Turning Big Bang into Big Bounce: I. Classical Dynamics

TL;DR

This paper analyzes the classical dynamics of the big bounce in loop cosmology, showing how loop geometry modifies classical theory to produce a bounce, with the energy scale depending on a parameter to be fixed by data or quantum theory.

Contribution

It provides a classical analysis of the big bounce within loop cosmology, identifying the phase space, observables, and the role of loop geometry in the bounce mechanism.

Findings

Loop geometry modifies classical dynamics to produce a big bounce.

The energy density at the bounce depends on a parameter.

Classical phase space and Dirac observables are explicitly constructed.

Abstract

The big bounce (BB) transition within a flat Friedmann-Robertson-Walker model is analyzed in the setting of loop geometry underlying the loop cosmology. We solve the constraint of the theory at the classical level to identify physical phase space and find the Lie algebra of the Dirac observables. We express energy density of matter and geometrical functions in terms of the observables. It is the modification of classical theory by the loop geometry that is responsible for BB. The classical energy scale specific to BB depends on a parameter that should be fixed either by cosmological data or determined theoretically at quantum level, otherwise the energy scale stays unknown.