Cosmological Perturbations in the Teleparallel analog of Horndeski gravity

TL;DR

This paper investigates cosmological perturbations within the teleparallel analog of Horndeski gravity, providing a detailed analysis of scalar, vector, and tensor modes to facilitate observational tests of these theories.

Contribution

It introduces a comprehensive perturbation analysis of the BDLS teleparallel Horndeski theory, expressing alpha parameters in terms of arbitrary functions and exploring their implications for cosmological observations.

Findings

Derived the scalar-vector-tensor decomposition of the theory.

Expressed alpha parameters in terms of arbitrary functions.

Analyzed perturbations up to second order, enabling parameter space exploration.

Abstract

In this work we study the cosmological perturbations in Bahamonde-Dialektopoulos-Levi Said (BDLS) theory, i.e. the teleparallel analog of Horndeski gravity. In order to understand the evolution of structure in a cosmological model, it is necessary to study its cosmology not only in the background but also perturbatively. Both Horndeski and its teleparallel analog have been analyzed a lot in the literature, but in order to study them quantitatively, we need to know their cosmological perturbations. That is why, we study here the scalar-vector-tensor decomposition of the theory and we also express the so-called alpha parameters in terms of the arbitrary functions of the theory, that designate the deviation from the {\Lambda}CDM model. We have explored tensor, vector and scalar perturbation of the action up to second order, which drastically opens up new possibilities on searches in the parameter space of scalar-tensor theories in the context of observations.