Construction of exact solutions in two-field cosmological models

S. Yu. Vernov

S. Yu. Vernov

Teoretičeskaâ i matematičeskaâ fizika, Tome 155 (2008) no. 1, pp. 47-61 Cet article a éte moissonné depuis la source Math-Net.Ru

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Résumé

We construct a dark energy model with a phantom scalar field, a standard scalar field, and a polynomial potential inspired by string field theory. We find a two-parameter set of exact solutions of the Friedmann equations. We find a potential satisfying the conditions obtained from the string theory and such that at large times, some of the exact solutions correspond to the state parameter $w_{\mathrm{DE}}>-1$ while the others correspond to $w_{\mathrm{DE}}<-1$. We demonstrate that the superpotential method is very effective for seeking new exact solutions.

Keywords: string field theory, cosmology, phantom, dark energy, superpotential method.
Mots-clés : exact solution

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     author = {S. Yu. Vernov},
     title = {Construction of exact solutions in two-field cosmological models},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {47--61},
     year = {2008},
     volume = {155},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2008_155_1_a4/}
}

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S. Yu. Vernov. Construction of exact solutions in two-field cosmological models. Teoretičeskaâ i matematičeskaâ fizika, Tome 155 (2008) no. 1, pp. 47-61. http://geodesic.mathdoc.fr/item/TMF_2008_155_1_a4/

Bibliographie
Cité par

[1] A. Riess et al., Astron. J., 116:3 (1998), 1009–1038 ; arXiv: astro-ph/9805201 | DOI

[2] D. N. Spergel et al., Astrophys. J. Suppl. Ser., 148:1 (2003), 175–194 ; ; Astrophys. J. Suppl. Ser., 170:2 (2007), 377–408 ; arXiv: astro-ph/0302209 arXiv: astro-ph/0603449 | DOI | DOI

[3] M. Tegmark et al., Phys. Rev. D, 69:10 (2004), 103501 ; arXiv: astro-ph/0310723 | DOI

[4] P. Astier et al., Astron. Astrophys., 447:1 (2006), 31–48 ; arXiv: astro-ph/0510447 | DOI

[5] E. J. Copeland, M. Sami, Sh. Tsujikawa, Internat. J. Modern Phys. D, 15:11 (2006), 1753–1935 ; arXiv: hep-th/0603057 | DOI | MR | Zbl

[6] Y. Gong, A. Wang, Phys. Rev. D, 75 (2007), 043520 ; arXiv: astro-ph/0612196 | DOI

[7] U. Alam, V. Sahni, A. A. Starobinsky, J. Cosmol. Astropart. Phys., 2007, no. 02, 011 ; arXiv: astro-ph/0612381 | DOI

[8] V. Sahni, A. A. Starobinsky, Internat. J. Modern Phys. D, 15:12 (2006), 2105–2132 ; arXiv: astro-ph/0610026 | DOI | MR | Zbl

[9] U. Alam, V. Sahni, T. D. Saina, A. A. Starobinsky, Mon. Not. R. Astron. Soc., 354:1 (2004), 275–291 ; arXiv: astro-ph/0311364 | DOI

[10] A. Vikman, Phys. Rev. D, 71:2 (2005), 023515 ; arXiv: astro-ph/0407107 | DOI

[11] Sh. Nojiri, S. D. Odintsov, J. Phys., 66:1 (2007), 012005 ; ; Phys. Lett. B, 639:3–4 (2006), 144–150 ; ; Gen. Relativ. Gravitation, 38:8 (2006), 1285–1304 ; ; Phys. Rev. D, 72:2 (2005), 023003 ; arXiv: hep-th/0611071 arXiv: hep-th/0606025 arXiv: hep-th/0506212 arXiv: hep-th/0505215 | DOI | MR | DOI | DOI | MR | Zbl | DOI | MR

[12] Sh. Nojiri, S. D. Odintsov, Sh. Tsujikawa, Phys. Rev. D, 71:6 (2005), 063004 ; ; Sh. Tsujikawa, Phys. Rev. D, 72:8 (2005), 083512 ; ; S. Nesseris, L. Perivolaropoulos, J. Cosmol. Astropart. Phys., 2007, no. 01, 018 ; ; R. Gannouji, D. Polarski, A. Ranquet, A. A. Starobinsky, J. Cosmol. Astropart. Phys., 2006, no. 09, 016 ; ; В. А. Рубаков, ТМФ, 149:3 (2006), 409–426 ; ; H. Mohseni Sadjadi, M. Alimohammadi, Phys. Rev. D, 74:10 (2006), 103007 ; ; M. Alimohammadi, H. Mohseni Sadjadi, Phys. Lett. B, 648:2–3 (2007), 113–118 ; ; H. Mohseni Sadjadi, M. Alimohammadi, Phys. Rev. D, 74:4 (2006), 043506 ; ; P. S. Apostolopoulos, N. Tetradis, Phys. Rev. D, 74:6 (2006), 064021 ; ; V. Sahni, Yu. Shtanov, J. Cosmol. Astropart. Phys., 2003, no. 11, 014 ; ; Wen Zhao, Yang Zhang, Phys. Rev. D, 73:12 (2006), 123509 ; ; Bo Feng, Xiulian Wang, Xinmin Zhang, Phys. Lett. B, 607:1–2 (2005), 35–41 ; ; Zong-Kuan Guo, Yun-Song Piao, Xinmin Zhang, Yuan-Zhong Zhang, Phys. Lett. B, 608:3–4 (2005), 177–182 ; ; Xiao-Fei Zhang, Hong Li, Yun-Song Piao, Modern Phys. Lett. A, 21:3 (2006), 231–241 ; ; Ming-zhe Li, Bo Feng, Xin-min Zhang, J. Cosmol. Astropart. Phys., 2005, no. 12, 002 ; ; Hrvoje Stefancic, Phys. Rev. D, 71:12 (2005), 124036 ; ; Rong-Gen Cai, Hong-Sheng Zhang, Anzhong Wang, Commun. Theor. Phys., 44 (2005), 948 ; ; Yi-Fu Cai, Hong Li, Yun-Song Piao, Xinmin Zhang, Phys. Lett. B, 646:4 (2007), 141–144 ; ; Xin Zhang, Phys. Rev. D, 74:10 (2006), 103505 ; ; Hongsheng Zhang, Zong-Hong Zhu, Phys. Rev. D, 75:2 (2007), 023510 ; arXiv: hep-th/0501025 arXiv: astro-ph/0508542 arXiv: astro-ph/0610092 arXiv: astro-ph/0606287 arXiv: hep-th/0604153 arXiv: gr-qc/0610080 arXiv: gr-qc/0608016 arXiv: gr-qc/0605143 arXiv: hep-th/0604014 arXiv: astro-ph/0202346 arXiv: astro-ph/0604460 arXiv: astro-ph/0404224 arXiv: astro-ph/0410654 arXiv: astro-ph/0501652 arXiv: hep-ph/0503268 arXiv: astro-ph/0504518 arXiv: hep-th/0505186 arXiv: gr-qc/0609039 arXiv: astro-ph/0609699 arXiv: astro-ph/0611834 | DOI | MR | DOI | MR | DOI | MR | DOI | DOI | MR | DOI | DOI | DOI | MR | DOI | DOI | MR | DOI | DOI | DOI | MR | DOI | DOI | DOI | DOI | DOI | MR | Zbl | DOI | MR | DOI | MR

[13] A. A. Andrianov, F. Cannata, A. Yu. Kamenshchik, J. Phys. A, 39:32 (2006), 9975–9982 ; arXiv: gr-qc/0604126 | DOI | MR | Zbl

[14] I. Ya. Aref'eva, A. S. Koshelev, JHEP, 2007, no. 02, 041 ; arXiv: hep-th/0605085 | DOI

[15] V. K. Onemli, R. P. Woodard, Class. Q. Grav., 19:17 (2002), 4607–4626 ; ; S. M. Carroll, M. Hoffman, M. Trodden, Phys. Rev. D, 68:2 (2003), 023509 ; ; St. D. H. Hsu, A. Jenkins, M. B. Wise, Phys. Lett. B, 597:3–4 (2004), 270–274 ; ; R. V. Buniy, St. D. H. Hsu, B. M. Murray, Phys. Rev. D, 74:6 (2006), 063518 ; ; B. McInnes, Nucl. Phys. B, 718:1–2 (2005), 55–82 ; ; V. Gorini, A. Yu. Kamenshchik, U. Moschella, V. Pasquier, A. A. Starobinsky, Phys. Rev. D, 72:10 (2005), 103518 ; ; E. O. Kahya, V. K. Onemli, Phys. Rev. D, 76:4 (2007), 043512 ; arXiv: gr-qc/0204065 arXiv: astro-ph/0301273 arXiv: astro-ph/0406043 arXiv: hep-th/0606091 arXiv: hep-th/0502209 arXiv: astro-ph/0504576 arXiv: gr-qc/0612026 | DOI | MR | Zbl | DOI | DOI | DOI | MR | DOI | MR | Zbl | DOI | DOI | MR

[16] I. Ya. Aref'eva, I. V. Volovich, On the null energy condition and cosmology, arXiv: hep-th/0612098

[17] I. Ya. Aref'eva, “Nonlocal string tachyon as a model for cosmological dark energy”, $p$-Adic Mathematical Physics: 2nd International Conference, AIP Conf. Proc., 826, eds. A. Yu. Khrennikov, Z. Rakic, I. V. Volovich, Amer. Inst. Phys., Melville, NY, 2006, 301–311 ; arXiv: astro-ph/0410443 | DOI | MR | Zbl

[18] I. Ya. Arefeva, A. S. Koshelev, S. Yu. Vernov, TMF, 148:1 (2006), 23–41 ; arXiv: astro-ph/0412619 | DOI | MR | Zbl

[19] A. Sen, Internat. J. Modern Phys. A, 20:24 (2005), 5513–5656 ; ; K. Ohmori, A review on tachyon condensation in open string field theories, ; I. Ya. Aref'eva, D. M. Belov, A. A. Giryavets, A. S. Koshelev, P. B. Medvedev, “Noncommutative field theories and (super)string field theories”, Particles and Fields, Proc. 11th Jorge André Swieca summer school (São Paulo, Brazil, January 14–27, 2001), ed. A. V. Gilvan, World Scientific, Singapore, 2002, 1–164 ; ; W. Taylor, Lectures on D-branes, tachyon condensation an string field theory, arXiv: hep-th/0410103 arXiv: hep-th/0102085 arXiv: hep-th/0111208 arXiv: hep-th/0301094 | DOI | MR | Zbl | DOI | MR | Zbl | MR

[20] I. Ya. Aref'eva, A. S. Koshelev, S. Yu. Vernov, Phys. Rev. D, 72:6 (2005), 064017 ; arXiv: astro-ph/0507067 | DOI

[21] I. Ya. Aref'eva, L. V. Joukovskaya, JHEP, 2005, no. 10, 087 ; arXiv: hep-th/0504200 | DOI | MR

[22] L. V. Joukovskaya, Ya. I. Volovich, Energy flow from open to closed strings in a toy model of rolling tachyon, arXiv: math-ph/0308034

[23] I. Ya. Aref'eva, A. S. Koshelev, S. Yu. Vernov, Phys. Lett. B, 628:1–2 (2005), 1–10 ; arXiv: astro-ph/0505605 | DOI

[24] I. Ya. Aref'eva, A. S. Koshelev, S. Yu. Vernov, Bulg. J. Phys., 33:Suppl. 1 (2006), 360–367 | MR | Zbl

[25] I. Ya. Arefeva, D. M. Belov, A. S. Koshelev, P. B. Medvedev, Nucl. Phys. B, 638:1–2 (2002), 3–20 ; arXiv: hep-th/0011117 | DOI | MR | Zbl

[26] I. Ya. Arefeva, D. M. Belov, A. S. Koshelev, P. B. Medvedev, Nucl. Phys. B, 638:1–2 (2002), 21–40 ; arXiv: hep-th/0107197 | DOI | MR | Zbl

[27] E. Witten, Nucl. Phys. B, 268:2 (1986), 253–294 | DOI | MR

[28] I. Ya. Aref'eva, P. B. Medvedev, A. P. Zubarev, Phys. Lett. B, 240:3–4 (1990), 356–362 | DOI | MR

[29] C. R. Preitschopf, C. B. Thorn, S. A. Yost, Nucl. Phys. B, 337:2 (1990), 363–433 | DOI | MR

[30] N. Berkovits, A. Sen, B. Zwiebach, Nucl. Phys. B, 587:1–3 (2000), 147–178 ; arXiv: hep-th/0002211 | DOI | MR | Zbl

[31] I. Ya. Aref'eva, L. V. Joukovskaya, A. S. Koshelev, JHEP, 2003, no. 9, 012 ; ; I. Ya. Aref'eva, Fortschr. Phys., 51:7–8 (2003), 652–657 arXiv: hep-th/0301137 | DOI | MR | DOI | MR | Zbl

[32] K. Ohmori, Phys. Rev. D, 69:2 (2004), 026008 ; arXiv: hep-th/0306096 | DOI | MR

[33] B. Zwiebach, Ann. Phys., 267:2 (1998), 193–248 ; arXiv: hep-th/9705241 | DOI | MR | Zbl

[34] O. DeWolfe, D. Z. Freedman, S. S. Gubser, A. Karch, Phys. Rev. D, 62:4 (2000), 046008 ; arXiv: hep-th/9909134 | DOI | MR

[35] A. G. Muslimov, Class. Q. Grav., 7:2 (1990), 231–237 | DOI | MR

[36] D. S. Salopek, J. R. Bond, Phys. Rev. D, 42:12 (1990), 3936–3962 | DOI | MR

[37] A. R. Liddle, D. H. Lyth, Cosmological Inflation and Large-Scale Structure, Cambridge University Press, Cambridge, 2000 | MR | Zbl

[38] D. Bazeia, M. J. dos Santos, R. F. Ribeiro, Phys. Lett. A, 208:1–2 (1995), 84–88 ; arXiv: hep-th/0311265 | DOI | MR | Zbl

[39] D. Bazeia, F. A. Brito, Phys. Rev. D, 61:10 (2000), 105019 ; arXiv: hep-th/9912015 | DOI | MR

[40] A. Brandhuber, K. Sfetsos, JHEP, 1999, no. 10, 013 ; arXiv: hep-th/9908116 | DOI | MR | Zbl

[41] E. B. Bogomolnyi, YaF, 24:4 (1976), 861–870 | MR

[42] D. Bazeia, C. B. Gomes, L. Losano, R. Menezes, Phys. Lett. B, 633:4–5 (2006), 415–419 ; ; D. Bazeia, L. Losano, J. J. Rodrigues, First-order formalism for scalar field in cosmology, arXiv: astro-ph/0512197 arXiv: hep-th/0610028 | DOI | MR | Zbl

[43] D. Bazeia, L. Losano, J. J. Rodrigues, R. Rosenfeld, First-order formalism for dust, arXiv: astro-ph/0611770

[44] A. S. Mikhailov, Yu. S. Mikhailov, M. N. Smolyakov, I. P. Volobuev, Class. Q. Grav., 24:1 (2007), 231–242 ; arXiv: hep-th/0602143 | DOI | MR | Zbl

[45] Yi-Fu Cai, Taotao Qiu, Yun-Song Piao, Mingzhe Li, Xinmin Zhang, JHEP, 2007, no. 10, 071 ; arXiv: 0704.1090 | DOI

[46] I. Ya. Aref'eva, L. V. Joukovskaya, S. Yu. Vernov, JHEP, 2007, no. 07, 087 ; ; Dynamics in nonlocal linear models in the Friedmann–Robertson–Walker metric, arXiv: hep-th/0701184 arXiv: 0711.1364 | DOI | MR

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