Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)2421810.22363/2658-4670-2020-28-2-131-140Mathematical models in PhysicsМатематические модели в физикеResearch ArticleSpinor field in a spherically symmetric Friedmann UniverseСпинорное поле в сферически симметричной Вселенной ФридманаSahaBijanСахаБиджан

Doctor of Physical and Mathematical Sciences, assistant professor of the Institute of Physical Research and Technologies of Peoples’ Friendship University of Russia (RUDN University), leading researcher at the Laboratory of Information Technologies of The Joint Institute for Nuclear Research

Институт физических исследований и технологий; Лаборатория информационных технологий

bijan64@mail.ruZakharovEvgeniy I.ЗахаровЕ. И.

student of the Institute of Physical Research and Technologies

Институт физических исследований и технологий

zakharov.eugene1998@gmail.comRikhvitskyVictor S.РихвицкийВ. С.

Master of physical and mathematical Sciences, Leading programmer of the Laboratory of Information Technologies

Лаборатория информационных технологий

rqvtsk@mail.ruPeoples’ Friendship University of Russia (RUDN University)Российский университет дружбы народовJoint Institute for Nuclear ResearchОбъединённый институт ядерных исследований15122020282VOL 28, NO2 (2020)ТОМ 28, №2 (2020)13114020072020Copyright ©; 2020, Saha В., Zakharov E.I., Rikhvitsky V.S.Copyright ©; 2020, Саха Б., Захаров Е.И., Рихвицкий В.С.2020Saha В., Zakharov E.I., Rikhvitsky V.S.Саха Б., Захаров Е.И., Рихвицкий В.С.http://creativecommons.org/licenses/by/4.0https://journals.rudn.ru/miph/article/view/24218

In recent years spinor field is being used by many authors to address some burning issues of modern cosmology. The motive behind using the spinor field as a source for gravitational field lies on the fact that the spinor field not only can describe the different era of the evolution but also can simulate different substances such as perfect fluid and dark energy. Moreover, the spinor field is very sensitive to the gravitational one and depending on the gravitational field the spinor field can react differently and change the spacetime geometry and the spinor field itself differently. This paper provides a brief description of the nonlinear spinor field in the FriedmannLemaitre-Robertson-Walker (FLRW) model. The results are compared in Cartesian and spherical coordinates. It is shown that during the transition from Cartesian coordinates to spherical ones, the energy-momentum tensor acquires additional nonzero non-diagonal components that can impose restrictions on either spinor functions or metric ones.

В последние годы спинорное поле используется многими авторами для решения некоторых актуальных вопросов современной космологии. Мотив использования спинорного поля в качестве источника гравитационного поля заключается в том, что спинорное поле может не только описывать различные этапы эволюции Вселенной, но и моделировать различные типы вещества, такие как идеальная жидкость и темная энергия. Кроме того, спинорное поле очень чувствительно к гравитационному, и в зависимости от гравитационного поля спинорное поле может реагировать по-разному, изменяя тем самым геометрию пространствавремени. В настоящей работе дается краткое описание нелинейного спинорного поля в модели Фридмана-Леметра-Робертсона-Уолкера (FLRW). Результаты сравниваются в декартовых и сферических координатах. Показано, что при переходе от декартовых координат к сферическим тензор энергии-импульса имеет дополнительные ненулевые недиагональные компоненты, которые могут накладывать ограничения как на спинорные функции, так и на метрические.

spinor fieldFLRW modelCartesian coordinatesspherical coordinatesспинорное полемодель FLRWдекартовы координатысферические координатыB. Saha and G. N. Shikin, “Interacting Spinor and Scalar Fields in Bianchi Type I Universe Filled with Perfect Fluid: Exact Self-consistent Solutions,” General Relativity and Gravitation, vol. 29, pp. 1099-1112, 1997. DOI: 10.1023/a:1018887024268.B. Saha and G. N. Shikin, “Nonlinear Spinor Field in Bianchi type-I Universe filled with Perfect Fluid: Exact Self-consistent Solutions,” Journal of Mathematical Physics, vol. 38, pp. 5305-5318, 1997. DOI: 10.1063/1.531944.B. Saha, “Spinor field in Bianchi type-I Universe: regular solutions,” Physical Review D, vol. 64, p. 123501, 2001. DOI: 10.1103/physrevd. 64.123501.B. Saha, “Nonlinear Spinor Field in cosmology,” Physical Review D, vol. 69, p. 124006, 2004. DOI: 10.1103/physrevd.69.124006.B. Saha and T. Boyadjiev, “Bianchi type-I cosmology with scalar and spinor fields,” Physical Review D, vol. 69, p. 124010, 2004. DOI: 10. 1103/physrevd.69.124010.B. Saha, “Spinor fields in Bianchi type-I Universe,” Physics of Particlesand Nuclei., vol. 37, S13-S44, 2006. DOI: 10. 1134 / s1063779606070021.N. J. Popławski, “Nonsingular, big-bounce cosmologyfrom spinor-torsion coupling,” Physical Review D, vol. 85, p. 107502, 2012. DOI: 10.1103/ physrevd.85.107502.M. O. Ribas, F. P. Devecchi, and G. M. Kremer, “Fermions as sources of accelerated regimes in cosmology,” Physical Review D, vol. 72, p. 123502, 2005. DOI: 10.1103/physrevd.72.123502.B. Saha, “Nonlinear spinor field in Bianchi type-I cosmology: inflation,isotropization, and late time acceleration,” Physical Review D, vol. 74, p. 124030, 2006. DOI: 10.1103/physrevd.74.124030.B. Saha, “Spinor field and accelerated regimes in cosmology,” Gravitation & Cosmology, vol. 12, no. 46-47, pp. 215-218, 2006.B. Saha, “Nonlinear spinor field in Bianchi type-???? cosmology: accelerated regimes,” Romanian Reports in Physics, vol. 59, pp. 649-660, 2007. arXiv: gr-qc/0608047.B. Saha, “Early inflation, isotropization and late-time acceleration of a Bianchi type-I universe,” Physics of Particles and Nuclei, vol. 40, pp. 656-673, 2009. DOI: 10.1134/s1063779609050037.N. J. Popławski, “Big bounce from spin and torsion,” General Releativity and Gravitation, vol. 44, p. 1007, 2012. DOI: 10.1007/s10714-0111323-2.N. J. Popławski, “Nonsingular Dirac particles in spacetime with torsion,” Physics Letters B, vol. 690, pp. 73-77, 2010. DOI: 10.1016/j.physletb. 2010.04.073.L. Fabbri, “A Discussion on Dirac Field Theory, No-Go Theorems and Renormalizability,” International Journal of Theoretical Physics, vol. 52, pp. 634-643, 2013. DOI: 10.1007/s10773-012-1370-9.L. Fabbri, “Conformal gravity with the most general ELKO matter,” Physical Review D., vol. 85, p. 047502, 2012. DOI: 10.1103/physrevd. 85.047502.S. Vignolo, L. Fabbri, and R. Cianci, “Dirac spinors in Bianchi-I f(R)cosmology with torsion,” Journal of Mathematical Physics, vol. 52, p. 112502, 2011. DOI: 10.1063/1.3658865.B. Saha, “Nonlinear Spinor Fields in Bianchi type-I spacetime: Problems and Possibilities,” Astrophysics and Space Science, vol. 357, p. 28, 2015. DOI: 10.1007/s10509-015-2291-x.B. Saha, “Spinor field nonlinearity and space-time geometry,” Physics of Particles and Nuclei, vol. 49, no. 2, pp. 146-212, 2018. DOI: 10.1134/ s1063779618020065.B. Saha, “Non-minimally coupled nonlinear spinor field in Bianchi type-I cosmology,” European Physical Journal - Plus, vol. 134, p. 419, 2019. DOI: 10.1140/epjp/i2019-12859-7.R. Cianci, L. Fabbri, and S. Vignolo, “Exact solutions for Weyl fermions with gravity,” European Physical Journal - Plus, vol. 75, p. 478, 2015. DOI: 10.1140/epjc/s10052-015-3698-9.K. A. Bronnikov, Y. P. Rybakov, and B. Saha, “Spinor fields in spherical symmetry. Einstein-Dirac and other space-time,” European Physical Journal - Plus, vol. 135, p. 124, 2020. DOI: 10.1140/epjp/s13360-02000150-z.B. Saha, “Spinor fields in spherically symmetric space-time,” European Physical Journal - Plus, vol. 133, p. 416, 2018. DOI: 10.1140/epjp/ i2018-12273-9.B. Saha, “Spinor Field Nonlinearity and Space-Time Geometry,” Physics of Particles and Nuclei, vol. 49, no. 2, pp. 146-212, 2018. DOI: 10.1134/ S1063779618020065.