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QUANTUM ANALYSIS FOR THE EVOLUTION OF THE COSMOLOGICAL CONSTANT VIA UNITARY TRANSFORMATION

JEONG RYEOL CHOI

Department of Physics and Advanced Materials Science, Sun Moon University, Asan 336-708, Republic of Korea

https://doi.org/10.1142/S0218271807010602Cited by:7 (Source: Crossref)

Abstract

The expectation value of the vacuum energy density tied to the cosmological constant is derived from the non-relativistic quantum description of the reheating process using the unitary transformation method. Our research is performed for two special cases, i.e. under the assumption of two different duration terms for the radiation-dominated era. We suppose that the radiation-dominated era lasted for 3,000 years in the first case, and for a very short time so that it can be ignored in the other case. For the former case, the resulting present cosmological constant is much higher than the previously known one. However, for the latter case, it is in good agreement with that obtained from recent cosmic microwave background radiation measurements. Hence, we cannot exclude the possibility that the change of the universe from the radiation-dominated era to the matter-dominated era might have progressed very swiftly after the beginning of reheating. The analysis shows that the vacuum energy density has been dissipated by the nonconservative force acting on the coherent oscillations of the scalar field according to the expansion of the universe.

Keywords:

PACS: 98.80.Cq, 98.80.Es, 98.80.Qc

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References

A. D. Linde, J. Exp. Theor. Phys. (Lett.) 19, 5 (1974). Web of Science, Google Scholar
M. Veltman, Phys. Rev. Lett. 34, 777 (1975), DOI: 10.1103/PhysRevLett.34.777. Web of Science, ADS, Google Scholar
V. A. Rubakov and M. E. Shaposhnikov, Phys. Lett. B 125, 139 (1983). Web of Science, ADS, Google Scholar
S. Weinberg, Rev. Mod. Phys. 61, 1 (1989), DOI: 10.1103/RevModPhys.61.1. Web of Science, ADS, Google Scholar
P. Coles, Nature 433, 248 (2005), DOI: 10.1038/nature03282. Web of Science, ADS, Google Scholar
S. K. Lamoreaux, Phys. Rev. Lett. 78, 5 (1997), DOI: 10.1103/PhysRevLett.78.5. Web of Science, ADS, Google Scholar
U. Mohideen and A. Roy, Phys. Rev. Lett. 81, 4549 (1998), DOI: 10.1103/PhysRevLett.81.4549. Web of Science, ADS, Google Scholar
A. Roy, C.-Y. Lin and U. Mohideen, Phys. Rev. D 60, 111101(R) (1999). Web of Science, ADS, Google Scholar
H. B. G. Casimir, Proc. K. Ned. Akad. Wet. 51, 793 (1948). Google Scholar
D. N. Spergelet al., Astrophys. J. Suppl. 148, 175 (2003), DOI: 10.1086/377226. Web of Science, ADS, Google Scholar
M. Tegmarket al., Phys. Rev. D 69, 103501 (2004), DOI: 10.1103/PhysRevD.69.103501. Web of Science, Google Scholar
S. Hananyet al., Astrophys. J. 545, L5 (2000), DOI: 10.1086/317322. Web of Science, Google Scholar
P. de Bernardiset al., Nature 404, 955 (2000), DOI: 10.1038/35010035. Web of Science, ADS, Google Scholar
A. H. Guth, Phys. Rev. D 23, 347 (1981), DOI: 10.1103/PhysRevD.23.347. Web of Science, ADS, Google Scholar
A. D. Linde, Phys. Lett. B 108, 389 (1982). Web of Science, ADS, Google Scholar
E. W. Kolb and M. S. Turner , The Early Universe ( Addison-Wesley , New York , 1990 ) . Google Scholar
S. Mukohyama and L. Randall, Phys. Rev. Lett. 92, 211302 (2004), DOI: 10.1103/PhysRevLett.92.211302. Web of Science, ADS, Google Scholar
J. Vinet and J. M. Cline, Phys. Rev. D 71, 064011 (2005), DOI: 10.1103/PhysRevD.71.064011. Web of Science, Google Scholar
A. Gomberoff, M. Henneaux and C. Teitelboim, Phys. Rev. D 71, 063509 (2005), DOI: 10.1103/PhysRevD.71.063509. Web of Science, Google Scholar
S. Weinberg, Phys. Rev. D 61, 103505 (2000), DOI: 10.1103/PhysRevD.61.103505. Web of Science, Google Scholar
I. Zlatev, L. Wang and P. J. Steinhardt, Phys. Rev. Lett. 82, 896 (1999), DOI: 10.1103/PhysRevLett.82.896. Web of Science, ADS, Google Scholar
A. Bonanno and M. Reuter, Phys. Lett. B 527, 9 (2002). Web of Science, ADS, Google Scholar
T.-V. Domenico and L. Amendola, Phys. Rev. D 65, 063508 (2002). Google Scholar
J. R. Choi, Quantum Mechanical Treatment of Time-Dependent Hamiltonians, Doctoral Thesis, Korea University, Seoul (2001), Chap. 4 . Google Scholar
J. R. Choi, C. I. Um and S. P. Kim, J. Korean Phys. Soc. 45, 1679 (2004). Web of Science, Google Scholar
H. Maeda and T. Harada, Phys. Lett. B 607, 8 (2005). Web of Science, ADS, Google Scholar
M. Kaplinghatet al., Phys. Rev. D 59, 043514 (1999), DOI: 10.1103/PhysRevD.59.043514. Web of Science, Google Scholar
B. L. Hu, Phys. Rev. D 18, 4460 (1978), DOI: 10.1103/PhysRevD.18.4460. Web of Science, ADS, Google Scholar
D. Boyanovsky, H. J. de Vega and R. Holman, Phys. Rev. D 49, 2769 (1994), DOI: 10.1103/PhysRevD.49.2769. Web of Science, ADS, Google Scholar
P. K. Suresh, Int. J. Theore. Phys. 43, 425 (2004), DOI: 10.1023/B:IJTP.0000028875.07382.4e. Web of Science, Google Scholar
D. Y. Song, Phys. Rev. Lett. 85, 1141 (2000), DOI: 10.1103/PhysRevLett.85.1141. Web of Science, ADS, Google Scholar
F.-L. Liet al., J. Phys. A: Math. Gen. 27, 985 (1994), DOI: 10.1088/0305-4470/27/3/036. ADS, Google Scholar
J. R. Choi, Int. J. Mod. Phys. B 18, 2307 (2004), DOI: 10.1142/S0217979204026135. Link, Web of Science, ADS, Google Scholar
M. A. Marchiolli and S. S. Mizrahi, J. Phys. A: Math. Gen. 30, 2619 (1997), DOI: 10.1088/0305-4470/30/8/011. ADS, Google Scholar
J. R. Choi and K. H. Yeon, Int. J. Mod. Phys. B 19, 2213 (2005), DOI: 10.1142/S0217979205029845. Link, Web of Science, ADS, Google Scholar
H. R. Lewis Jr. and W. B. Riesenfeld, J. Math. Phys. 10, 1458 (1969), DOI: 10.1063/1.1664991. Web of Science, ADS, Google Scholar
S. Zhanget al., J. Korean Phys. Soc. 40, 325 (2002). Web of Science, Google Scholar
S. Zhanget al., Phys. Lett. A 294, 319 (2002), DOI: 10.1016/S0375-9601(02)00062-2. Web of Science, ADS, Google Scholar
C. Degli Esposti Boschi, L. Ferran and H. R. Lewis Jr., Phys. Rev. A 61, 010101(R) (1999), DOI: 10.1103/PhysRevA.61.010101. Web of Science, Google Scholar
K. H. Yeonet al., Phys. Rev. A 38, 6224 (1988), DOI: 10.1103/PhysRevA.38.6224. Web of Science, ADS, Google Scholar
J. H. Gweon and J. R. Choi, J. Korean Phys. Soc. 42, 325 (2003). Web of Science, Google Scholar
C. M. A. Dantas, I. A. Pedrosa and B. Baseia, Phys. Rev. A 45, 1320 (1992), DOI: 10.1103/PhysRevA.45.1320. Web of Science, ADS, Google Scholar
X.-C. Gaoet al., Phys. Rev. D 53, 4374 (1996), DOI: 10.1103/PhysRevD.53.4374. Web of Science, ADS, Google Scholar
J. R. Choi, Mod. Phys. Lett. B 17, 1365 (2003), DOI: 10.1142/S021798490300644X. Link, Web of Science, ADS, Google Scholar
K. H. Yeonet al., J. Phys. A: Math. Gen. 34, 7719 (2001), DOI: 10.1088/0305-4470/34/37/321. ADS, Google Scholar
O. Bertolami, Il Nuovo Cimento B 93, 36 (1986), DOI: 10.1007/BF02728301. Web of Science, ADS, Google Scholar
O. Bertolami, Fortschr. Phys. 34, 829 (1986). Web of Science, Google Scholar
M. S. Berman and M. M. Som, Int. J. Theor. Phys. 29, 1411 (1990), DOI: 10.1007/BF00674120. Web of Science, Google Scholar
M. S. Berman, M. M. Som and F. de Mello Gomide, Gen. Relativ. Gravit. 21, 287 (1989), DOI: 10.1007/BF00764101. Web of Science, ADS, Google Scholar
M. S. Berman, Int. J. Theor. Phys. 29, 567 (1990), DOI: 10.1007/BF00672031. Web of Science, Google Scholar
M. S. Berman, Int. J. Theor. Phys. 29, 1419 (1990), DOI: 10.1007/BF00674122. Web of Science, Google Scholar
M. S. Berman, Phys. Rev. D 43, 1075 (1991), DOI: 10.1103/PhysRevD.43.1075. Web of Science, Google Scholar
M. S. Berman, Int. J. Theor. Phys. 31, 1217 (1992), DOI: 10.1007/BF00673922. Web of Science, Google Scholar
M. S. Berman, Int. J. Theor. Phys. 31, 1451 (1992), DOI: 10.1007/BF00673978. Web of Science, Google Scholar
J. Stelmach, Phys. Rev. D 53, 7362 (1996), DOI: 10.1103/PhysRevD.53.7362. Web of Science, ADS, Google Scholar
C. Brans and R. Dicke, Phys. Rev. 124, 925 (1961), DOI: 10.1103/PhysRev.124.925. Web of Science, ADS, Google Scholar
A. Berera, Nucl. Phys. B (Proc. Suppl.) 117, 135 (2003), DOI: 10.1016/S0920-5632(03)90509-3. ADS, Google Scholar
G. Whitrow, Nature 158, 165 (1946), DOI: 10.1038/158165b0. Web of Science, ADS, Google Scholar
G. Whitrow and D. Randall, Mon. Not. R. Astron. Soc. 111, 455 (1951). Web of Science, ADS, Google Scholar
S. P. Kim, (1995) , hep-th/9511082v1 . Google Scholar