Quantization of Bianchi type universe

Astronomy and Astrophysics – Astrophysics

Scientific paper

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Scientific paper

In this paper we have used the square root formulation of the Wheeler-De Witt equation to quantize a minisuperspace consisting of the Bianchi Type-I universe and a source of radiation field. We have derived a wavefunction of the universe with a conserved current and a positive-definite probability density. We have also explored the quantization of Bianchi Type-III universe using a procedure similar to that used in the ordinary quantum theory in curved spacetime. We have given the wavefunction satisfied by the Wheeler-De Witt equation. Regarding the wavefunction as an operator in a minisuperspace we have not only avoided the difficulty of probabilistic interpretation in quantum cosmology, but also obtained the conclusion of multiple production of universe. We have estimated the mean numbers of various types of universes generated from nothing and shown the distribution of the generated universes to be Planckian.

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