States of Low Energy in bouncing inflationary scenarios in Loop Quantum Cosmology

TL;DR

This paper explores the use of States of Low Energy as vacua in bouncing inflationary models within Loop Quantum Cosmology, showing they produce stable, observationally consistent power spectra and are insensitive to specific smearing functions.

Contribution

It demonstrates the viability of SLEs as vacua in hybrid Loop Quantum Cosmology, with insensitivity to smearing function choices and compatibility with observational data.

Findings

SLEs are unique and exact Hadamard states for each smearing function.

Power spectra from SLEs are insensitive to smearing function shape.

Results align with observational constraints on cosmological parameters.

Abstract

In generic Friedmann-Lema\^itre-Robertson-Walker spacetimes, States of Low Energy (SLEs) are defined to minimize the regularized energy density smeared along the time-like curve of an isotropic observer, which is specified via a smearing function. For every smearing function, SLEs are unique (up to a phase) and are shown to be exact Hadamard states. In this work, we investigate the viability of SLEs as the vacuum for cosmological perturbations in hybrid Loop Quantum Cosmology, motivated by the fact that SLEs have been shown to provide suitable vacua in models where a period of kinetic dominance precedes inflation. We find that there are two classes of smearing functions that can be seen as natural choices within this context, for which the corresponding SLEs and the resulting power spectra at the end of inflation are quite insensitive to the exact shape and support of the smearing function. Furthermore, a preliminary analysis of the tensor-to-scalar ratio and of the spectral index indicates as good an agreement with observations as that of standard cosmology.