Capozziello, Salvatore; De Laurentis, Mariafelicia Noether symmetries in extended gravity quantum cosmology. (English) Zbl 1291.83181 Int. J. Geom. Methods Mod. Phys. 11, No. 2, Article ID 1460004, 20 p. (2014). Summary: We summarize the use of Noether symmetries in Minisuperspace Quantum Cosmology. In particular, we consider minisuperspace models, showing that the existence of conserved quantities gives selection rules that allow to recover classical behaviors in cosmic evolution according to the so-called Hartle criterion. Such a criterion selects correlated regions in the configuration space of dynamical variables whose meaning is related to the emergence of classical observable universes. Some minisuperspace models are worked out starting from Extended Gravity, in particular coming from scalar-tensor, \(f(R)\) and \(f(T)\) theories. Exact cosmological solutions are derived. Cited in 18 Documents MSC: 83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories 83F05 Relativistic cosmology 83C15 Exact solutions to problems in general relativity and gravitational theory 81T20 Quantum field theory on curved space or space-time backgrounds Keywords:quantum cosmology; Noether symmetries; minisuperspace models PDFBibTeX XMLCite \textit{S. Capozziello} and \textit{M. De Laurentis}, Int. J. Geom. Methods Mod. Phys. 11, No. 2, Article ID 1460004, 20 p. (2014; Zbl 1291.83181) Full Text: DOI arXiv References: [1] DOI: 10.1007/BF02742992 · doi:10.1007/BF02742992 [2] Noether E., Nachr. Akad. Wiss. Göttingen Math. Phys. Kl. pp 235– [3] DOI: 10.3390/sym2020970 · Zbl 1302.58006 · doi:10.3390/sym2020970 [4] Capozziello S., European Phys. J. C 72 [5] Halliwell J. J., Quantum Cosmology and Baby Universes (1991) [6] DOI: 10.1007/978-1-4757-1693-1 · doi:10.1007/978-1-4757-1693-1 [7] Marmo G., A Differential Geometric Approach to Symmetry and Reduction (1985) · Zbl 0592.58031 [8] DOI: 10.1023/A:1001935510837 · Zbl 0974.83036 · doi:10.1023/A:1001935510837 [9] DOI: 10.1016/j.physletb.2010.08.030 · doi:10.1016/j.physletb.2010.08.030 [10] DOI: 10.1142/S0219887807001928 · Zbl 1112.83047 · doi:10.1142/S0219887807001928 [11] DOI: 10.1007/s10714-007-0551-y · Zbl 1137.83302 · doi:10.1007/s10714-007-0551-y [12] Capozziello S., Open Astron. J. 2 pp 49– [13] DOI: 10.1016/j.physrep.2011.09.003 · doi:10.1016/j.physrep.2011.09.003 [14] DOI: 10.1016/j.physrep.2011.04.001 · doi:10.1016/j.physrep.2011.04.001 [15] DOI: 10.1016/0375-9601(93)90364-6 · doi:10.1016/0375-9601(93)90364-6 [16] DOI: 10.1088/0264-9381/11/1/013 · doi:10.1088/0264-9381/11/1/013 [17] DOI: 10.1103/PhysRevD.52.3288 · doi:10.1103/PhysRevD.52.3288 [18] DOI: 10.1103/PhysRevD.32.2511 · doi:10.1103/PhysRevD.32.2511 [19] DOI: 10.1023/A:1026651129626 · Zbl 0946.83048 · doi:10.1023/A:1026651129626 [20] DOI: 10.1103/PhysRevD.50.5039 · doi:10.1103/PhysRevD.50.5039 [21] Capozziello S., J. Cosmol. Astropart. Phys. 0808 pp 016– [22] Capozziello S., J. Cosmol. Astropart. Phys. 12 pp 009– [23] Paliathanasis A., Phys. Rev. D 84 [24] Basilakos S., Phys. Rev. D 83 [25] Einstein A., Sitzungsber. Preuss. Akad. Wiss. Phys. Math. Kl. pp 224– [26] DOI: 10.1007/BF01782370 · JFM 56.0734.01 · doi:10.1007/BF01782370 [27] DOI: 10.1103/PhysRevD.19.3524 · Zbl 1267.83090 · doi:10.1103/PhysRevD.19.3524 [28] Bengochea G., Phys. Rev. D 79 [29] DOI: 10.1016/j.physletb.2008.05.008 · Zbl 1328.83220 · doi:10.1016/j.physletb.2008.05.008 [30] DOI: 10.1103/PhysRevD.42.1091 · doi:10.1103/PhysRevD.42.1091 [31] DOI: 10.1016/j.physletb.2011.12.039 · doi:10.1016/j.physletb.2011.12.039 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.