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Can Brans-Dicke universes in five dimensions be interpreted as 4-dimensional general relativity cosmologies?

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Abstract

The 5-dimensional Jordan-Brans-Dicke cosmologies in vacuum are found for the Bianchi type I metric, their relation with general relativity cosmologies is studied. Two solutions are possible, both produce effective pressure and energy density in the 4-dimensional G.R.-universes. One is a power-law relation, with two cases, the first one is forp effeff and the other forp eff=αρeff(− 1 < α < 1) has a behaviour as the open flat universe. The second solution is an exponential only valid forp eff=−ρeff. In all cases the three-space expansion reaches infinity ast→∞ and the fifth dimension can be made to decrease approaching zero. The scalar field can increase or decrease with time.

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Benítez, J., Morales, A.N. & Obregón, O. Can Brans-Dicke universes in five dimensions be interpreted as 4-dimensional general relativity cosmologies?. Astrophys Space Sci 182, 221–225 (1991). https://doi.org/10.1007/BF00645002

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Keywords

  • Energy Density
  • General Relativity
  • Scalar Field
  • Effective Pressure
  • Bianchi Type