General second order scalar-tensor theory, self tuning, and the Fab Four

TL;DR

This paper identifies a unique scalar-tensor action enabling self-tuning of the cosmological constant on FLRW backgrounds, using four base Lagrangians with a geometric structure, allowing curvature screening and novel cosmological solutions.

Contribution

It derives the specific form of the scalar-tensor action that supports self-tuning, expanding the understanding of how scalar fields can screen vacuum energy effects.

Findings

Unique action for self-tuning on FLRW backgrounds

Combination of four base Lagrangians with geometric dependence

Potential for non-trivial cosmological solutions

Abstract

Starting from the most general scalar-tensor theory with second order field equations in four dimensions, we establish the unique action that will allow for the existence of a consistent self-tuning mechanism on FLRW backgrounds, and show how it can be understood as a combination of just four base Lagrangians with an intriguing geometric structure dependent on the Ricci scalar, the Einstein tensor, the double dual of the Riemann tensor and the Gauss-Bonnet combination. Spacetime curvature can be screened from the net cosmological constant at any given moment because we allow the scalar field to break Poincar\'e invariance on the self-tuning vacua, thereby evading the Weinberg no-go theorem. We show how the four arbitrary functions of the scalar field combine in an elegant way opening up the possibility of obtaining non-trivial cosmological solutions.