Universal features of quantum bounce in loop quantum cosmology

TL;DR

This paper analytically studies the evolution of the universe and its perturbations in loop quantum cosmology, revealing features in the power spectra influenced by pre-inflation dynamics that can be tested observationally.

Contribution

It provides an analytical solution for perturbations during the pre-inflationary phase in LQC, linking quantum bounce effects to observable power spectrum features.

Findings

Pre-inflation dynamics induce particle creation.

Power spectra exhibit testable features.

Universe must have expanded at least 141 e-folds since bounce.

Abstract

In this Letter, we study analytically the evolutions of the flat Friedmann-Lemaitre-Robertson-Walker (FLRW) universe and its linear perturbations in the framework of {\em the dressed metric approach} in loop quantum cosmology (LQC). Assuming that the evolution of the background is dominated by the kinetic energy of the inflaton at the quantum bounce, we find that both evolutions of the background and its perturbations are independent of the inflationary potentials during the pre-inflationary phase. During this period the effective potentials of the perturbations can be well approximated by a P\"oschl-Teller (PT) potential, from which we find analytically the mode functions and then calculate the corresponding Bogoliubov coefficients at the onset of the slow-roll inflation, valid for any inflationary model with a single scalar field. Imposing the Bunch-Davies (BD) vacuum in the contracting phase prior to the bounce when the modes are all inside the Hubble horizon, we show that particles are generically created due to the pre-inflation dynamics. Matching them to those obtained in the slow-roll inflationary phase, we investigate the effects of the pre-inflation dynamics on the scalar and tensor power spectra and find features that can be tested by current and forthcoming observations. In particular, to be consistent with the Planck 2015 data, we find that the universe must have expanded at least $141$ e-folds since the bounce.