An approximate solution of the Yang - Mills equation on a spatially flat FRW cosmological background
DOI:
https://doi.org/10.14419/ijpr.v7i2.29775Keywords:
Friedmann-Robertson-Walker Universe, Homotopy Perturbation Method, Yang-Mills Equation.Abstract
In this paper, an approximate solution for the Yang - Mills equation in a spatially flat Friedmann-Robertson-Walker universe is obtained. For this purpose, the well known method of solution of non-linear differential equations is used, viz. the homotopy perturbations method. This method has been developed as effective technique for solving different non-linear problems. Here, this method allowed us to obtain approximate solution for the essentially non-linear equation for the SO3 Yang-Mills fields on the curved space-time background of the spatially flat Friedmann-Robertson-Walker universe.
References
[1] A. G. Riess , et al. , â€Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constantâ€, Astronomical Journal, Vol.
116, (1998), 1009. http://dx.doi.org/10.1086/300499[2] S. Perlmutter, et al., â€Measurements of Omega and Lambda from 42 High-Redshift Supernovaeâ€, Astrophysical Journal, Vol. 517 (1999), 565.
http://dx.doi.org/10.1086/307221[3] N. Jarosik, C.L. Bennett, et al., â€Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Sky Maps, Systematic Errors, and Basic
Resultsâ€, Astrophysical Journal Supplement Series, 192 (2011), 14. http://dx.doi.org/10.1088/0067-0049/192/2/14.[4] Abdel Nasser Tawfik and Eiman Abou El Dahab3, â€Review on Dark Energy Modelsâ€, Gravitation and Cosmology, 2019, Vol. 25, No. 2, pp. 103-115.
http://dx.doi.org/10.1134/S0202289319020154[5] D. Huterer and D. L. Shafer, â€Dark energy two decades after: Observables, probes, consistency testsâ€, Rept. Prog. Phys., 81, 016901 (2018).
http://dx.doi.org/10.1088/1361-6633/aa997e[6] L. Sebastiani, S. Vagnozzi, and R. Myrzakulov, â€Mimetic Gravity: A Review of Recent Developments and Applications to Cosmology and Astrophysicsâ€,
Advances in High Energy Physics, Volume 2017, Article ID 3156915, 43 pages. https://doi.org/10.1155/2017/3156915[7] C.N. Yang , R.L. Mills , â€Conservation of isotopic spin and isotopic gauge invarianceâ€, Physical Review, 96, 1 (1954), pp. 191 - 195.
http://dx.doi.org/10.1103/PhysRev.96.191[8] D. V. Gal’tsov, E.A. Davydov, â€Yang-Mills Condensates in Cosmology, International Journal of Modern Physics: Conference Series, 14 (2012) 316-325.
http://dx.doi.org/10.1142/S201019451200743X[9] V. K. Shchigolev, â€Modelling Cosmic Acceleration in Modified Yang-Mills Theoryâ€, Gravitation and Cosmology, Vol. 17, No. 3 (2011) 272-275.
http://dx.doi.org/10.1134/S0202289311030078[10] V. K. Shchigolev, G. N. Orekhova, â€Non-Minimal Cosmological Model in modified Yang-Mills Theoryâ€, Modern Physics Letters A, Vol. 56, No. 2
(2011) 389-396. http://dx.doi.org/10.1142/S0217732311036462[11] V. K. Shchegolev, K. Samaroo, â€Generalized Exact Cosmologies with Interacting Yang-Mills and Nonlinear Scalar Fieldsâ€, General Relativity and
Gravitation, 36(7) (2004), 1661. http://dx.doi.org/10.1023/B:GERG.0000032158.16161.1b[12] V. K. Shchigolev, D. N. Bezbatko, â€Exact Cosmological Models with Yang - Mills Fields on Lyra Manifoldâ€, Gravit. Cosmol., 24 (2018), 161.
https://doi.org/10.1134/S0202289318020135[13] J.-H. He, â€Homotopy perturbation techniqueâ€, Computer Methods in Applied Mechanics and Engineering, 178 (1999), 257-262.
http://dx.doi.org/10.1016/S0045-7825(99)00018-3[14] J.-H. He, â€A coupling method of homotopy technique and perturbation technique for nonlinear problemsâ€, International Journal of Non-Linear
Mechanics, 35 (1) (2000), 37-43. http://dx.doi.org/10.1016/S0020-7462(98)00085-7[15] L. Cveticanin, â€Homotopy-perturbation method for pure nonlinear differential equationâ€, Chaos, Solitons & Fractals, vol. 30, No. 5, 1221 - 1230, 2006.
doi:10.1016/j.chaos.2005.08.180[16] V. Shchigolev, â€Homotopy Perturbation Method for Solving a Spatially Flat FRW Cosmological Modelâ€, Universal Journal of Applied Mathematics,
2(2) (2014), 99-103. http://dx.doi.org/10.13189/ujam.2014.020204[17] V. Shchigolev, â€Analytical Computation of the Perihelion Precession in General Relativity via the Homotopy Perturbation Methodâ€, Universal Journal
of Computational Mathematics, 3(4) (2015), 45-49. http://dx.doi.org/10.13189/ujcmj.2015.030401[18] V. K. Shchigolev, â€Calculating Luminosity Distance versus Redshift in FLRW Cosmology via Homotopy Perturbation Methodâ€, Gravitation and
Cosmology, 23 (2017) 142. http://dx.doi.org/10.1134/S0202289317020098[19] V. K. Shchigolev, D.N. Bezbatko â€Studying Gravitational Deflection of Light by Kiselev Black Hole via Homotopy Perturbation Methodâ€, General
Relativity and Gravitation, (2019) 51:34. http://dx.doi.org/10.1007/s10714-019-2521-6[20] Abdul Aziz, Saibal Ray, Farook Rahaman, â€A generalized model for compact starsâ€, European Physical Journal C, 76 (2016), 248.
http://dx.doi.org/10.1140/epjc/s10052-016-4090-0[21] F. Rahaman, S. Ray, A. Aziz, S. R. Chowdhury, D. Deb, Exact Radiation Model For Perfect Fluid Under Maximum Entropy Principle, Online available
from arXiv:1504.05838 (2015)[22] A. Aziz, S. Ray, F. Rahaman, M. Khlopov and B. K. Guha, â€Constraining values of bag constant for strange star candidatesâ€, International Journal of
Modern Physics D, http://dx.doi.org/10.1142/S0218271819410062
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Received date: August 19, 2019
Accepted date: September 14, 2019
Published date: September 21, 2019