Year: 2008
Type: article
Abstract: In this paper we calculate $\mathcal{O}({\ensuremath{\mu}}^{4})$ corrections from holonomies in the loop quantum gravity, usually not taken into account. Allowance of the corrections of this kind is equivalent with the choice of the new quatization scheme. Quantization ambiguities in the loop quantum cosmology allow for this additional freedom and presented corrections are consistent with the standard approach. We apply these corrections to the flat Friedmann-Robertson-Walker cosmological model and calculate the modified Friedmann equation. We show that the bounce appears in the models with the standard $\mathcal{O}({\ensuremath{\mu}}^{2})$ quantization scheme and is shifted to the higher energies ${\ensuremath{\rho}}_{\mathrm{bounce}}=3{\ensuremath{\rho}}_{\mathrm{c}}$. Also, a pole in the Hubble parameter appears for ${\ensuremath{\rho}}_{\mathrm{pole}}=\frac{3}{2}{\ensuremath{\rho}}_{\mathrm{c}}$ corresponding to hyperinflation/deflation phases. This pole represents a curvature singularity at which the scale factor is finite. In this scenario the singularity and bounce coexist. Moreover, we find that an ordinary bouncing solution appears only when quantum corrections in the lowest order are considered. Higher order corrections can lead to nonperturbative effects.
Authors: Jakub Mielczarek, Marek Szydłowski
Institutions: University of Copenhagen, Jagiellonian University
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2082498975