLPV) theories, we derive both vacuum and interior Schwarzschild solutions under the condition that the derivatives of a scalar field $\phi$ with respect to the radius $r$ vanish. If the parameter $\alpha_{\rm H}$ characterizing the deviation from Horndeski theories approaches a non-zero constant at the center of a spherically symmetric body, we find that the conical singularity arises at $r=0$ with the Ricci scalar given by $R=-2\alpha_{\rm H}/r^2$. This originates from violation of the geometrical structure of four-dimensional curvature quantities. The conical singularity can disappear for the models in which the parameter $\alpha_{\rm H}$ vanishes in the limit that $r \to 0$. We propose explicit models without the conical singularity by properly designing the classical Lagrangian in such a way that the main contribution to $\alpha_{\rm H}$ comes from the field derivative $\phi'(r)$ around $r=0$. We show that the extension of covariant Galileons with a diatonic coupling allows for the recovery of general relativistic behavior inside a so-called Vainshtein radius. In this case, both the propagation of a fifth force and the deviation from Horndeski theories are suppressed outside a compact body in such a way that the model is compatible with local gravity experiments inside the solar system.