Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2001-11-20
Class.Quant.Grav. 18 (2001) 5329-5352
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
To be published in Classical and Quantum Gravity
Scientific paper
10.1088/0264-9381/18/24/301
We study a fundamental issue in cosmology: Whether we can rely on a cosmological model to understand the real history of the Universe. This fundamental, still unresolved issue is often called the ``model-fitting problem (or averaging problem) in cosmology''. Here we analyze this issue with the help of the spectral scheme prepared in the preceding studies. Choosing two specific spatial geometries that are very close to each other, we investigate explicitly the time evolution of the spectral distance between them; as two spatial geometries, we choose a flat 3-torus and a perturbed geometry around it, mimicking the relation of a ``model universe'' and the ``real Universe''. Then we estimate the spectral distance between them and investigate its time evolution explicitly. This analysis is done efficiently by making use of the basic results of the standard linear structure-formation theory. We observe that, as far as the linear perturbation of geometry is valid, the spectral distance does not increase with time prominently,rather it shows the tendency to decrease. This result is compatible with the general belief in the reliability of describing the Universe by means of a model, and calls for more detailed studies along the same line including the investigation of wider class of spacetimes and the analysis beyond the linear regime.
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