Symmetry of the Friedmann-Lemaître-Robertson-Walker universe
Bobur Turimov
1,*
,
Ashfaq Bokhari
2
,
Bobomurat Ahmedov
3,4
1 Ulugh Beg Astronomical Institute , Astronomy St. 33, Tashkent 100052, Uzbekistan
2 Mathematics Department, College of Computing and Mathematics, King Fahd University of Petroleum and Minerals (KFUPM) , P.O. Box 31261, Dhahran, 31262, Saudi Arabia
3 Institute for Advanced Studies, New Uzbekistan University , Movarounnahr str. 1, Tashkent 100000, Uzbekistan
4 Institute of Theoretical Physics, National University of Uzbekistan , Tashkent 100174, Uzbekistan
Abstract
We present a detailed analysis of the symmetries and physical dynamics of the Friedmann–Lemaître–Robertson–Walker (FLRW) universe, highlighting its foundational role in modern cosmology. By explicitly solving the Killing equations, we derive the six spatial isometries three translations and three rotations characteristic of the maximal symmetry inherent to homogeneous and isotropic spacetimes. Focusing on two representative scale factor scenarios, hyperbolic and exponential expansions, we investigate the resulting energy-momentum dynamics. In both cases, we find that classical energy conditions are violated during cosmic expansion, suggesting the need for either exotic forms of matter or extensions to general relativity to consistently describe the observed universe.
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Cite this article
Turimov, B., Bokhari, A. and Ahmedov, B., Symmetry of the Friedmann-Lemaître-Robertson-Walker universe, Turanian J. Vol. 1, No. 2 (010201), 2025.