SCALAR FIELD IN THE OSCILLATING DE SITTER UNIVERSE AND REFLECTION FROM A COSMOLOGICAL BARRIER
Abstract
Recently it has been shown that the Lobachevsky geometry simulates an ideal mirror distributed in the space. Since the Lobachevsky model enters some cosmological models of the Universe, using theses models we need to take into account the presence of the «cosmological mirror». The earlier analysis assumed a static character of the space-time geometry. In this article, the generalization of the cosmological reflection effect to the oscillating de Sitter Universe is given for the scalar field. It is shown that the vanishing factor cos2 t in the metric of space-time does not lead to a singular behavior of solutions of the wave equation for the scalar field; instead, the solutions have a simple phase factor behavior in the time variable t, so the squared modulus of the wave function at cos t → 0 turns to be 1.
About the Authors
E. M. Оvsiyuk
Mozyr State Pedagogical University named after I. P. Shamyakin
Belarus
Belarus
Ph. D. (Physics and Mathematics), Assistant Professor
A. D. Koralkov
Mozyr State Pedagogical University named after I. P. Shamyakin
Belarus
Belarus
Student
References
1. Red’kov V. M., Tokarevskaya N. G., Ovsiyuk E. M., Spix G. J. Maxwell equations in Riemannian space-time, geometry effect on material equations in media. Nonlinear Phenomena in Complex Systems, 2009, vol. 12, no. 3, pp. 232–250.
2. Ovsiyuk E. M., Red’kov V. M. Solutions of the Maxwell equations in the quasi-Cartesian coordinates in the Lobachevsky space. Vestsі Natsyianal’nai akademіі navuk Belarusі. Seryia fіzіka-matematychnykh navuk [Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics series], 2009, no. 4, pp. 99–105 (in Russian).
3. Ovsiyuk E. M., Veko O. V., Kisel’ V. V., Red’kov V. M. New problems in quantum mechanics and the Heun equation. Nauchno-tekhnicheskie vedomosti SPbGPU. Ser. fiz.-mat. nauki [St. Petersburg State Polytechnic University Journal. Physics and Mathematics], 2012, vol. 1, no. 141, pp. 137–145 (in Russian).
4. Ovsiyuk E. M., Veko O. V. On Modeling a Potential Barrier in Schrödinger Theory by Geometry of the Lobachevsky Space. Vesn. Brestskaga unіversiteta. Ser. 4: Fizika, matematyka [Vesnik of Brest University. Series 4: Physics, Mathematics], 2011, no. 2, pp. 30–36 (in Russian).
5. Ovsiyuk E. M., Veko O. V. Plane-wave solutions for a particle with spin 1/2 in the Lobachevsky space. Vestsі Natsyianal’nai akademіі navuk Belarusі. Seryia fіzіka-matematychnykh navuk [Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics series], 2012, no. 4, pp. 80–83 (in Russian).
6. Ovsiyuk E. M., Veko O. V., Red’kov V. M. On simulating a medium with special reflecting properties by Lobachevsky geometry. Nonlinear Phenomena in Complex Systems, 2013, vol. 16, no. 4, pp. 331–344.
7. Ovsiyuk E. M., Veko O. V., Red’kov V. M. Modeling of a medium with the property of a perfect mirror for the light and spin 1/2 particles. Vestsі Natsyianal’nai akademіі navuk Belarusі. Seryia fіzіka-matematychnykh navuk [Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics series], 2015, no. 1, pp. 76–85 (in Russian).
8. Red’kov V. M. Particle fields in the Riemann space and the Lorents group. Minsk, Belorusskaya nauka Publ., 2009. 496 p. (in Russian).
9. Beitmen G., Erdeii A. Higher transcendental functions. Vol. 1: Gauss hypergeometric function. Legendre function. Мoscow, Nauka Publ., 1973, 294 p. (in Russian).
10. Red’kov V. M., Ovsiyuk E. M., Ishkhanyan A. M. Particle in the magnetic field: 2D Riemann spherical space and complex analogue of the Poincaré half-plane. Doklady Natsional’noi akademii nauk Belarusi [Doklady of the National Academy of Sciences of Belarus], 2013, vol. 57, no. 1, pp. 55–62 (in Russian).
Review
Views: 902
Email this article 