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

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, ${\alpha }_{\mathrm{B}}(z)$, 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.

18 pages, 13 figures; Version as accepted in PRD - minor changes;

References in corpus (22)

• The NumPy array: a structure for efficient numerical computation
• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• Dynamics of dark energy
• Multi-messenger Observations of a Binary Neutron Star Merger
• Gravitational Waves and Gamma-rays from a Binary Neutron Star Merger: GW170817 and GRB 170817A
• Cosmology and the Fate of Dilatation Symmetry
• An Ordinary Short Gamma-Ray Burst with Extraordinary Implications: Fermi-GBM Detection of GRB 170817A
• Causality, Analyticity and an IR Obstruction to UV Completion
• Dark Energy after GW170817: dead ends and the road ahead
• INTEGRAL Detection of the First Prompt Gamma-Ray Signal Coincident with the Gravitational Wave Event GW170817
• Strong constraints on cosmological gravity from GW170817 and GRB 170817A
• Implications of the Neutron Star Merger GW170817 for Cosmological Scalar-Tensor Theories
• Reconstructing Dark Energy
• Imperfect Dark Energy from Kinetic Gravity Braiding
• Exploring gravitational theories beyond Horndeski
• Maximal freedom at minimum cost: linear large-scale structure in general modifications of gravity
• New positivity bounds from full crossing symmetry
• Symmetries, Sum Rules and Constraints on Effective Field Theories
• Gravitational positivity bounds
• Challenges in Connecting Modified Gravity Theory and Observations
• Parametrizing modified gravity for cosmological surveys
• Theoretical priors in scalar-tensor cosmologies: Thawing quintessence