Bouhmadi Lopez, M.Garay Elizondo, Luis JavierGonzález Díaz, Pedro F.2023-06-202023-06-202002-09-15[1] E.M. Lifshitz, Sov. J. Phys. 10, 116 (1945); E.M. Lifshitz and I.M. Khalatnikov, Adv. Phys. 12, 185 (1963). [2] P. Ginsparg and M.J. Perry, Nucl. Phys. B222, 245 (1983). [3] J.B. Hartle and S.W. Hawking, Phys. Rev. D 28, 2960 (1983); S.W. Hawking, Nucl. Phys. B239 257 (1984). [4] A.D. Linde, Lett. Nuovo Cimento 39, 401 (1984). [5] A. Vilenkin, Phys. Rev. D 30, 509 (1984); 33, 3560 (1986); 37, 888 (1988). [6] J.J. Halliwell and S.W. Hawking, Phys. Rev. D 31, 1777 (1985). [7] S. Wada, Nucl. Phys. B276, 729 (1986). [8] T. Vachaspati and A. Vilenkin, Phys. Rev. D 37, 898 (1988). [9] V.A. Rubakov, Phys. Lett. 148B, 280 (1984). [10] C. Barceló, L.J. Garay, P.F. González-Díaz, and G.A. Mena Marugán, Phys. Rev. D 53, 3162 (1996). [11] C. Barceló and L.J. Garay, Phys. Rev. D 57, 5291 (1998); Int. J. Mod. Phys. D 7, 623 (1998). [12] J.J. Halliwell and R. Laflamme, Class. Quantum Grav. 6, 1839 (1989). [13] O. Bertolami et al., Int. J. Mod. Phys. A 6, 4149 (1991); O. Bertolami and J. M Mourão, Class. Quantum Grav. 8, 1271 (1991). [14] B.S. DeWitt, Phys. Rev. 160, 1113 (1967); J. A. Wheeler, in Relativity, Groups and Topology, edited by C. DeWitt and B. S. DeWitt (Gordon and Breach, London, 1964); in Battelle Rencontres: 1967 Lectures on Mathematics and Physics, edited by C. Dewitt and J. A. Wheeler (W. Benjamin and Co., New York, 1968). [15] C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (Freeman, New York, 1973). [16] C. Barceló, Int. J. Mod. Phys. D 8, 325 (1999). [17] Handbook of Mathematical Functions, edited by M. Abramowitz and A. Stegun (Dover, New York, 1972). [18] I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series and Products (Academic Press, New York, 1980). [19] E. L. Ince, Ordinary Differential Equations (Dover, New York, 1944). [20] H. Bateman, Higher Transcendental Functions (McGraw-Hill, New York, 1953), Vol. 2.0556-282110.1103/PhysRevD.66.083504https://hdl.handle.net/20.500.14352/59508© 2002 The American Physical Society. M.B.L. is thankful to Alexander Vilenkin for his kindness and suggesting this work during a visit to Tufts Institute of Cosmology. M.B.L. is supported by a grant of the Spanish Ministry of Science and Technology. This work was supported by the DGESIC under Research Projects No. PB97-1218 and No. PB98-0684.We study the quantum vacuum fluctuations around closed Friedmann-Robertson-Walker (FRW) radiation-filled universes with a nonvanishing cosmological constant. These vacuum fluctuations are represented by a conformally coupled massive scalar field and are treated in the lowest order of perturbation theory. In the semiclassical approximation, the perturbations are governed by differential equations which, properly linearized, become generalized Lame equations. The wave function thus obtained must satisfy appropriate regularity conditions which ensure its finiteness for every field configuration. We apply these results to asymptotically anti-de Sitter Euclidean wormhole spacetimes and show that there is no catastrophic particle creation in the Euclidean region, which would lead to divergences of the wave function.engjournal articlehttp://dx.doi.org/10.1103/PhysRevD.66.083504http://journals.aps.org/http://lib-arxiv-008.serverfarm.cornell.edu/pdf/gr-qc/0204072.pdfopen access51-73MholesWave-functionStateCosmologyCreationFísica-Modelos matemáticosFísica matemática