No-Go theorem in the cubic subclass of Horndeski theory for spherically symmetric dynamical background

TL;DR

This paper investigates the stability and existence of solutions in the cubic subclass of Horndeski theory for spherically symmetric backgrounds, establishing a no-go theorem that rules out certain singular and stable configurations.

Contribution

It formulates a generalized no-go theorem for the cubic Horndeski subclass, including cases with weak coordinate dependence, and shows many singular solutions are prohibited.

Findings

No stable, non-singular solutions exist under the specified conditions.

The no-go theorem applies to scenarios with weak dependence on time or radial coordinates.

Many singular solutions are ruled out within this theory subclass.

Abstract

We consider a general dynamical, spherically symmetric background in the cubic subclass of Horndeski theory and obtain the quadratic action for the perturbations using the DPSV approach. We analyse the stability conditions for high-energy modes and study the issue of the no-go theorem in the current subclass of Horndeski theory. We formulate the no-go theorem for weak dependence on one variable (time or radial) and derive its generalization to the cases which could be reduced by coordinate transformation to scenarios where the scalar field has weak dependence on one of the coordinates. Moreover we show that wide class of singular solutions are also prohibited within the cubic subclass of Horndeski theory.