Conical singularities and the Vainshtein screening in full GLPV theories

Abstract

Abstract. In Gleyzes-Langlois-Piazza-Vernizzi (GLPV) theories, it is known that the conical singularity arises at the center of a spherically symmetric body (r = 0) in the case where the parameter α H4 characterizing the deviation from the Horndeski Lagrangian L 4 approaches a non-zero constant as r → 0. We derive spherically symmetric solutions around the center in full GLPV theories and show that the GLPV Lagrangian L 5 does not modify the divergent property of the Ricci scalar R induced by the non-zero α H4 . Provided that α H4 = 0, curvature scalar quantities can remain finite at r = 0 even in the presence of L 5 beyond the Horndeski domain. For the theories in which the scalar field φ is directly coupled to R, we also obtain spherically symmetric solutions inside/outside the body to study whether the fifth force mediated by φ can be screened by non-linear field self-interactions. We find that there is one specific model of GLPV theories in which the effect of L 5 vanishes in the equations of motion. We also show that, depending on the sign of a L 5 -dependent term in the field equation, the model can be compatible with solar-system constraints under the Vainshtein mechanism or it is plagued by the problem of a divergence of the field derivative in high-density regions.

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

“…The quintic Lagrangian L 5 of GLPV theories does not modify the property of singularities generated by L 4 [22]. Hence the Lagrangian L 4 is crucial for the existence of solid angle deficit singularities.…”

“…The matter density ρ m (r) can be also expanded around r = 0, but the variation of ρ m (r) does not affect the discussion of solid angle deficit singularities [21,22]. Hence it is sufficient to consider the case of constant ρ m .…”

“…In Refs. [21,22], the authors considered more general cases in which additional functions G 2 , G 3 , G 4 , f 4 to the model (3.7) are taken into account. Provided α H = 0 at r = 0, it was shown that these additional contributions do not modify the existence of solid angle deficit singularities.…”

“…In such models, not only the problem of solid angle deficit singularities is absent, but also the Vainshtein screening can be at work outside the compact body [21,22].…”

“…[21,22] that a solid angle deficit singularity appears in the case where the parameter α H characterizing the departure from Horndeski theories approaches a non-zero constant at the center of a spherically symmetric body. In this case, the Ricci scalar has the dependence R = −2α H /r 2 around the center of body (r = 0), so R exhibits the divergence at r = 0.…”