# Priors on the effective Dark Energy equation of state in scalar-tensor theories

## TL;DR

This paper derives theoretical prior covariances for the dark energy equation of state in scalar-tensor theories, aiding non-parametric reconstructions and reducing bias in cosmological data analysis.

## Contribution

It introduces a method to compute prior covariances for w(z) based on scalar-tensor theories, including viability conditions, enhancing cosmological parameter estimation.

## Key findings

- Prior favors tracking behaviors in scalar-tensor theories
- Covariance matrices enable bias-reducing priors for w(z)
- Method applicable to various parametrizations of dark energy

## Abstract

Constraining the Dark Energy (DE) equation of state, w, is one of the primary science goals of ongoing and future cosmological surveys. In practice, with imperfect data and incomplete redshift coverage, this requires making assumptions about the evolution of w with redshift z. These assumptions can be manifested in a choice of a specific parametric form, which can potentially bias the outcome, or else one can reconstruct w(z) non-parametrically, by specifying a prior covariance matrix that correlates values of w at different redshifts. In this work, we derive the theoretical prior covariance for the effective DE equation of state predicted by general scalar-tensor theories with second order equations of motion (Horndeski theories). This is achieved by generating a large ensemble of possible scalar-tensor theories using a Monte Carlo methodology, including the application of physical viability conditions. We also separately consider the special sub-case of the minimally coupled scalar field, or quintessence. The prior shows a preference for tracking behaviors in the most general case. Given the covariance matrix, theoretical priors on parameters of any specific parametrization of w(z) can also be readily derived by projection.