Speaker
Description
Although the universe presently looks homogenous and isotropic at cosmological scales, there exist small-scale inhomogeneities and anisotropies. In fact, Bianchi had proposed a few anisotropic classical models of the universe which are important in the context of quantum cosmology. In particular, anisotropy is expected to be prominent during the early phase of the universe when it was dominated by quantum mechanical fluctuations.
In this work, we consider the Bianchi type I model of the universe in the Wheeler-DeWitt quantization scheme with the matter field represented by a scalar field $\phi$. Consequently, the quantum mechanical equation of the universe is obtained in the minisuperspace consisting of the Misner variables $(\alpha, \beta_+, \beta_-)$ and the scalar field $\phi$. In order to obtain a self-adjoint Hamiltonian via Dirac decomposition, we choose the Misner variable $\alpha$ to play the role of time in the quantum universe. The Schrodinger-type equation so obtained involves Pauli matrices and the wavefunction of the universe becomes a two-component spinor for both expanding and contracting solutions.
We further find that the minisuperspace angular momentum operator does not commute with the Hamiltonian. Consequently, we obtain the missing part of the angular momentum so that the total angular momentum commutes with the Hamiltonian. This missing part of the angular momentum acts on the spinor space and we identify it as the spin of the quantum universe. We further note that the emergence of three-component spin vector is owing to the presence of anisotropy in the universe which is absent in any quantized isotropic models of the universe.
| vishal.phiitg@iitg.ac.in | |
| Affiliation | IIT Guwahati |
