Spectral Evolution of the Universe

Details Spectral Evolution of the Universe Spectral Evolution of the Universe

2000-03-10

arxiv.org/abs/gr-qc/0003042v2

Phys.Rev. D62 (2000) 023516

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

To appear in Phys. Rev. D

Scientific paper

10.1103/PhysRevD.62.023516

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.

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