Quantum Newtonian cosmology revisited

TL;DR

This paper revisits Newtonian cosmology by incorporating a cosmological constant, deriving the Hamiltonian via affine quantization, and providing wave functions and eigenvalues for a matter-dominated universe with negative cosmological constant.

Contribution

It introduces a quantum formulation of Newtonian cosmology with a cosmological constant using affine quantization, deriving the Hamiltonian and wave functions.

Findings

Derived the Hamiltonian operator for Newtonian cosmology with a cosmological constant.

Obtained wave functions and eigenvalues for a matter-dominated universe with negative cosmological constant.

Demonstrated the application of affine quantization to cosmological models.

Abstract

We formulate the Lagrangian of the Newtonian cosmology where the cosmological constant is also introduced. Following the affine quantization procedure, the Hamiltonian operator is derived. The wave functions of the Newtonian universe and the corresponding eigenvalues for the case of matter dominated by a negative cosmological constant are given.