Gravity's Islands: Parametrizing Horndeski Stability

TL;DR

This paper explores how different parametrizations of Horndeski gravity affect stability analyses and observational interpretations, emphasizing the importance of robust parametrizations for understanding cosmic acceleration.

Contribution

It demonstrates the dependence of stability results on parametrization choices in Horndeski gravity and discusses approaches to improve physical interpretability and observational constraints.

Findings

Parametrization choice significantly impacts stability conclusions.

Robust physical interpretations favor parametrizations aligned with observational strengths.

Future CMB B-mode observations can probe aspects of gravity beyond current constraints.

Abstract

Cosmic acceleration may be due to modified gravity, with effective field theory or property functions describing the theory. Connection to cosmological observations through practical parametrization of these functions is difficult and also faces the issue that not all assumed time dependence or parts of parameter space give a stable theory. We investigate the relation between parametrization and stability in Horndeski gravity, showing that the results are highly dependent on the function parametrization. This can cause misinterpretations of cosmological observations, hiding and even ruling out key theoretical signatures. We discuss approaches and constraints that can be placed on the property functions and scalar sound speed to preserve some observational properties, but find that parametrizations closest to the observations, e.g. in terms of the gravitational strengths, offer more robust physical interpretations. In addition we present an example of how future observations of the B-mode polarization of the cosmic microwave background from primordial gravitational waves can probe different aspects of gravity.