Making a Universe

TL;DR

This paper proposes a method to construct and analyze quantized universes using dynamical triangulation, aiming to understand cosmic microwave background anisotropies through numerical simulations in various dimensions.

Contribution

It introduces a novel construction rule for quantized universes based on simplicial quantum gravity and demonstrates its application through numerical simulations in 2D and 4D.

Findings

Simulation results agree with matrix model and Liouville theory in 2D

4D simulation indicates potential for analyzing cosmic anisotropies

Method provides a new way to connect quantum gravity models with observational data

Abstract

For understanding the origin of anisotropies in the cosmic microwave background, rules to construct a quantized universe is proposed based on the dynamical triangulation method of the simplicial quantum gravity. A $d$-dimensional universe having the topology $ D^d $ is created numerically in terms of a simplicial manifold with $d$-simplices as the building blocks. The space coordinates of a universe are identified on the boundary surface $ S^{d-1} $, and the time coordinate is defined along the direction perpendicular to $ S^{d-1} $. Numerical simulations are made mainly for 2-dimensional universes, and analyzed to examine appropriateness of the construction rules by comparing to analytic results of the matrix model and the Liouville theory. Furthermore, a simulation in 4-dimension is made, and the result suggests an ability to analyze the observations on anisotropies by comparing to the scalar curvature correlation of a $ S^2 $-surface formed as the last scattering surface in the $ S^3 $ universe.