A method for generating exact solutions of the equations of the scalar field dynamics in the case of flat Friedmann–Robertson–Walker space on the basis of form-invariant transformations is considered. A method for estimating the divergence of the exact and approximate solutions from the number of e-folds and the parameters of the cosmological perturbations is proposed.
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References
A. A. Starobinsky, Phys. Lett. B, 91, No. 1, 99–102 (1980).
A. H. Guth, Phys. Rev. D, 23, No. 2, 347–356 (1981).
S. J. Perlmutter, G. Aldering, G. Goldhaber, et al., Astrophys. J., 517, 565 (1999).
A. D. Linde, Particle Physics and Inflationary Cosmology, Harwood Academic Publishers, Amsterdam (1990).
A. R. Liddle, Phys. Rept., 307, 53–60 (1998).
A. R. Liddle, P. Parsons, and J. D. Barrow, Phys. Rev. D, 50, 7222–7232 (1994).
P. A. R. Ade et al., Astron. Astrophys., 594, No. A13, 11 (2016).
G. F. R. Ellis and M. S. Madsen, Class. Quantum Grav., 8, 667 (1991).
V. M. Zhuravlev, S. V. Chervon, and V. K. Shchigolev, J. Exp. Theor. Phys., 87, 223 (1998).
S. Capozziello, A. Feoli, and G. Lambiase, Int. J. Mod. Phys. D, 9, 14 (2000).
T. Harko, F. S. N. Lobo, and M. K. Mak, Eur. Phys. J. C, 74, 2784 (2014).
A. V. Yurov and V. A. Yurov, J. Math. Phys., 51, 082503 (2010).
A. G. Muslimov, Class. Quant. Grav., 7, 231 (1990).
F. E. Schunck and E. W. Mielke, Phys. Rev. D, 50, 4794 (1994).
A. T. Kruger and J. W. Norbury, Phys. Rev. D, 61, 087303 (2000).
T. Harko, F. S. N. Lobo, and M. K. Mak, Eur. Phys. J. C, 74, 2784 (2014).
T. Charters and J. P. Mimoso, J. Cosmol. Astroparticle Phys., 022, 1008 (2010).
S. V. Chervon, Gen. Relat. Grav., 7, 1547 (2004).
G. G. Ivanov, in: Gravitation and Theory of Relativity, Collection of Articles, Issue 18, Kazan University Publishing House, Kazan (1981), p. 54.
D. S. Salopec and J. R. Bond, Phys. Rev. D, 42, 3936 (1990).
R. De Ritis et al., Phys. Rev. D, 42, 1091 (1990).
S. Capozziello and M. Roshan, Phys. Lett. B, 726, 471 (2013).
N. Dimakis et. al., Phys. Rev. D, 93, No. 12, 123518 (2016).
L. P. Chimento, M. G. Richarte, and I. E. G. Sanchez, Mod. Phys. Lett. A, 28, 1250236 (2013).
S. Nojiri and S. D. Odintsov, Phys. Rep., 505, 59–144 (2010).
T. Clifton et al., Phys. Rep., 513, 1–189 (2012).
T. P. Sotiriou and V. Faraoni, Rev. Mod. Phys., 82, 451 (2010).
A. Y. Kamenshchik et al., Class. Quant. Grav., 33, No. 1, 015004 (2016).
S. V. Chervon, Quantum Matter, 2, 71–82 (2013).
S. V. Chervon, M. Novello, and R. Triay, Grav. Cosmol., 11, No. 4(44), 329–332 (2005).
S. V. Chervon and I. V. Fomin, Grav. Cosmol., 13, No. 2(50), 163–167 (2007).
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 46–56, March, 2017.
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Fomin, I.V., Chervon, S.V. Exact and Approximate Solutions in the Friedmann Cosmology. Russ Phys J 60, 427–440 (2017). https://doi.org/10.1007/s11182-017-1091-x
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DOI: https://doi.org/10.1007/s11182-017-1091-x