Theoretical priors in scalar-tensor cosmologies: Shift-symmetric Horndeski models

TL;DR

This paper derives narrower, theoretically motivated priors for shift-symmetric scalar-tensor cosmologies, improving constraints on dark energy models by linking phenomenological parameters to fundamental theory.

Contribution

It introduces a simple parametrisation of key functions in shift-symmetric theories and derives their statistical distributions, connecting phenomenological models with underlying Lagrangian theories.

Findings

Theoretical priors can tighten constraints on cosmological parameters by up to an order of magnitude.

Shift-symmetric models without a cosmological constant are consistent with current observations.

A two-parameter description effectively captures the evolution of key functions in these theories.

Abstract

Attempts at constraining theories of late time accelerated expansion often assume broad priors for the parameters in their phenomenological description. Focusing on shift-symmetric scalar-tensor theories with standard gravitational wave speed, we show how a more careful analysis of their dynamical evolution leads to much narrower priors. In doing so, we propose a simple and accurate parametrisation of these theories, capturing the redshift dependence of the equation of state, $w(z)$, and the kinetic braiding parameter, $\alpha_{\rm B}(z)$, with only two parameters each, and derive their statistical distribution (a.k.a. theoretical priors) that fit the cosmology of the underlying model. We have considered two versions of the shift-symmetric model, one where the energy density of dark energy is given solely by the scalar field, and another where it also has a contribution from the cosmological constant. By including current data, we show how theoretical priors can be used to improve constraints by up to an order of magnitude. Moreover, we show that shift-symmetric theories without a cosmological constant are observationally viable. We work up to quartic order in first derivatives of the scalar in the action and our results suggest this truncation is a good approximation to more general shift-symmetric theories. This work establishes an actionable link between phenomenological parameterisations and Lagrangian-based theories, the two main approaches to test cosmological gravity and cosmic acceleration.