Geodesic
Cosmological inflation models in the kinetic approximation
Teoretičeskaâ i matematičeskaâ fizika, Tome 191 (2017) no. 2, pp. 354-365 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider the construction of cosmological inflation models with an approximate linear dependence of the kinetic energy of the scalar field on the state parameter. We compare the obtained solutions with known cosmological models and calculate the main parameters of cosmological perturbations.
Mots-clés : inflation, cosmological perturbation.
Keywords: scalar field 
@article{TMF_2017_191_2_a15,
     author = {I. V. Fomin},
     title = {Cosmological inflation models in the~kinetic approximation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {354--365},
     year = {2017},
     volume = {191},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2017_191_2_a15/}
}
TY  - JOUR
AU  - I. V. Fomin
TI  - Cosmological inflation models in the kinetic approximation
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2017
SP  - 354
EP  - 365
VL  - 191
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2017_191_2_a15/
LA  - ru
ID  - TMF_2017_191_2_a15
ER  - 
%0 Journal Article
%A I. V. Fomin
%T Cosmological inflation models in the kinetic approximation
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2017
%P 354-365
%V 191
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2017_191_2_a15/
%G ru
%F TMF_2017_191_2_a15
I. V. Fomin. Cosmological inflation models in the kinetic approximation. Teoretičeskaâ i matematičeskaâ fizika, Tome 191 (2017) no. 2, pp. 354-365. http://geodesic.mathdoc.fr/item/TMF_2017_191_2_a15/

[1] A. A. Starobinsky, “A new type of isotropic cosmological models without singularity”, Phys. Lett. B., 91:1 (1980), 99–102 | DOI

[2] A. H. Guth, “Inflationary universe: a possible solution to the horizon and flatness problems”, Phys. Rev. D, 23:2 (1981), 347–356 | DOI

[3] S. J. Perlmutter, G. Aldering, G. Goldhaber et al. (The Supernova Cosmology Project), “Measurements of $\Omega$ and $\Lambda$ from 42 high-redshift Supernovae”, Astrophys. J., 517 (1999), 565–586, arXiv: ; A. G. Riess, A. V. Filippenko, P. Challis et al., “Observational evidence from Supernovae for an accelerating universe and a cosmological constant”, Astron. J., 116:3 (1998), 1009, arXiv: astro-ph/9812133astro-ph/9805201 | DOI | DOI

[4] A. G. Riess, L. G. Strolger, J. Tonry et al., “Type Ia supernova discoveries at $z > 1$ from the Hubble Space Telescope: evidence for past deceleration and constraints on dark energy evolution”, Astrophys. J., 607:2 (2004), 665–687, arXiv: astro-ph/0402512 | DOI

[5] D. N. Spergel, L. Verde, H. V. Peiris et al., “First-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: determination of cosmological parameters”, Astrophys. J. Suppl., 148:2 (2003), 175–194, arXiv: astro-ph/0302209 | DOI

[6] A. D. Linde, “Inflationary cosmology”, Particle Physics and Inflationary Cosmology, Proceedings of the First International Symposium (Northeastern University, Boston, MA, March 27–31, 1990), eds. P. Nath, S. Reucroft, World Sci., Singapore, 1990, 635–656 | MR

[7] A. R. Liddle, “Inflation and the cosmic microwave background”, Phys. Rep., 307:1–4 (1998), 53–60, arXiv: astro-ph/9801148 | DOI

[8] P. J. E. Peebles, A. Vilenkin, “Quintessential inflation”, Phys. Rep. D., 59:6 (1999), 063505, 6 pp., arXiv: astro-ph/9810509 | DOI

[9] R. R. Caldwell, R. Dave, P. J. Steinhardt, “Cosmological imprint of an energy component with general equation of state”, Phys. Rev. Lett., 80 (1998), 1582–1585, arXiv: astro-ph/9708069 | DOI

[10] C. Armendáriz-Picón, T. Damour, V. Mukhanov, “$k$-Inflation”, Phys. Lett. B., 458:2–3 (1999), 209–218, arXiv: hep-th/9904075 | DOI | MR | Zbl

[11] C. G. Böhmer, G. Caldera-Cabral, R. Lazkoz, R. Maartens, “Dynamics of dark energy with a coupling to dark matter”, Phys. Rev. D, 78:2 (2008), 023505, 8 pp., arXiv: 0801.1565 | DOI

[12] A. Y. Kamenshchik, U. Moschella, V. Pasquier, “An alternative to quintessence”, Phys. Lett. B., 511:2–4 (2001), 265–268, arXiv: gr-qc/0103004 | DOI | Zbl

[13] P. Singh, M. Sami, N. Dadhich, “Cosmological dynamics of a phantom field”, Phys. Rev. D, 68:2 (2003), 023522, 7 pp., arXiv: hep-th/0305110 | DOI

[14] N. C. Tsamis, R. P. Woodard, “Improved estimates of cosmological perturbations”, Phys. Rev. D, 69:8 (2004), 084005, 14 pp., arXiv: astro-ph/0307463 | DOI

[15] J. Martin, H. Motohashi, T. Suyama, “Ultra slow-roll inflation and the non-Gaussianity consistency relation”, Phys. Rev. D, 87:2 (2013), 023514, 10 pp., arXiv: 1211.0083 | DOI

[16] H. Motohashi, A. A. Starobinsky, J. Yokoyama, “Inflation with a constant rate of roll”, JCAP, 09 (2015), 018, arXiv: 1411.5021 | DOI | MR

[17] N. Bose, A. S. Majumdar, “$k$-essence model of inflation, dark matter, and dark energy”, Phys. Rev. D, 79:10 (2009), 103517, 7 pp., arXiv: 0812.4131 | DOI

[18] T. Chiba, T. Okabe, M. Yamaguchi, “Kinetically driven quintessence”, Phys. Rev. D, 62:2 (2000), 023511, 8 pp., arXiv: astro-ph/9912463 | DOI

[19] A. T. Kruger, J. W. Norbury, “Another exact inflationary solution”, Phys. Rev. D, 61:8 (2000), 087303, 4 pp., arXiv: gr-qc/0004039 | DOI

[20] G. G. Ivanov, Izv. vuzov. Ser. Fizika, 12 (1980), 22–25

[21] D. S. Salopek, J. R. Bond, “Nonlinear evolution of long-wavelength metric fluctuations in inflationary models”, Phys. Rev. D, 42:12 (1990), 3936–3962 | DOI | MR

[22] S. V. Chervon, “Inflationary cosmological models without restrictions on a scalar field potential”, Gen. Relativ. Gravit., 36:7 (2004), 1547–1553 | DOI | MR | Zbl

[23] A. V. Yurov, V. A. Yurov, S. V. Chervon, M. Sami, “Potentsial polnoi energii kak superpotentsial v integriruemykh kosmologicheskikh modelyakh”, TMF, 166:2 (2011), 299–311 | DOI | DOI | Zbl

[24] L. Kofman, A. Linde, A. A. Starobinsky, “Reheating after Inflation”, Phys. Rev. Lett., 73:24 (1994), 3195–3198, arXiv: hep-th/9405187 | DOI

[25] J. García-Bellido, “20+ years of inflation”, Nuc. Phys. B Proc. Suppl., 114 (2003), 13–26 | DOI | Zbl

[26] G. Felder, J. García-Bellido, P. B. Greene, L. Kofman, A. Linde, I. Tkachev, “Dynamics of symmetry breaking and tachyonic preheating”, Phys. Rev. Lett., 87:1 (2001), 011601, 4 pp., arXiv: hep-ph/0012142 | DOI

[27] G. Felder, L. Kofman, A. Linde, “Inflation and preheating in nonoscillatory models”, Phys. Rev.D, 60:10 (1999), 103505, 10 pp., arXiv: hep-ph/9903350 | DOI

[28] L. A. Ureña-López, M. J. Reyes-Ibarra, “On the dynamics of a quadratic scalar field potential”, Internat. J. Modern Phys. D, 18:4 (2009), 621–634, arXiv: 0709.3996 | DOI | Zbl

[29] T. J. Zhang, Y. G. Shen, “Quantum cosmology with a complex $\phi^4$ field at finite temperature”, Internat. J. Theor. Phys., 38:7 (1999), 1969–1979 | DOI | Zbl

[30] A. Linde, “Inflationary cosmology”, Inflationary Cosmology, Lecture Notes in Physics, 738, eds. M. Lemoine, J. Martin, P. Peter, Springer, Berlin, 2008, 1–54, arXiv: 0705.0164 | DOI | MR | Zbl

[31] A. Albrecht, P. Steinhardt, “Cosmology for grand unified theories with radiatively induced symmetry breaking”, Phys. Rev. Lett., 48:17 (1982), 1220–1223 | DOI

[32] V. F. Mukhanov, H. A. Feldman, R. H. Brandenberger, “Theory of cosmological perturbations”, Phys. Rep., 215:5–6 (1992), 203–333 | DOI | MR

[33] S. V. Chervon, M. Novello, R. Triay, “Exact cosmology and specification of an inflationary scenario”, Gravit. Cosmol., 11:4(44) (2005), 329–332 | Zbl

[34] S. V. Chervon, I. V. Fomin, “On calculation of the cosmological parameters in exact models of inflation”, Gravit. Cosmol., 14:2 (2008), 163–167 | DOI | MR | Zbl

[35] S. V. Chervon, I. V. Fomin, “Kvantovoe rozhdenie nachalnykh kosmologicheskikh vozmuschenii”, Izv. vuzov (Povolzhskii region). Fiz.-matem. nauki, 2008, no. 4, 97–107

[36] P. A. R. Ade, N. Aghanim, M. Arnaud et al. [Planck Collab.], “Planck 2015 results. XIII. Cosmological parameters”, Astron. Astrophys., 594 (2016), A13, 63 pp., arXiv: 1502.01589 | DOI

[37] J. D. Barrow, “Exact inflationary universes with potential minima”, Phys. Rev. D, 49:6 (1994), 3055–3058 | DOI | MR