Linear perturbations in Horndeski theories with spatial curvature

TL;DR

This paper investigates how spatial curvature influences linear perturbations in Horndeski theories of modified gravity, revealing couplings with scalar field perturbations using a model-independent EFT approach.

Contribution

It provides a theoretical framework for understanding the effects of spatial curvature on perturbations in Horndeski theories, extending previous flat-universe analyses.

Findings

Spatial curvature couples with scalar field perturbations.

The EFT formalism captures curvature effects at linear order.

Implications for cosmological observations and model constraints.

Abstract

We analyse the implications of the presence of spatial curvature in modified gravity models. As it is well known, the current standard cosmological model, the $\Lambda$CDM, is assumed to be spatially flat based on the results of many experiments. However, this statement does not necessarily hold for a modified gravity (MG) model, and this leads to couplings of the spatial curvature with the parameters of the chosen cosmological model. In this paper, we illustrate the theoretical development of how spatial curvature affects the equations of motion at linear order for scalar and tensor perturbations modes using a model-independent approach based on the formalism of the Effective Field Theory (EFT) of dark energy (DE). The results show that spatial curvature gives rise to a coupling with the scalar field perturbations and the functions parameterizing the model.