Non-oscillating power spectra in Loop Quantum Cosmology

TL;DR

This paper analytically characterizes conditions for vacuum states in Loop Quantum Cosmology that produce non-oscillating power spectra, especially near the bounce, aiding observational access to quantum gravity effects.

Contribution

It provides a theoretical framework for selecting vacuum states that yield non-oscillating power spectra in Loop Quantum Cosmology, including a unique asymptotic expansion in the ultraviolet regime.

Findings

Non-oscillating spectra are optimal for observing quantum gravity effects.

A consistent method to obtain non-oscillating spectra using hyperbolic equations in hybrid quantization.

Existence of a unique asymptotic expansion in the ultraviolet regime.

Abstract

We characterize in an analytical way the general conditions that a choice of vacuum state for the cosmological perturbations must satisfy to lead to a power spectrum with no scale-dependent oscillations over time. In particular, we pay special attention to the case of cosmological backgrounds governed by effective Loop Quantum Cosmology and in which the Einsteinian branch after the bounce suffers a pre-inationary period of deccelerated expansion. This is the case more often studied in the literature because of the physical interest of the resulting predictions. In this context, we argue that non-oscillating power spectra are optimal to gain observational access to those regimes near the bounce where Loop Quantum Cosmology effects are non-negligible. In addition, we show that non-oscillatory spectra can indeed be consistently obtained when the evolution of the perturbations is ruled by the hyperbolic equations derived in the hybrid loop quantization approach. Moreover, in the ultraviolet regime of short wavelength scales we prove that there exists a unique asymptotic expansion of the power spectrum that displays no scale-dependent oscillations over time. This expansion would pick out the natural Poincar\'e and Bunch Davies vacua in Minkowski and de Sitter spacetimes, respectively, and provides an appealing candidate for the choice of a vacuum for the perturbations in Loop Quantum Cosmology based on physical motivations.