Hysteresis and beats in loop quantum cosmology

Abstract

Differences in pressure during expansion and contraction stages in cosmic evolution can result in a hysteresis-like phenomena in non-singular cyclic models sourced with scalar fields. We discuss this phenomena for spatially closed isotropic spacetime in loop quantum cosmology (LQC) for a quadratic and a cosh-like potential, with and without a negative cosmological constant using effective spacetime description of the underlying quantum geometry. Two inequivalent loop quantizations of this spacetime, one based on holonomies of the Ashtekar-Barbero connection using closed loops, and another based on the connection operator, are discussed. Due to quantum geometric effects, both models avoid classical singularities, but unlike the holonomy based quantization, connection based quantization results in two quantum bounces. In spite of differences in non-singular effective dynamics of both the models, the phenomena of hysteresis is found to be robust for the $\phi^2$ potential. Quasi-periodic beats exist for a cosh-like potential, irrespective of the nature of classical recollapse whether by spatial curvature, or a negative cosmological constant. An interplay of negative cosmological constant and spatial curvature in presence of potentials results in rich features such as islands of cluster of bounces separated by accelerated expansion, and a universe which either undergoes a step like expansion with multiple turnarounds or quasi-periodic beats depending on a "tuning" of the steepness parameter of the potential.