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.
References
[1] Carroll, S. M., Spacetime and Geometry: An Introduction to General Relativity (Cambridge Univ. Press, 2019)
[2] Weinberg, S., Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, John Wiley and Sons, New York, 1972
[3] Green, S. R., and Wald, R. M., Classical and Quantum Gravity 31, 234003 (2014)
[4] Aluri, P. K., Cea, P., Chingangbam, P., Chu, M.-C., Clowes, R. G., and et al., Classical and Quantum Gravity 40, 094001 (2023)
[5] Melia, F., Modern Physics Letters A 37, 2250016 (2022)
[6] Ryden, B. S., Introduction to Cosmology, 2nd ed., Cambridge University Press, 2017
[7] Melia, F., Frontiers of Physics 11, 119801 (2016)
[8] Robertson, H. P., Astrophys. J. 82, 284 (1935)
[9] Räsänen, S., Bolejko, K., and Finoguenov, A., Phys. Rev. Lett. 115, 101301 (2015)
[10] Clarkson, C., and Barrett, R., Classical and Quantum Gravity 16, 3781 (1999)
[11] Breton, M.-A., and Fleury, P., Astronomy & Astrophysics 656, A143 (2021)
[12] Roy, X., Buchert, T., Carloni, S., and Obadia, N.-E., Classical and Quantum Gravity 28, 165004 (2011)
[13] Astier, P., and Pain, R., Comptes Rendus Physique 13, 521 (2012)
[14] Riess, A. G., Macri, L. M., Hoffmann, S. L., Scolnic, D., Casertano, S., Filippenko, A. V., Tucker, B. E., Reid, M. J., Jones, D. O., Silverman, J. M., Chornock, R., Challis, P., Yuan, W., Brown, P. J., and Foley, R. J., The Astrophysical Journal 826, 56 (2016)
[15] Planck Collaboration, Astron. Astrophys. 641, A1 (2020)
[16] Planck Collaboration, Astronomy & Astrophysics 641, A6 (2020)
[17] Dodelson, S., and Schmidt, F., Modern Cosmology, 2nd ed., Academic Press, 2020
[18] Tsamparlis, M., and Apostolopoulos, P. S., Journal of Mathematical Physics 41, 7573 (2000)
[19] Eisenstein, D. et al., The Astrophysical Journal 633, 560 (2005)
[20] Dark Energy Survey Collaboration, Phys. Rev. D 105, 023520 (2021)
[21] Bokhari, A. H., Hussain, T., Hussain, W., and Khan, F., Modern Physics Letters A 36, 2150208 (2021)
[22] Bokhari, A. H., Hussain, T., Khan, J., and Nasib, U., Results in Physics 25, 104299 (2021)
[23] Maartens, R., and Maharaj, S. D., Classical and Quantum Gravity 3, 1005 (1986)
[24] Yan, M.-L., arXiv:1707.04153 [gr-qc] (2017)
[25] Dass, N. D. H., and Desiraju, H., arXiv:1511.07142 [gr-qc] (2015)
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.