Geodesic
Potential dominated scalar-tensor cosmologies in the general relativity limit
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 153 (2011) no. 3, pp. 185-195 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

We consider Friedmann–Lemaître–Robertson–Walker flat cosmological models in the framework of general Jordan frame scalar-tensor theories of gravity with arbitrary coupling function and potential. For the era when the cosmological energy density of the scalar potential dominates over the energy density of ordinary matter, we use a nonlinear approximation of the decoupled scalar field equation for the regime close to the so-called limit of general relativity where the local weak field constraints are satisfied. We consider the phase space of the scalar field and provide a complete classification of possible phase portraits. We give the solutions in cosmological time with a particular attention to the classes of models asymptotically approaching general relativity. The latter can be subsumed under two types: (i) exponential convergence, and (ii) damped oscillations around general relativity.
Keywords: general relativity limit, dark energy.
Mots-clés : scalar-tensor cosmologies 
@article{UZKU_2011_153_3_a16,
     author = {L. J\"arv and P. Kuusk and M. Saal},
     title = {Potential dominated scalar-tensor cosmologies in the general relativity limit},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {185--195},
     year = {2011},
     volume = {153},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2011_153_3_a16/}
}
TY  - JOUR
AU  - L. Järv
AU  - P. Kuusk
AU  - M. Saal
TI  - Potential dominated scalar-tensor cosmologies in the general relativity limit
JO  - Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
PY  - 2011
SP  - 185
EP  - 195
VL  - 153
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/UZKU_2011_153_3_a16/
LA  - en
ID  - UZKU_2011_153_3_a16
ER  - 
%0 Journal Article
%A L. Järv
%A P. Kuusk
%A M. Saal
%T Potential dominated scalar-tensor cosmologies in the general relativity limit
%J Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
%D 2011
%P 185-195
%V 153
%N 3
%U http://geodesic.mathdoc.fr/item/UZKU_2011_153_3_a16/
%G en
%F UZKU_2011_153_3_a16
L. Järv; P. Kuusk; M. Saal. Potential dominated scalar-tensor cosmologies in the general relativity limit. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 153 (2011) no. 3, pp. 185-195. http://geodesic.mathdoc.fr/item/UZKU_2011_153_3_a16/

[1] Will C. M., “The confrontation between the general relativity and experiment”, Living Rev. Rel., 9 (2006), 3 http://www.livingreviews.org/lrr-2006-3

[2] Jain B., Khoury J., “Cosmological Tests of Gravity”, Ann. Phys., 325:7 (2010), 1479–1516 | DOI | MR | Zbl

[3] Lidsey J. E., Wands D., Copeland E. J., “Superstring Cosmology”, Phys. Repts., 337 (2000), 343–492 | DOI | MR

[4] Misner C. W., Thorne K. S., Wheeler J. A., Gravitation, W. H. Freeman and Co., San Francisco, 1973, XXVI+1279 pp. | MR

[5] Perlmutter S. et al., “Measurements of $\Omega$ and $\Lambda$ from 42 high-redshift supernovae”, (Supernova Cosmology Project Collaboration), Astrophys. J., 517:2 (1999), 565–586 | DOI

[6] Riess A. G. et al., “Observational evidence from supernovae for an accelerating Universe and a cosmological constant”, (Supernova Search Team Collaboration), Astronom. J., 116:3 (1998), 1009–1038 | DOI

[7] Tsujikawa S., Dark energy: investigation and modeling, 2010, 49 pp., arXiv: 1004.1493v1

[8] Faraoni V., Cosmology in Scalar-Tensor Gravity, Kluwer Acad. Publ., Dordrecht, 2004, XIII+267 pp. | Zbl

[9] Fujii Y., Maeda K., The Scalar-Tensor Theory of Gravitation, Cambridge Univ. Press, Cambridge, 2003, XIV+246 pp. | MR | Zbl

[10] Järv L., Kuusk P., Saal M., “Scalar-tensor cosmology at the general relativity limit: Jordan vs Einstein frame”, Phys. Rev. D, 76:10 (2007), 103506-1–103506-9 | DOI | MR

[11] Järv L., Kuusk P., Saal M., “Scalar-tensor cosmologies: fixed points of the Jordan frame scalar field”, Phys. Rev. D, 78:8 (2008), 083530-1–083530-11 | DOI | MR

[12] Järv L., Kuusk P., Saal M., “Scalar-tensor cosmologies with a potential in the general relativity limit: phase space view”, Phys. Rev. D, 81:10 (2010), 104007-1–104007-10 | DOI | MR

[13] Järv L., Kuusk P., Saal M., “Scalar-tensor cosmologies with a potential in the general relativity limit: time evolution”, Phys. Lett. B, 694:1 (2010), 1–5 | DOI | MR

[14] Esposito-Farese G., Polarski D., “Scalar-tensor gravity in an accelerating universe”, Phys. Rev. D, 63:6 (2001), 063504-1–063504-20 | DOI

[15] Lyagina L. S., “Integral'nye krivye uravneniya $y'=\frac{ax^2+bxy+cy^2}{dx^2+exy+fy^2}$”, Uspekhi Mat. Nauk, 6:2(42) (1951), 171–183 | MR | Zbl