Cosmological perturbations in the teleparallel analog of Horndeski gravity

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 ΛCDM 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.

Quartic Horndeski-Cartan theories: a review on the stability of nonsingular cosmologies

“…If one wishes, however, to avoid these assumptions one could for instance explore Teleparallel Horndeski [20,21] or Beyond Horndeski or Horndeski-Cartan theories, as we will show below. In the latter, there is a new interesting link between nonsingular, stable and no-ghosty solutions with the speed of the graviton.…”

“…Besides a handful of special assumptions to avoid the instabilities in Horndeski theory such as "asymptotically strong gravity" or very specific models [11,[15][16][17], the alternative of Horndeski theory on spacetimes with torsion has been recently analyzed in [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]. In particular, it has been shown that in Horndeski-Cartan gravity (considering torsion in the second order, metric formalism), a similar No-Go theorem also holds (in up to the quartic case ) [19]: namely, the alltime sub/luminality, stability and nonsingularity of an spatially flat FLRW cosmology are mutually inconsistent, up to a few special cases.…”

“…This amounts to introduce torsion in the second order formalism, because the equations for the metric remain of second order. Other approaches in the context of Horndeski have been recently analyzed in[20][21][22][23][24][25][26][27][28][29][30][31][32][33] …”

Healthy Horndeski cosmologies with torsion

“…Even for Horndeski theory there are very particular solutions to the global stability issue [16, 18, 21-23, 35, 36], but one is restricted to one of the following three options: either the model propagates no scalar perturbation about a nonsingular Friedmann-Lemaître-Robertson -Walker (FLRW) background -which may be unsatisfactory because we do expect small deviations from FLRW on cosmological scales -or the scalar perturbation propagates about Minkowski spacetime [35], or one is forced to consider non conventional asymptotics, such as gravity being the strongest force in the past [16,36]. Finally, substantially reconsidering Horndeski theory, now on a flat spacetime and with extra terms, fully exchanging curvature for torsion through the teleparallel connection, the usual No-Go theorems break [37].…”

“…Namely, we assume from the start that the action can be written with a connection that can be expressed in terms of the Christoffel connection plus torsion[43,44]. See[37,[45][46][47][48][49][50][51][52][53][54][55][56][57] for other formalisms and modifications of Horndeski.…”