Abstract:
We show that the dynamics of a spatially dosed Friedmann-Robertson-Walker universe conformally coupled to a real, free, massive scalar field, is chaotic, for large enough field amplitudes. We do so by proving that this system is integrable under the adiabatic approximation, but that the corresponding KAM tori break up when non-adiabatic terms are considered. This finding is confirmed by numerical evaluation of the Lyapunov exponents associated with the system, among other criteria. Chaos sets strong limitations on our ability to predict the value of the field at the big crunch, from its given value at the big bang.
Referencias:
- Belinskii, VA, Khalatnikov, ZM, Lifschitz, EM, (1970) Adv. Phys., 19 (80), pp. 525-573
- Landau, L, Lifschitz, EM, (1975); Khalatnikov, IM, Lifschitz, EM, Khanin, KM, Shchur, LN, Sinai Ya, G, (1985) J. Stat. Phys., 38 (1-2), pp. 97-114
- Misner, CW, (1970), pp. 55-79; Misner, CW, (1969) Phys. Rev., 186 (5), pp. 1319-1327
- Misner, CW, (1969) Phys. Rev., 186 (5), pp. 1328-1333
- Chitre, DM, (1972); Ryan, M, (1972); Ryan, M, Shepley, L, (1975); Barrow, JD, (1982) Phys. Rep., 85 (1), pp. 1-49
- Barrow, JD, (1987), p. 18; Barrow, JD, Sirousse-Zia, H, (1989) Phys. Rev., 39 (8), pp. 2187-2191
- Zardecki, A, (1983) Phys. Rev., 28 (6), pp. 1235-1242
- Francisco, G, Matsas, GEA, (1988) Gen. Rel. Grav., 20 (10), pp. 1047-1054
- Burd, A, Buric, N, Ellis, G, (1990) Gen. Rel. Grav., 22 (3), pp. 349-363
- Berger, BK, (1989) Phys. Rev., 39 (8), pp. 2426-2429
- Berger, BK, (1990) Class. Quantum Grav., 7 (2), pp. 203-216
- Berger, BK, (1992); Burd, A, Buric, N, Tavakol, RK, (1991) Class. Quantum Grav., 8 (1), pp. 123-133
- Pullin, J, (1991), pp. 189-197; Hobill, D, Bernstein, D, Wedge, M, Simkins, D, (1991) Class. Quantum Grav., 8 (6), pp. 1155-1171
- Hobill, D, (1991) Ann. NY Acad. Sci., 631 (1 nlinear pro), pp. 15-30
- Rugh, SE, (1991); Burd, A, Tavakol, RK, (1992); Tavakol, RK, (1992); Balasz, NL, Voros, A, (1986) Phys. Rep., 143 (3), p. 109
- Lockhart, CM, Misra, B, Prigogine, I, (1982) Phys. Rev., 25 (4), pp. 921-929
- Tomaschitz, R, (1991) J. Math. Phys., 32 (10), pp. 2571-2579
- Gurzadyan, V, Kocharyan, A, (1991); Contopoulos, G, Periodic Orbits and Chaos around Two Black Holes (1990) Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 431 (1881), p. 183
- Contopoulos, G, Periodic Orbits and Chaos around Two Fixed Black Holes. II (1991) Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 435 (1895), pp. 551-562
- Contopoulos, G, (1991) Ann. NY Acad. Sci., 631 (1 nlinear pro), pp. 143-155
- Buchler, JR, (1985); Buchler, JR, Eichhorn, H, (1987) Ann. NY Acad. Sci., 497
- Buchler, JR, Ipser, JR, Williams, CA, Preface (1988) Annals of the New York Academy of Sciences, 536
- Buchler, JR, Detweiler, SL, Ipser, JR, Preface (1991) Annals of the New York Academy of Sciences, 631
- Bombelli, L, Calzetta, E, (1992) Class. Quantum Grav., 9 (12), p. 2573
- Guckenheimer, J, Holmes, P, (1983); Wiggins, S, (1988); Arnold, VI, Avez, A, (1968); Chirikov, BV, (1979) Phys. Rep., 52, p. 263
- Reichl, LE, Zheng, WM, (1987); Zaslavsky, GM, Sagdeev, RZ, Usikov, DA, Chernikov, AA, (1991); Berry, M, (1983), p. 171; Ozorio de Almeida, AM, (1988); Hawking, SW, (1985) Phys. Rev., 32 (10), pp. 2489-2495
- Page, D, (1985) Phys. Rev., 32 (10), pp. 2496-2499
- Page, D, (1991); Prigogine, I, Elskens, Y, (1987); Courbage, M, (1983) Physica, 122 A (3), pp. 459-482
- Calzetta, E, (1991) J. Math. Phys., 32 (10), p. 2903
- Abbott, LF, (1981) Nucl. Phys., 185 (1), p. 233
- (1985) Phys. Lett., 155 B (4), pp. 232-236
- (1985) Zh. Eksp. Teor. Fiz., 89 (2), pp. 346-360
- Gottlober, S, Muller, V, Starobinsky, A, (1991) Phys. Rev., 43 (8), pp. 2510-2520
- Futamase, T, Rothman, T, Matzner, R, (1989) Phys. Rev., 39 (2), pp. 405-411
- Maeda, K, Stein-Schabes, J, Futamase, T, (1989) Phys. Rev., 39 (10), pp. 2848-2853
- Amendola, L, Litterio, M, Occhionero, F, THE PHASE-SPACE VIEW OF INFLATION I: THE NON-MINIMALLY COUPLED SCALAR FIELD (1990) International Journal of Modern Physics A, 5 (20), pp. 3861-3886
- Demianski, M, (1991) Phys. Rev., 44 (10), pp. 3136-3146
- Demianski, M, de Ritis, R, Rubano, C, Scudellaro, P, (1992) Phys. Rev., 46 (4), pp. 1391-1398
- Kiefer, C, (1989) Phys. Lett., 225 B (3), pp. 227-232
- Parker, L, (1968) Phys. Rev. Lett., 21 (3), p. 562
- Parker, L, (1969) Phys. Rev., 183 (5), p. 1057
- Hartle, JB, (1981) Phys. Rev., 23 (10), p. 2121
- Calzetta, E, Castagnino, M, (1984) Phys. Rev., 29 (8), pp. 1609-1617
- Calzetta, E, (1991) Phys. Rev., 44 (10), p. 3043
- Calzetta, E, Mazzitelli, F, (1990) Phys. Rev., 42 (12), pp. 4066-4069
- Wolf, A, Swift, J, Swinney, H, Vastano, J, (1985) Physica, 16 (3), pp. 285-317
- Misner, C, Thorne, K, Wheeler, A, (1972); Hartle, J, Kuchar, K, (1984), pp. 315-326; Courant, R, Hilbert, D, (1953), p. 531; Whittaker, E, Watson, G, (1940); Rey Pastor, J, Pi Calleja, P, Trejo, C, (1959), pp. 176-188; McCracken, D, Dorn, W, (1964); Arnold, VI, (1978); Arnold, VI, Kozlov, VV, Neishtadt, AI, (1988); Shields, P, (1974); Ornstein, D, (1974); Hawking, S, (1987); Hartle, J, Hawking, S, (1983) Phys. Rev., 28 (12), p. 2960
Citas:
---------- APA ----------
Calzetta, E. & El Hasi, C.
(1993)
. Chaotic Friedmann-Robertson-Walker cosmology. Classical and Quantum Gravity, 10(9), 1825-1841.
http://dx.doi.org/10.1088/0264-9381/10/9/022---------- CHICAGO ----------
Calzetta, E., El Hasi, C.
"Chaotic Friedmann-Robertson-Walker cosmology"
. Classical and Quantum Gravity 10, no. 9
(1993) : 1825-1841.
http://dx.doi.org/10.1088/0264-9381/10/9/022---------- MLA ----------
Calzetta, E., El Hasi, C.
"Chaotic Friedmann-Robertson-Walker cosmology"
. Classical and Quantum Gravity, vol. 10, no. 9, 1993, pp. 1825-1841.
http://dx.doi.org/10.1088/0264-9381/10/9/022---------- VANCOUVER ----------
Calzetta, E., El Hasi, C. Chaotic Friedmann-Robertson-Walker cosmology. 1993;10(9):1825-1841.
http://dx.doi.org/10.1088/0264-9381/10/9/022