Numerical evolution of squeezed and non-Gaussian states in loop quantum cosmology

TL;DR

This paper demonstrates through numerical simulations that the quantum bounce in loop quantum cosmology persists even for highly non-Gaussian and squeezed initial states, confirming its robustness across diverse quantum states.

Contribution

It introduces a numerical approach using the Chimera scheme to analyze non-Gaussian states in loop quantum cosmology, extending understanding beyond Gaussian initial conditions.

Findings

Quantum bounce occurs for highly squeezed and non-Gaussian states.

The evolution of these states is similar to Gaussian states with constraints on fluctuation growth.

Effective dynamics underestimates the bounce volume but captures qualitative behavior.

Abstract

In recent years, numerical simulations with Gaussian initial states have demonstrated the existence of a quantum bounce in loop quantum cosmology in various models. A key issue pertaining to the robustness of the bounce and the associated physics is to understand the quantum evolution for more general initial states which may depart significantly from Gaussianity and may have no well defined peakedness properties. The analysis of such states, including squeezed and highly non-Gaussian states, has been computationally challenging until now. In this manuscript, we overcome these challenges by using the Chimera scheme for the spatially flat, homogeneous and isotropic model sourced with a massless scalar field. We demonstrate that the quantum bounce in this model occurs even for states which are highly squeezed or are non-Gaussian with multiple peaks and with little resemblance to semi-classical states. The existence of the bounce is found to be robust, being independent of the properties of the states. The evolution of squeezed and non-Gaussian states turns out to be qualitatively similar to that of Gaussian states, and satisfies strong constraints on the growth of the relative fluctuations across the bounce. We also compare the results from the effective dynamics and find that, although it captures the qualitative aspects of the evolution for squeezed and highly non-Gaussian states, it always underestimates the bounce volume. We show that various properties of the evolution, such as the energy density at the bounce, are in excellent agreement with the predictions from an exactly solvable loop quantum cosmological model for arbitrary states.