Quantization of the Bianchi type universe

In this paper, we have used a square root formulation of the Wheeler-De Witt equation to quantize a minisuperspace model consisting of the Bianchi-I type universe with a radiation field source. We have derived a wavefunction with a conserved current and a positive-definite probability density.

We have also explored the third quantization of the Bianchi type universe using a procedure usual in the quantum field theory of curved space-time. We have given the wave function that satisfies the Wheeler-De Witt equation. By regarding the wave function as the universe field operator in a minisuperspace, we have not only circumvented the difficulty of a probabilistic interpretation in quantum cosmology, we have also reached the conclusion that multiple universes would result. We have estimated the average number of universes produced from ‘nothing’, and have given their distribution, which turned out to be a Planck distribution.