Abstract
We study a spatially flat Friedmann model containing a pressureless perfect fluid (dust) and a scalar field with an unbounded from below potential of the form \(V(\varphi ) = W_0 - V_0 {\text{ sinh(}}\sqrt {{\text{3/2}}} \kappa \varphi {\text{)}}\), where the parameters W 0 and V 0 are arbitrary and \(\kappa = \sqrt {{8\pi }G_N } = M_p^{ - 1} \). The model is integrable and all exact solutions describe the recollapsing universe. The behavior of the model near both initial and final points of evolution is analyzed. The model is consistent with the observational parameters. We single out the exact solution with the present-day values of acceleration parameter q 0=0.5 and dark matter density parameter Ωρ0=0.3 describing the evolution within the time approximately equal to 2H 0 −1.
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REFERENCES
Melnikov, V. N. (1994). In Gravitation and Cosmology, (Ed.) Novello, M. Proceedings of the International Conference on Gravitation and Cosmology, Rio de Janeiro, 1993, Edition Frontieres, Singapore, p. 147.
Melnikov, V. N. (1993). Multidimensional Classical and Quantum Cosmology and Gravitation: Exact Solutions and Variations of Constants, CBPF-Notas de Fisica-051/93, Rio de Janeiro, Brazil, 93 pp.
Melnikov, V. N. (1996). In Gravitation and Cosmology II, Novello, M. (Ed.), Edition Frontieres, Singapore, p. 465.
Melnikov, V. N. (1995). Multidimensional Cosmology and Gravitation, CBPF-MO-002/95, Rio de Janeiro, Brazil, 210 pp.
Melnikov, V. N. (2002). Exact Solutions in Multidimensional Gravity and Cosmology III, CBPFMO-003/02, Rio de Janeiro, Brazil.
Ferreira, P. G., and Joice, M. (1998). Phys. Rev. D 58, 023503 (arXiv: astro-ph/9711102).
Townsend, P. K. (2001). Quintessence From M-theory (arXiv: hep-th/0110072).
Starobinsky, A. A. (1998). JETP Lett. 68, 757.
Heard, I. P. C., and Wands, D. (2002). Class. Quant. Grav. 19, 5435 (arXiv: gr-qc/0206085).
Dehnen, H., Gavrilov, V. R., and Melnikov, V. N. (2003). Grav. Cosmol. 3(35), 189 (arXiv: gr-qc/0212107).
Kallosh, R., and Linde, A. (2003). Dark Energy and the Fate of the Universe (arXiv: astroph/ 0301087).
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Gavrilov, V.R., Melnikov, V.N. & Abdyrakhmanov, S.T. Flat Friedmann Universe Filled by Dust and Scalar Field with Multiple Exponential Potential. General Relativity and Gravitation 36, 1579–1592 (2004). https://doi.org/10.1023/B:GERG.0000032150.44910.97
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DOI: https://doi.org/10.1023/B:GERG.0000032150.44910.97