- Published 2010

It is argued that it is the regularization of the classical Hamiltonian—first step in loop cosmology in order to build a well-defined quantum theory—what 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.

@inproceedings{Haro2010LoopCR,
title={Loop Cosmology: Regularization vs. Quantization},
author={Jaume Haro and E. Elizalde},
year={2010}
}