Homogeneous noncommutative quantum cosmology

Using the Groenewold-Moyal product, the noncommutative Bianchi IX model is constructed by imposing commutation relations on the minisuperspace variables $(\Omega ,{\beta }_{+},{\beta }_{-})$. A noncommutative “wormhole” solution to the corresponding Wheeler-DeWitt equation is constructed and its behavior at fixed $\Omega$ is analyzed.

Figure 1

Probability $|\Psi (1,{\beta }_{+},{\beta }_{-}){|}_{\mathrm{NC}}^2$ of the state function of the universe with $|{\theta }_c^{\pm }|=\frac{e^2}{2}\approx 3.69$.