Abstract
Applying the Jacobi method of second variation to the Bianchi IX system in Misner variables (), we specialize to the Taub space background () and obtain the governing equations for linearized homogeneous perturbations () thereabout. Employing a canonical transformation, we isolate two decoupled gauge-invariant linearized variables ( and ), together with their conjugate momenta and linearized Hamiltonians. These two linearized Hamiltonians are of time-dependent harmonic oscillator form, and we quantize them to get time-dependent Schrödinger equations. For the case of , we are able to solve for the discrete solutions and the exact quantum squeezed states.
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