The Well-Tempered Cosmological Constant: The Horndeski Variations

TL;DR

This paper explores how specific Horndeski scalar-tensor models can dynamically cancel a large cosmological constant, ensuring a stable de Sitter universe and consistent cosmic evolution, thus addressing the cosmological constant problem.

Contribution

It derives general constraints and explicit models within Horndeski gravity that achieve well tempering, providing a framework for testing modified gravity against cosmological observations.

Findings

Identified conditions for Horndeski models to admit stable de Sitter solutions.

Constructed explicit scalar-tensor models that reproduce standard cosmic history.

Provided relations between Horndeski functions to simplify testing against data.

Abstract

Well tempering is one of the few classical field theory methods for solving the original cosmological constant problem, dynamically canceling a large (possibly Planck scale) vacuum energy and leaving the matter component intact, while providing a viable cosmology with late time cosmic acceleration and an end de Sitter state. We present the general constraints that variations of Horndeski gravity models with different combinations of terms must satisfy to admit an exact de Sitter spacetime that does not respond to an arbitrarily large cosmological constant. We explicitly derive several specific scalar-tensor models that well temper and can deliver a standard cosmic history including current cosmic acceleration. Stability criteria, attractor behavior of the de Sitter state, and the response of the models to pressureless matter are considered. The well tempered conditions can be used to focus on particular models of modified gravity that have special interest -- not only removing the original cosmological constant problem but providing relations between the free Horndeski functions and reducing them to a couple of parameters, suitable for testing gravity and cosmological data analysis.