Cosmic crystallography: the euclidean isometries
A. Bernui, A.F.F. Teixeira
TL;DR
This paper derives exact probability density expressions for conjugate pair separations in euclidean isometries, enhancing cosmic crystallography analysis by providing theoretical foundations for observed histograms.
Contribution
It introduces precise mathematical formulas for conjugate pair separations in euclidean isometries, including fixed point and orientation reversing cases, advancing the theoretical understanding of cosmic crystallography.
Findings
Derived exact probability density expressions for conjugate pairs
Analyzed isometries with fixed points and orientation reversal
Provided theoretical counterparts to computer simulation histograms
Abstract
Exact expressions for probability densities of conjugate pair separation in euclidean isometries are obtained, for the cosmic crystallography.These are the theoretical counterparts of the mean histograms arising from computer simulation of the isometries. For completeness, also the isometries with fixed points are examined, as well as the orientation reversing isometries.
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Taxonomy
TopicsScientific Research and Discoveries · Astro and Planetary Science · Cosmology and Gravitation Theories