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

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 parametrization of these theories, capturing the redshift dependence of the equation of state, w(z), and the kinetic braiding parameter, alpha(B)(z), with only two parameters each, and derive their statistical distribution (also known as 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 parametrizations and Lagrangian-based theories, the two main approaches to test cosmological gravity and cosmic acceleration.

Automated summary

Efforts to constrain theories of late time accelerated expansion have shown that a more careful analysis of their dynamical evolution can lead to narrower prior settings, improving precision constraints. By studying shift-symmetric scalar-tensor theories, a simplified and accurate parameterization method has been proposed, suitable for observing cosmic evolution.