A Class of Effective Field Theory Models of Cosmic Acceleration

TL;DR

This paper develops a comprehensive effective field theory framework for cosmic acceleration involving a scalar field coupled to matter, revealing nine free functions and analyzing perturbation regimes relevant for dark energy models.

Contribution

It introduces a novel class of scalar-tensor models with nine free functions, derived from pseudo-Nambu-Goldstone bosons, and explores their perturbation behavior and different theoretical representations.

Findings

The theory contains nine independent free functions at four derivatives.

Perturbations are weakly coupled and natural on subhorizon scales.

Strong nonlinearities are outside the theory's validity domain.

Abstract

We explore a class of effective field theory models of cosmic acceleration involving a metric and a single scalar field. These models can be obtained by starting with a set of ultralight pseudo-Nambu-Goldstone bosons whose couplings to matter satisfy the weak equivalence principle, assuming that one boson is lighter than all the others, and integrating out the heavier fields. The result is a quintessence model with matter coupling, together with a series of correction terms in the action in a covariant derivative expansion, with specific scalings for the coefficients. After eliminating higher derivative terms and exploiting the field redefinition freedom, we show that the resulting theory contains nine independent free functions of the scalar field when truncated at four derivatives. This is in contrast to the four free functions found in similar theories of single-field inflation, where matter is not present. We discuss several different representations of the theory that can be obtained using the field redefinition freedom. For perturbations to the quintessence field today on subhorizon lengthscales larger than the Compton wavelength of the heavy fields, the theory is weakly coupled and natural in the sense of t'Hooft. The theory admits a regime where the perturbations become modestly nonlinear, but very strong nonlinearities lie outside its domain of validity.