Analytical investigation of pre-inflationary effects in the primordial power spectrum: from General Relativity to hybrid Loop Quantum Cosmology

Abstract

This work is an analytical study of the main differences between classical inflationary effects of a fast-roll regime and imprints of hybrid Loop Quantum Cosmology (LQC) on the primordial power spectrum. Effective LQC solutions of phenomenological interest typically contain a classical period of kinetic dominance prior to slow-roll inflation, with consequences on the power spectrum that here we try and tell apart from those of phenomena occuring in the vicinity of a bounce in hybrid LQC. For this comparison, we use the same criterion for the choice of a vacuum state of the primordial perturbations, both in the context of relativistic cosmology and on the LQC cosmological background. As a first approximation to the problem, our study ignores the influence of a quasi-de Sitter evolution (rather than de Sitter) in the slow-roll inflationary regime, and of a typically short transition between the kinetically dominated era and the slow-roll period. Our results show that, while the two studied types of effects can lead to a drastic power suppression in the infrared sector of the spectrum, the mode scale at which this happens is much larger for LQC than for classical relativistic cosmology, the corresponding scales being related to the spacetime curvature at the bounce and at the onset of inflation, respectively.