2026/02/23 by Anonymous, Shinji Yamashita
Physics and Astronomy · Mathematics · #Noncommutative and Quantum Gravity Theories #Advanced Operator Algebra Research #Black Holes and Theoretical Physics
paper · pdf · doi:10.1103/rgj9-8r3d
We present a quantization of unimodular gravity in the connection representation for a homogeneous, isotropic, and spatially flat cosmological model without matter. In this model, the wave function is governed by a Schrödinger-type equation derived from a reduced phase space approach. Our analysis suggests that, within this minimal setting, the regularity of the operators and the self-adjointness of the Hamiltonian operator are incompatible with a negative cosmological constant. For a positive cosmological constant, the wave functions vanish at zero spatial volume. This behavior emerges as a consequence of enforcing the unimodular condition at the quantum level. Semiclassical fluctuations of the geometry are evaluated and discussed in relation to the cosmological constant problem.