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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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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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