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2024年10月30日
Chinese Physics C> 2011, Vol. 35> Issue(3) : 233-242 DOI: 10.1088/1674-1137/35/3/005

An approach to dark energy problem through linear invariants

  •  Department of Radiologic Technology, Daegu Health College, Taejeon 1-dong, Buk-gu, Daegu 702-722, Republic of Korea;2. Division of Semiconductor and Display Engineering, College of IT Engineering, Kyungpook National University, Daegu 702-701, Republic of Korea

  • The time evolution of vacuum energy density is investigated in the coherent states of inflationary universe using a linear invariant approach. The linear invariants we derived are represented in terms of annihilation operators. On account of the fact that the coherent state is an eigenstate of an annihilation operator, the wave function in the coherent state is easily evaluated by solving the eigenvalue equation of the linear invariants. The expectation value of the vacuum energy density is derived using this wave function. Fluctuations of the scalar field and its conjugate momentum are also investigated. Our theory based on the linear invariant shows that the vacuum energy density of the universe in a coherent state is decreased continuously with time due to nonconservative force acting on the coherent oscillations of the scalar field, which is provided by the expansion of the universe. In effect, our analysis reveals that the vacuum energy density decreases in proportion to tβ where β is 3/2 for radiation-dominated era and 2 for matter-dominated era. In the case where the duration term of radiation-dominated era is short enough to be negligible, the estimation of the relic vacuum energy density agrees well with the current observational data.
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    [1] Scranton R et al. (SDSS collaboration). Preprint astro-ph/0307335 (2003)2 Riess A G et al. (Supernova Search Team collaboration). Astron. J., 2003, 116: 10093 Perlmutter S et al. (Supernova Cosmology Project collab-oration). Astrophys. J., 1999, 517: 5654 Goldhaber G et al. (The Supernova Cosmology Project collaboration). Astrophys. J., 2001, 558: 3595 Tonry J L et al. (Supernova Search Team collaboration). Astrophys. J., 2003, 594: 16 Riess A G et al. (Supernova Search Team collaboration). Astrophys. J., 2004, 607: 6657 Riess A G et al. Astrophys. J., 2007, 659: 988 Astier P et al. (SNLS collaboration). Astron. Astrophys., 2006, 447: 319 Masi S et al. Prog. Part. Nucl. Phys., 2002, 48: 24310 Spergel D N et al. Astrophys. J. Supp., 2003, 148: 17511 Tegmark M et al. Phys. Rev. D, 2004, 69: 10350112 Choi J R. Int. J. Mod. Phys. D, 2007, 16: 111913 Guth A H, PI S Y. Phys. Rev. D, 1985, 32: 189914 GAO X C, GAO J, QIAN T Z, XU J B. Phys. Rev. D, 1996, 53: 437415 Guven J, Lieberman B, Hill C T. Phys. Rev. D, 1989, 39: 43816 Abe S. Phys. Rev. D, 1993, 47: 71817 Bertoni C, Finelli F, Venturi G. Phys. Lett. A, 1998, 237: 33118 Pedrosa I A, Furtado C, Rosas A. Phys. Lett. B, 2007, 651: 38419 Choi J R, Um C I, Kim S P. J. Korean Phys. Soc., 2004, 45: 167920 Kim S P. Preprint hep-th/9511082v1, 199521 Farley A N St J, D'Eath P D. Phys. Lett. B, 2006, 634: 41922 Blome H J, Wilson T L. Adv. Space Res., 2005, 35: 11123 Kiefer C. Nucl. Phys. B, 1990, 341: 27324 Matacz A L. Phys. Rev. D, 1994, 49: 78825 Berger B K. Phys. Rev. D, 1982, 25: 220826 Guth A, Steinhardt P. The in ationary universe, In P. C. W. Davies (Ed.), The New Physics. Cambridge: Cambridge University Press, 1989. 34-6027 Abdalla M S, Choi J R. Ann. Phys. (NY), 2007, 322: 279528 Abdalla M S, Leach P G L. J. Phys. A: Math Gen., 2005, 38: 88129 Schrade G, Man'ko V I, Schleich W P, and Glauber R J. Quantum Semicl. Opt., 1995, 7: 30730 GAO X C, XU J B, QIAN T Z. Phys. Rev. A, 1991, 44: 701631 GAO X C, XU J B, QIAN T Z. Ann. Phys. (NY), 1990, 204: 23532 de Lima A L, Rosas A, Pedrosa I A. Ann. Phys. (NY), 2008, 323: 225333 Straumann N. Lect. Notes Phys., 2007, 721: 32734 Maeda H, Harada T. Phys. Lett. B, 2005, 607: 835 Kaplinghat M, Steigman G, Tkachev I, Walker T P. Phys. Rev. D, 1999, 59: 04351436 Kolb E W, Turner M S. The Early Universe. New York: Addison-Wesley, 199037 HU B L. Phys. Rev. D, 1978, 18: 446038 Boyanovsky D, de Vega H J, Holman R. Phys. Rev. D, 1994, 49: 276939 SONG D Y. Phys. Rev. Lett., 2000, 85: 114140 Glauber R J. Phys. Rev., 1963, 131: 276641 Ali S T, Antoine J P, Gazeau J P. Coherent StatesWavelets and Their Generalisation. New York: Springer-Verlag, 200042 Tara K, Agarwal G S. Phys. Rev. A, 1994, 50: 287043 Sakharov A. Zh. Eksp. Teor. Fiz., 1965, 49: 24544 MarchiolliM A, Mizrahi S S. J. Phys. A: Math. Gen., 1997, 30: 261945 Choi J R, Yeon K H. Int. J. Mod. Phys. B, 2005, 19: 221346 Cohen H. Mathematics for Scientists Engineers. New Jersey: Prentice-Hall, 1992. 380-38147 Louisell W H. Quantum Statistical Properties of Radia-tion. New York: John Wiley and Sons, 197348 Choi J R, Kim D W. J. Korean Phys. Soc., 2004, 45: 142649 Whitrow G. Nature, 1946, 158: 16550 Amendola L, Tsujikawa S, Sami M. Phys. Lett. B, 2006, 632: 15551 Pavon D, Zimdahl W. Phys. Lett. B, 2005, 628: 20652 Olivares G, Atrio-Barandela F, Pavon D. Phys. Rev. D, 2006, 74: 04352153 WANG B, ZANG J, LIN C Y, Abdalla E, Micheletti S. Nucl. Phys. B, 2007, 778: 6954 Das S, Corasaniti P S, Khoury J. Phys. Rev. D, 2006, 73: 08350955 Coles P. Nature, 2005, 433: 24856 Weinberg S. Rev. Mod. Phys., 1989, 61: 157 Harrison E. Cosmology. Cambridge: Cambridge Univ. Press, 2000. 458-47358 McCabe G. Stud. Hist. Philos. Mod. Phys., 2005, 36: 67

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Jeong Ryeol. An approach to dark energy problem through linear invariants[J]. Chinese Physics C, 2011, 35(3): 233-242. doi: 10.1088/1674-1137/35/3/005
Jeong Ryeol. An approach to dark energy problem through linear invariants[J]. Chinese Physics C, 2011, 35(3): 233-242.  doi: 10.1088/1674-1137/35/3/005 shu
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Received: 2010-05-13
Revised: 2010-06-12
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An approach to dark energy problem through linear invariants

  • Department of Radiologic Technology, Daegu Health College, Taejeon 1-dong, Buk-gu, Daegu 702-722, Republic of Korea;2. Division of Semiconductor and Display Engineering, College of IT Engineering, Kyungpook National University, Daegu 702-701, Republic of Korea
  • Received Date: 2010-05-13
  • Accepted Date: 2010-06-12
  • Available Online: 2011-03-05

Abstract: The time evolution of vacuum energy density is investigated in the coherent states of inflationary universe using a linear invariant approach. The linear invariants we derived are represented in terms of annihilation operators. On account of the fact that the coherent state is an eigenstate of an annihilation operator, the wave function in the coherent state is easily evaluated by solving the eigenvalue equation of the linear invariants. The expectation value of the vacuum energy density is derived using this wave function. Fluctuations of the scalar field and its conjugate momentum are also investigated. Our theory based on the linear invariant shows that the vacuum energy density of the universe in a coherent state is decreased continuously with time due to nonconservative force acting on the coherent oscillations of the scalar field, which is provided by the expansion of the universe. In effect, our analysis reveals that the vacuum energy density decreases in proportion to tβ where β is 3/2 for radiation-dominated era and 2 for matter-dominated era. In the case where the duration term of radiation-dominated era is short enough to be negligible, the estimation of the relic vacuum energy density agrees well with the current observational data.

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