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This paper introduces the Wheeler-Dewitt (W-D) equation in the five-dimensional R+R2 theory of gravity, and gets solutions of the W-D equation by separation of variables. Using the Kaluza-Klein theory, the Robertson-Walker metric is extended to the five-dimensional spacetime. With the field equations of the spacetime, the relationship between energy and the cosmological term can be obtained.
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Keywords:
- Wheeler-Dewitt equation /
- cosmological term /
- five-dimensional spacetime /
- metric
[1] [1]Whitt B 1984 Phys. Lett. B 145 176
[2] [2]Pimentel L O, Stein-Schabes J 1989 Phys. Lett. B 216 27
[3] [3]Kasper U 1993 Class. Quan. Grav. 7 L17
[4] [4]Li X Z, Yuan N Y, Liu D J, Hao J G 2000 Acta Phys. Sin. 49 1031 (in Chinese) [李新洲、袁宁一、刘道军、郝建纲 2000 49 1031]
[5] [5]Shao D, Shao L, Shao C G, Chen Y H 2004 Acta Phys. Sin. 53 367 (in Chinese) [邵丹、邵亮、邵常贵、陈贻汉 2004 物2理学报 53 367]
[6] [6]Fujii Y, Maeda K I 2003 The Scalar-Tensor Theory of Gravitation (Cammbridge: Cammbridge University Press) p2
[7] [7]Brans C, Dicke R H 1961 Phys. Rev. 124 925
[8] [8]Abbott L F, Deser S 1982 Nucl. Phys. B 195 76
[9] [9]Weinberg S 1972 Gravitation and Cosmology (New York: Wiley) p468
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[1] [1]Whitt B 1984 Phys. Lett. B 145 176
[2] [2]Pimentel L O, Stein-Schabes J 1989 Phys. Lett. B 216 27
[3] [3]Kasper U 1993 Class. Quan. Grav. 7 L17
[4] [4]Li X Z, Yuan N Y, Liu D J, Hao J G 2000 Acta Phys. Sin. 49 1031 (in Chinese) [李新洲、袁宁一、刘道军、郝建纲 2000 49 1031]
[5] [5]Shao D, Shao L, Shao C G, Chen Y H 2004 Acta Phys. Sin. 53 367 (in Chinese) [邵丹、邵亮、邵常贵、陈贻汉 2004 物2理学报 53 367]
[6] [6]Fujii Y, Maeda K I 2003 The Scalar-Tensor Theory of Gravitation (Cammbridge: Cammbridge University Press) p2
[7] [7]Brans C, Dicke R H 1961 Phys. Rev. 124 925
[8] [8]Abbott L F, Deser S 1982 Nucl. Phys. B 195 76
[9] [9]Weinberg S 1972 Gravitation and Cosmology (New York: Wiley) p468
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