An Expansion of Well Tempered Gravity

TL;DR

This paper extends the well tempered gravity framework by deriving new relationships between scalar field terms in shift symmetric theories, simplifying the parameter space for testing modified gravity against cosmological data.

Contribution

It generalizes the connection between kinetic and braiding terms to polynomial and infinite series expansions, enhancing the theoretical foundation of well tempered gravity.

Findings

Derived the relation between K and G_3 for arbitrary polynomial degrees

Presented an example with an infinite series expansion

Reduced the parameter space for testing modified gravity theories

Abstract

When faced with two nigh intractable problems in cosmology -- how to remove the original cosmological constant problem and how to parametrize modified gravity to explain current cosmic acceleration -- we can make progress by counterposing them. The well tempered solution to the cosmological constant through degenerate scalar field dynamics also relates disparate Horndeski gravity terms, making them contrapuntal. We derive the connection between the kinetic term $K$ and braiding term $G_3$ for shift symmetric theories (including the running Planck mass $G_4$), extending previous work on monomial or binomial dependence to polynomials of arbitrary finite degree. We also exhibit an example for an infinite series expansion. This contrapuntal condition greatly reduces the number of parameters needed to test modified gravity against cosmological observations, for these "golden" theories of gravity.