Effective Hamiltonian of the k=+1 FRW model from the K-Quantization method in LQC
| Autor: | Hasseine, Akram |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In the effective theory of loop quantum cosmology LQC, the influence of the holonomy correction (with $\overline{\mu}$-scheme) on the homogeneous and the inhomogeneous cosmological models have been extensively studied in the case of flat space. In this paper,using the K-Quantization method and the $\overline{\mu}$-scheme,in the same framework of LQC,we construct the Hamiltonian constraint operator of the closed FRW model (k=+1), we show that the effective semi-classical limit gives the same holonomy correction expression that was already used in the case of a flat space. We also derive the modified Friedman equation. The numerical investigation is performed to plot the effective evolution of the massless scalar field in term of the volume,which indicate a minimum volume at the bounce and also a suitable infrared behavior.The condition that we apply to constrain the value of $\overline{\mu}$ in the semi-classical limit is consistent with the numerical results. Comment: 23 pages, 3 figures in preparation for submitting in a journal |
| Databáze: | arXiv |
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