Turning big bang into big bounce: II. Quantum dynamics

TL;DR

This paper investigates the quantum dynamics of the big bounce in loop quantum cosmology, revealing a discrete volume spectrum and potential observable spacetime foam effects.

Contribution

It introduces a nonstandard LQC approach with a free parameter to analyze the quantum transition from big bang to big bounce, highlighting spectral properties of key operators.

Findings

Energy density spectrum is bounded and continuous.

Volume spectrum is bounded from below and discrete.

Potential spacetime foam detectable in cosmological observations.

Abstract

We analyze the big bounce transition of the quantum FRW model in the setting of the nonstandard loop quantum cosmology (LQC). Elementary observables are used to quantize composite observables. The spectrum of the energy density operator is bounded and continuous. The spectrum of the volume operator is bounded from below and discrete. It has equally distant levels defining a quantum of the volume. The discreteness may imply a foamy structure of spacetime at semiclassical level which may be detected in astro-cosmo observations. The nonstandard LQC method has a free parameter that should be fixed in some way to specify the big bounce transition.