Well-Tempered Minkowski Solutions in Teleparallel Horndeski Theory

TL;DR

This paper extends well-tempering mechanisms to teleparallel Horndeski theories, enabling models that screen large vacuum energies and maintain Minkowski solutions, with analysis of their dynamics and stability.

Contribution

It introduces a broader class of teleparallel Horndeski models capable of self-tuning Minkowski vacua, demonstrating the uniqueness of well-tempering in this context.

Findings

Models can screen large vacuum energies using degeneracy in field equations.

Well-tempering is the unique method for self-tuning flat solutions in these theories.

Minkowski vacuum remains stable under linear perturbations and phase transitions.

Abstract

Well-tempering stands among the few classical methods of screening vacuum energy to deliver a late-time, low energy vacuum state. We build on the class of Horndeski models that admit a Minkowski vacuum state despite the presence of an arbitrarily large vacuum energy to obtain a much larger family of models in teleparallel Horndeski theory. We set up the routine for obtaining these models and present a variety of cases, all of which are able to screen a natural particle physics scale vacuum energy using degeneracy in the field equations. We establish that well-tempering is the unique method of utilizing degeneracy in Horndeski scalar-tensor gravity -- and its teleparallel generalisation -- that can accommodate self-tuned flat Minkowski solutions, when the explicit scalar field dependence in the action is minimal (a tadpole and a conformal coupling to the Ricci scalar). Finally, we study the dynamics of the well-tempered teleparallel Galileon. We generate its phase portraits and assess the attractor nature of the Minkowski vacuum under linear perturbations and through a phase transition of vacuum energy.