Inherently stable effective field theory for dark energy and modified gravity

TL;DR

This paper introduces a stable and flexible effective field theory framework for dark energy and modified gravity, ensuring theoretical consistency and computational efficiency for cosmological data analysis.

Contribution

It proposes a new parametrisation of the effective field theory basis functions that guarantees stability and broad applicability to known theories.

Findings

The parametrisation can avoid ghost and gradient instabilities.

It is computationally efficient with a simple approximation.

No fundamental stability limitations on current phenomenological parameters.

Abstract

The growing wealth of cosmological observations places increasingly more stringent constraints on dark energy and alternative gravity models. Particularly successful in efficiently probing the vast model space has been the effective field theory of dark energy and modified gravity, providing a unified framework for generalised cosmological predictions. However, the optimal parametrisation of the free time-dependent functions inherent to the formalism is still unresolved. It should respect a multitude of requirements, ranging from simplicity, generality, and representativity of known theories to computational efficiency. But in particular, for theoretical soundness, the parameter space should adhere to strict stability requirements. We have recently proposed an inherently stable effective field theory with physical basis of Planck mass evolution, sound speed of the scalar field fluctuation, kinetic coefficient, and background expansion, which covers Horndeski models with luminal speed of gravity. Here we devise a parametrisation of these basis functions that can straightforwardly be configured to evade theoretical pathologies such as ghost or gradient instabilities or to accommodate further theoretical priors such as (sub)luminal scalar sound speed. The parametrisation is simple yet general, conveniently represents a broad range of known dark energy and gravitational theories, and with a simple additional approximation can be rendered numerically highly efficient. Finally, by operating in our new basis, we show that there are no general limitations from stability requirements on the current values that can be assumed by the phenomenological modification of the Poisson equation and the gravitational slip besides the exclusion of anti-gravity. The inherently stable effective field theory is ready for implementation in parameter estimation analyses employing linear cosmological observations.