On the resolution of the big bang singularity in isotropic Loop Quantum Cosmology

Abstract

In contrast to previous work in the field, we construct the Loop Quantum Cosmology (LQC) of the flat isotropic model with a massless scalar field in the absence of higher order curvature corrections to the gravitational part of the Hamiltonian constraint. The matter part of the constraint contains the inverse triad operator which can be quantized with or without the use of a Thiemann- like procedure. With the latter choice, we show that the LQC quantization is identical to that of the standard Wheeler DeWitt theory (WDW) wherein there is no singularity resolution. We argue that the former choice leads to singularity resolution in the sense of a well defined, regular (backward) evolution through and beyond the epoch where the size of the universe vanishes. Our work along with that of the seminal work of Ashtekar, Pawlowski and Singh (APS) clarifies the role, in singularity resolution, of the three `exotic' structures in this LQC model, namely: curvature corrections, inverse triad definitions and the `polymer' nature of the kinematic representation. We also critically examine certain technical assumptions made by APS in their analysis of WDW semiclassical states and point out some problems stemming from the infrared behaviour of their wave functionsComment: 26 pages, no figure