Phenomenology with fluctuating quantum geometries in loop quantum cosmology

TL;DR

This paper investigates the effects of large quantum geometric fluctuations in the early universe within loop quantum cosmology, finding that such fluctuations do not produce observable differences from less fluctuating states, but can be mimicked by adjusting pre-inflationary parameters.

Contribution

It introduces methods to analyze highly fluctuating quantum states in loop quantum cosmology and shows their observational effects are degenerate with simpler models by varying pre-inflationary e-folds.

Findings

Large fluctuations do not alter the primordial power spectrum within observational errors.

The effects of large quantum fluctuations can be simulated by changing the number of pre-inflationary e-folds.

Results generalize previous work focusing on sharply peaked quantum states.

Abstract

The goal of this paper is to probe phenomenological implications of large fluctuations of quantum geometry in the Planck era, using cosmology of the early universe. For the background (Friedmann, Lema\^{i}tre, Robertson, Walker) \emph{quantum} geometry, we allow `widely spread' states in which the \emph{relative} dispersions are as large as $168\%$ in the Planck regime. By introducing suitable methods to overcome the ensuing conceptual and computational issues, we calculate the power spectrum $P_{\mathcal{R}}(k)$ and the spectral index $n_s(k)$ of primordial curvature perturbations. These results generalize the previous work in loop quantum cosmology which focused on those states which were known to remain sharply peaked throughout the Planck regime. Surprisingly, even though the fluctuations we now consider are large, their presence does not add new features to the final $P_{\mathcal{R}}(k)$ and $n_s(k)$: Within observational error bars, their effect is degenerate with a different freedom in the theory, namely the number of \emph{pre-inflationary} e-folds $N_{{\rm B}\,\star}$ between the bounce and the onset of inflation. Therefore, with regard to observational consequences, one can simulate the freedom in the choice of states with large fluctuations in the Planck era using the simpler, sharply peaked states, simply by allowing for different values of $N_{{\rm B}\,\star}$.