# Positivity in the sky

## TL;DR

This paper derives positivity bounds for Horndeski theories and demonstrates their effectiveness in tightening cosmological parameter constraints through combined theoretical and observational analysis.

## Contribution

It introduces the first application of positivity bounds to cosmological data analysis for Horndeski theories, significantly improving parameter constraints.

## Key findings

- Positivity bounds eliminate over 60% of the allowed parameter space.
- Including bounds in parameter estimation improves constraints on dark energy models.
- Additional priors like subluminal gravitational waves further tighten constraints.

## Abstract

Positivity bounds - the consequences of requiring a unitary, causal, local UV completion - place strong restrictions on theories of dark energy and/or modified gravity. We derive and investigate such bounds for Horndeski scalar-tensor theories and for the first time pair these bounds with a cosmological parameter estimation analysis, using CMB, redshift space distortion, matter power spectrum and BAO measurements from the Planck, SDSS/BOSS and 6dF surveys. Using positivity bounds as theoretical priors, we show that their inclusion in the parameter estimation significantly improves the constraints on dark energy/modified gravity parameters. Considering as an example a specific class of models, which are particularly well-suited to illustrate the constraining power of positivity bounds, we find that these bounds eliminate over 60% of the previously allowed parameter space. We also discuss how combining positivity requirements with additional theoretical priors has the potential to further tighten these constraints: for instance also requiring a subluminal speed of gravitational waves eliminates all but 1% of the previously allowed parameter space.