Spectral Evolution of the Universe

TL;DR

This paper derives evolution equations for the spectral properties of the universe, enabling analysis of its geometric evolution and introducing a universal formula for spectral distance between close universes, aiding cosmological model assessment.

Contribution

It introduces the first evolution equations for the spectra of the universe and a universal spectral distance formula, advancing spectral analysis in cosmology.

Findings

Universal formula for spectral distance between close universes

Spectral distance evolution equations derived

Criteria for cosmological model evaluation based on spectral distance

Abstract

We derive the evolution equations for the spectra of the Universe. Here "spectra" means the eigenvalues of the Laplacian defined on a space, which contain the geometrical information on the space. These equations are expected to be useful to analyze the evolution of the geometrical structures of the Universe. As an application, we investigate the time evolution of the spectral distance between two Universes that are very close to each other; it is the first necessary step for the detailed analysis of the model-fitting problem in cosmology with the spectral scheme. We find out a universal formula for the spectral distance between two very close Universes, which turns out to be independent of the detailed form of the distance nor the gravity theory. Then we investigate its time evolution with the help of the evolution equations we derive. We also formulate the criteria for a good cosmological model in terms of the spectral distance.