Advances in Loop Quantum Cosmology

Dear Colleagues,

You are cordially invited to submit papers to the Special Issue of “Advances in Loop Quantum Cosmology”, which focuses on comprehending the pre-inflationary cosmological era, which is believed to be governed by quantum gravity (QG).

Loop quantum gravity (LQG) is a background independent, non-perturbative approach aimed at unifying general relativity (GR) and quantum physics. Loop quantum cosmology (LQC) is the application of LQG to cosmological settings. This new paradigm has provided some remarkable insights on QG, and has allowed for a systematic exploration of the very early Universe.

The scope of this Special Issue is to highlight recent developments on conceptual issues of LQC as well as the resulting phenomenological implications.

Cosmological spacetimes can provide the most appropriate setting to render significant progress on many conceptual and technical problems of QG. In cosmological models, Einstein’s equations hold to an excellent degree of approximation at low curvature, but they undergo major modifications in the Planck regime. In LQC, the current paradigm of cosmology changes and, hence, several unresolved questions can be addressed, as, for example, the avoidance of classical singularities; the way that a smooth, continuous spacetime can emerge from an underlying quantum theory; the way that the QG effects modify the classical field equations; the nature of time; quantum probabilities in the presence of external fields; and so on. Recently, the scalar–tensor reconstruction techniques were also extended to the context of LQC, and the holonomy corrections were taken into account. One of the striking results was that, when the holonomy corrections are considered, there are no Big Rip singularities at all.

Today, LQC can successfully face many of the long-standing problems of QG. New effects, originating from Planck-scale physics, can resolve the initial singularity of GR, while ensuring an agreement with Einstein’s theory at a low curvature. Clearly, the LQC framework has already been advanced sufficiently in order to meet phenomenology and observations.

Prof. Kostas Kleidis
Guest Editor

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2. Ashtekar, A.; Pawlowski, T.; Singh, P. Quantum nature of the Big Bang: An analytical and numerical investigation. Phys. Rev. D 2006, 73, 124038, arXiv: gr-qc/0604013.
3. Ashtekar, A.; Pawlowski, T.; Singh, P. Quantum nature of the Big Bang: Improved dynamics. Rev. D 2006, 74, 084003, arXiv: gr-qc/0607039
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9. Ashtekar, A.; Singh, P. Loop Quantum Cosmology: A status report. Class. Quantum Grav. 2011, 28, 213001, arXiv: 1108.0893 [gr-qc].
10. Haro, J.; Makarenko, A.N.; Myagky, A.N.; Odintsov, S.D.; Oikonomou, V.K. Bouncing loop quantum Cosmology in Gauss–Bonnet gravity. Rev. D 2015, 92, 124026, doi:10.1103/Phys. Rev. D 92 124026, arXiv: 1506.08273 [gr-qc].
11. Oikonomou, K. Reconstructing the evolution of the Universe from loop quantum Cosmology scalar fields. Phys. Rev. D 2016, 94, 044004, doi:10.1103/Phys. Rev. D.94.044004, arXiv: 1607.07107 [gr-qc].
12. Salo, L.A.; Amoros, J.; de Haro, J. Qualitative study in loop quantum Cosmology. Class. Quantum Grav. 2017, 34, 235001, doi:10.1088/1361-6382/aa9311, arXiv: 1612.05480 [gr-qc].
13. Agullo, I.; Singh, P. Loop Quantum Cosmology: A Brief Review. In 100 Years of General Relativity; Ashtekar, A., Pullin, J. (eds.); World Scientific: Singapore, 2017, doi:10.1142/97898132200030007
14. Kleidis, K.; Oikonomou, V.K. Loop quantum Cosmology scalar field models. Int. J. Geom. Methods Mod. Phys. 2018, 15, 1850071, doi:10.1142/S0219887818500718.

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• loop quantum gravity
• loop quantum cosmology
• quantum geometry
• planck epoch
• pre-inflationary era
• initial singularity
• hamiltonian formulation