Geodesic
Can quantum effects due to a massless conformally coupled field avoid gravitational singularities?
Teoretičeskaâ i matematičeskaâ fizika, Tome 171 (2012) no. 1, pp. 162-176

Voir la notice de l'article provenant de la source Math-Net.Ru

Using quantum corrections from massless fields conformally coupled to gravity, we study the possibility of avoiding singularities that appear in the flat Friedmann–Robertson–Walker model. We assume that the universe contains a barotropic perfect fluid with the state equation $p=\omega\rho$, where $p$ is the pressure and $\rho$ is the energy density. We study the dynamics of the model for all values of the parameter $\omega$ and also for all values of the conformal anomaly coefficients $\alpha$ and $\beta$. We show that singularities can be avoided only in the case where $\alpha>0$ and $\beta<0$. To obtain an expanding Friedmann universe at late times with $\omega>-1$ (only a one-parameter family of solutions, but no a general solution, has this behavior at late times), the initial conditions of the nonsingular solutions at early times must be chosen very exactly. These nonsingular solutions consist of a general solution (a two-parameter family) exiting the contracting de Sitter phase and a one-parameter family exiting the contracting Friedmann phase. On the other hand, for $\omega<-1$ (a phantom field), the problem of avoiding singularities is more involved because if we consider an expanding Friedmann phase at early times, then in addition to fine-tuning the initial conditions, we must also fine-tune the parameters $\alpha$ and $\beta$ to obtain a behavior without future singularities: only a one-parameter family of solutions follows a contracting Friedmann phase at late times, and only a particular solution behaves like a contracting de Sitter universe. The other solutions have future singularities.
Keywords: cosmological singularity avoidance, semiclassical approximation, conformal anomaly. 
J. Haro. Can quantum effects due to a massless conformally coupled field avoid gravitational singularities?. Teoretičeskaâ i matematičeskaâ fizika, Tome 171 (2012) no. 1, pp. 162-176. http://geodesic.mathdoc.fr/item/TMF_2012_171_1_a14/
@article{TMF_2012_171_1_a14,
     author = {J. Haro},
     title = {Can quantum effects due to a~massless conformally coupled field avoid gravitational singularities?},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {162--176},
     year = {2012},
     volume = {171},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2012_171_1_a14/}
}
TY  - JOUR
AU  - J. Haro
TI  - Can quantum effects due to a massless conformally coupled field avoid gravitational singularities?
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2012
SP  - 162
EP  - 176
VL  - 171
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2012_171_1_a14/
LA  - ru
ID  - TMF_2012_171_1_a14
ER  - 
%0 Journal Article
%A J. Haro
%T Can quantum effects due to a massless conformally coupled field avoid gravitational singularities?
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2012
%P 162-176
%V 171
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2012_171_1_a14/
%G ru
%F TMF_2012_171_1_a14

[1] C. Molina-París, M. Visser, Phys. Lett. B, 455:1–4 (1999), 90–95, arXiv: ; S. W. Hawking, R. Penrose, The Nature of Space and Time, The Isaac Newton Institute Series of Lectures, Princeton Univ. Press, Princeton, NJ, 1996 ; S. W. Hawking, G. F. R. Ellis, The Large Scale Structure of Space-Time, Cambridge Monographs on Mathematical Physics, 1, Cambridge Univ. Press, Cambridge, 1973 gr-qc/9810023 | DOI | MR | Zbl | MR | Zbl | MR | Zbl

[2] P. C. W. Davies, Phys. Lett. B, 68:4 (1977), 402–404 | DOI

[3] A. A. Starobinsky, Phys. Lett. B, 91:1 (1980), 99–102 | DOI

[4] T. Azuma, S. Wada, Prog. Theor. Phys., 75 (1986), 845–861 | DOI | MR

[5] S. Wada, Phys. Rev. D, 31:10 (1985), 2470–2475 | DOI | MR

[6] R. R. Caldwell, M. Kamionkowski, N. N. Weinberg, Phys. Rev. Lett., 91:7 (2003), 071301, 4 pp., arXiv: astro-ph/0302506 | DOI

[7] S. Nojiri, S. Odintsov, S. Tsujikawa, Phys. Rev. D, 71:6 (2005), 063005, 21 pp. | DOI | MR

[8] A. O. Barvinsky, A. Yu. Kamenshchik, Phys. Rev. D, 74:12 (2006), 121502, 5 pp. | DOI

[9] A. O. Barvinsky, A. Yu. Kamenshchik, JCAP, 09 (2006), 014, arXiv: hep-th/0605132 | DOI

[10] R. M. Wald, Phys. Rev. D, 17:6 (1978), 1477–1484 | DOI

[11] S. W. Hawking, T. Hertog, H. S. Reall, Phys. Rev. D, 63:8 (2001), 083504, 23 pp., arXiv: hep-th/0010232 | DOI | MR

[12] A. Vilenkin, Phys. Rev. D, 32:10 (1985), 2511–2521 | DOI | MR

[13] M. V. Fischetti, J. B. Hartle, B. L. Hu, Phys. Rev. D, 20:8 (1979), 1757–1771 | DOI | MR

[14] P. Anderson, Phys. Rev. D, 28:2 (1983), 271–285 | DOI | MR

[15] H. Calderón, W. A. Hiscock, Class. Quantum Grav., 22:4 (2005), L23–L26 | DOI | MR | Zbl

[16] A. Ashtekar, T. Pawlowski, P. Singh, Phys. Rev. D, 73:12 (2006), 124038, 33 pp., arXiv: gr-qc/0604013 | DOI | MR

[17] S. Sami, P. Singh, S. Tsujikawa, Phys. Rev. D, 74:4 (2006), 043514, 6 pp., arXiv: gr-qc/0605113 | DOI | MR

[18] J. Haro, E. Elizalde, J. Phys. A, 42:20 (2009), 202002, 15 pp. | DOI | MR | Zbl

[19] E. Elizalde, J. Haro, J. Phys. A, 42:47 (2009), 472001, 9 pp. | DOI | MR | Zbl