Non-oscillating vacuum states and the quantum homogeneity and isotropy hypothesis in Loop Quantum Cosmology

TL;DR

This paper examines whether the quantum homogeneity and isotropy hypothesis in Loop Quantum Cosmology can select vacuum states that produce non-oscillating power spectra, finding that these criteria are compatible.

Contribution

It clarifies the relationship between the QHIH and non-oscillatory vacuum states, highlighting a feasible way to satisfy both in LQC.

Findings

The original set of states satisfying QHIH can include non-oscillatory vacua.

The procedure for selecting vacua has an ununivocal step affecting the outcome.

Compatibility between QHIH and non-oscillatory vacua is possible within the analyzed framework.

Abstract

We study the compatibility of the quantum homogeneitiy and isotropy hypothesis (QHIH), proposed by Ashtekar and Gupt to restrict the choice of vacuum state for the cosmological perturbations in Loop Quantum Cosmology (LQC), with the requirement that the selected vacuum should lead to a power spectrum that does not oscillate. We inspect in close detail the procedure that these authors followed to construct a set of states satisfying the QHIH, and how a preferred vacuum can be determined within this set. We find a step that is not univocally specified in this procedure, in relation with the replacement of the set of states that was originally allowed by the QHIH with an alternative set that is more manageable. In fact, the first of these sets does not contain the state that has been used in most of the implementations of the QHIH to the analysis of the power spectrum of the perturbations in LQC. We focus our attention on the original set picked out by the QHIH and investigate whether some of its elements may display a non-oscillatory behavior. We show that, to the extent to which the techniques used in this paper apply, this possibility is feasible. Thus, the two aforementioned criteria for the physical restriction of the vacuum state in LQC are compatible with each other and not exclusive.