A model Universe with variable space dimension: its dynamics and wave function

TL;DR

This paper explores a cosmological model where the spatial dimension varies with the Universe's expansion, analyzing its dynamics and wave function, and connecting it to standard quantum cosmology solutions.

Contribution

It introduces a variable space dimension model with a free parameter, extending traditional cosmological models and analyzing its quantum wave function and probability density.

Findings

Wave function approaches Hartle-Hawking or Linde forms in constant dimension limit

Model includes a parameter fixing space dimension at Planck time

Provides a Lagrangian formulation for a variable dimension universe

Abstract

Assuming the space dimension is not constant, but varies with the expansion of the Universe, a Lagrangian formulation for a toy model Universe is given. There is a free paremeter in the theory, $C$, with which we can fix the dimension of space at the Planck time. The standard FRW model corresponds to the limiting case $C \to +\infty$. We study the Wheeler-De Witt equation and the wave function of the Universe and the probability density in our model Universe. In the limit of constant space dimension, our wave function approaches to the Hartle-Hawking wave function or to a modified Linde wave function.