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Tunneling Newtonian Universe

Eugene B. Kolomeisky

TL;DR

The paper investigates a quantum-mechanical version of Newtonian cosmology to address the initial density singularity and possible inflation-like dynamics. It recasts the scale factor as a radial coordinate in a central-field quantum problem and incorporates zero-point motion and a small positive cosmological constant, yielding metastable, tunneling-driven evolution. In the Omega=0 limit, the model exhibits quantized curvature and a Bohr-like spectrum for closed universes, while Omega>0 produces quasi-stationary states that decay via tunneling, creating a three-stage evolution: gestation, rapid tunneling-driven expansion, and subsequent slower Hubble expansion. As a toy model, it reproduces qualitative inflation-like behavior and highlights how quantum effects and a cosmological constant can shape early-universe dynamics in a non-relativistic setting, suggesting directions for future quantum cosmology research.

Abstract

We analyze quantum-mechanical counterpart of Newtonian cosmology and show that effects of zero-point motion eliminate classical density singularity. Quantum effects are particularly significant for closed Universes where without the cosmological constant the energy spectrum and space curvature are quantized. When small positive cosmological constant is included, these states become quasi-stationary and decay via tunneling. Corresponding metastable Universes evolve in three stages: long period of gestation followed by rapid tunneling expansion further followed by slower Hubble expansion. This closely resembles inflation scenario of modern cosmology.

Tunneling Newtonian Universe

TL;DR

The paper investigates a quantum-mechanical version of Newtonian cosmology to address the initial density singularity and possible inflation-like dynamics. It recasts the scale factor as a radial coordinate in a central-field quantum problem and incorporates zero-point motion and a small positive cosmological constant, yielding metastable, tunneling-driven evolution. In the Omega=0 limit, the model exhibits quantized curvature and a Bohr-like spectrum for closed universes, while Omega>0 produces quasi-stationary states that decay via tunneling, creating a three-stage evolution: gestation, rapid tunneling-driven expansion, and subsequent slower Hubble expansion. As a toy model, it reproduces qualitative inflation-like behavior and highlights how quantum effects and a cosmological constant can shape early-universe dynamics in a non-relativistic setting, suggesting directions for future quantum cosmology research.

Abstract

We analyze quantum-mechanical counterpart of Newtonian cosmology and show that effects of zero-point motion eliminate classical density singularity. Quantum effects are particularly significant for closed Universes where without the cosmological constant the energy spectrum and space curvature are quantized. When small positive cosmological constant is included, these states become quasi-stationary and decay via tunneling. Corresponding metastable Universes evolve in three stages: long period of gestation followed by rapid tunneling expansion further followed by slower Hubble expansion. This closely resembles inflation scenario of modern cosmology.
Paper Structure (7 sections, 41 equations, 1 figure)

This paper contains 7 sections, 41 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Review of Newtonian Cosmology
  3. Quantized Newtoninan Cosmology
  4. Newtonian units
  5. Stationary states
  6. Quasi-stationary states and tunneling
  7. Conclusions

Figures (1)

  • Figure 1: Sketches of the potential energy $U(a)$, Eqs. (\ref{['potential_energy0']}), (\ref{['potential_energy1']}) without the cosmological constant (dashed), and with it (solid). The turning points of the classical motion $a=b$ and $a=d$ are solutions to the equation $U(a)=E$. Opaque band around the $E=U$ line symbolizes width $\Gamma$ of a quasi-stationary state in the presence of a small cosmological constant. The line $U=E_{0}$ corresponds to Einstein's static model of the Universe.