Loop cosmology: Regularization vs. quantization

¹  Departament de Matemàtica Aplicada I, Universitat Politècnica de Catalunya - Diagonal 647, 08028 Barcelona, Spain, EU
²  Instituto de Ciencias del Espacio (CSIC) and Institut d'Estudis Espacials de Catalunya (IEEC/CSIC), Facultat de Ciències, UAB - Torre C5-Parell-2a planta, 08193 Bellaterra (Barcelona) Spain, EU

Corresponding authors: jaime.haro@upc.edu elizalde@ieec.fcr.es elizalde@math.mit.edu

Received: 2 December 2009
Accepted: 2 March 2010

Abstract

It is argued that it is the regularization of the classical Hamiltonian —the first step in loop cosmology in order to build a well-defined quantum theory— that is already able to avoid the Big Bang and Big Rip singularities, rather than the usually invoked quantum corrections coming from the quantization of the Hamiltonian. To prove such statement, the classical regularized Hamiltonian corresponding to loop gravity is obtained, and it is shown that it coincides, up to terms of order , with the so-called effective Hamiltonian which is calculated from the quantum regularized Hamiltonian using semi-classical techniques. From that comparison it is concluded that both types of singularities are avoided at the “classical level” already, i.e., using loop cosmology, in the sense that only the quantum nature of the geometry is invoked (the loop cut-off) in order to construct the regularized Hamiltonian and to fix the parameter on which it depends. Such finding constitutes a key manifestation of the intrinsic power of loop gravity, as compared with other alternatives.