Quantum Gravity and String Theory

   

Wave Function of the Universe Near Cosmological Singularity in Three Dimensions III

Authors: Tatsuyuki Sugawa

In this short report we investigate the wave function of the Universe near Cosmological Singularity in pure Einstein Gravity. The space time is considered in three dimensions for simplicity. We use the minisuperspace model and the canonical quantization . We extend the Hamiltonian Constraint , concretely , from H= 0 to H≈0. So we obtain the Schrodinger equation instead of the Wheeler-De Witt equation. Theresulting wave functions and the energy levels are represented by the Harmonic Oscillator. Our models treat dS spacetime ( k = 1,Λ > 0), which explains the closed expanding universe. However when we consider the neighborhood of the Big Bang Singularity, within the Planck scale, the space time has to be treated as quantum gravity. So our most interested wave function of the universe is the one near the singularity. However the identity of the Hamiltonian constraint is an open question in quantum gravity. Originally Quantum Cosmology was considered as the candidate of the quantum gravity , which is represented by the wave function instead of the metric structure.

Comments: 12 Pages.

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Submission history

[v1] 2025-10-08 18:41:01

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