Cosmological perturbations in teleparallel Loop Quantum Cosmology

Abstract

Cosmological perturbations in Loop Quantum Cosmology (LQC) are usually studied incorporating either holonomy corrections, where the Ashtekar connection is replaced by a suitable sinus function in order to have a well-defined quantum analogue, or inverse-volume corrections coming from the eigenvalues of the inverse-volume operator.In this paper we will develop an alternative approach to calculatecosmological perturbations in LQC based on the fact that, holonomycorrected LQC in the flat Friedmann-Lemaître-Robertson-Walker(FLRW) geometry could be also obtained as a particular case ofteleparallel F(T) gravity (teleparallel LQC). The main idea of ourapproach is to mix the simple bounce provided by holonomy correctionsin LQC with the non-singular perturbation equations given by F(T)gravity, in order to obtain a matter bounce scenario as a viablealternative to slow-roll inflation.In our study, we have obtained an scale invariant power spectrum ofcosmological perturbations. However, the ratio of tensor to scalarperturbations is of order 1, which does not agree with the currentobservations. For this reason, we suggest a model where a transitionfrom the matter domination to a quasi de Sitter phase is produced inorder to enhance the scalar power spectrum.