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 parametrization of these theories, capturing the redshift dependence of the equation of state, $w(z)$, and the kinetic braiding parameter, ${\ensuremath{\alpha}}_{\mathrm{B}}(z)$, 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.
Highlights
There is some hope that the evidence of accelerated expansion [1,2,3,4,5,6] is an indication that new physics is at play on cosmological scales
One way of putting this is that the underlying physical model will impose quite strict physical priors on these functions and these should be taken into account when undertaking parameter constraints with cosmological data
We have a robust process for determining fw0; wa; α B; mg for each choice of the physical priors: minimizing Eq (21) allows us to find the set of parameters that reproduce the observables H, DA, and f with the accuracy needed by next-generation surveys
Summary
There is some hope that the evidence of accelerated expansion [1,2,3,4,5,6] is an indication that new physics is at play on cosmological scales. A particular Horndeski model can be associated with a choice of w and αX In this way, the exercise of constraining scalar-tensor gravity reduces to finding constraints on these free functions. One way of putting this is that the underlying physical model will impose quite strict physical priors on these functions and these should be taken into account when undertaking parameter constraints with cosmological data. Using a different and complementary approach, we have tackled this problem of physical priors in the case of thawing quintessence where, remarkably, we could construct an analytic prior for wðaÞ [65] By parametrizing it as w 1⁄4 w0 þ wað1 − aÞ; ð2Þ we found that if fw0; wag were chosen to fit the observables, those could be reproduced with the accuracy required by next-generation surveys up to recombination.
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