Authors

Abstract

In this paper, we consider a massive charged scalar field coupled to a uniform electric field background in a 3 dimensional de Sitter spacetime. We consider the value of the dimensionless coupling constant of the scalar field to the scalar curvature of a 3 dimensional de Sitter spacetime equal to 1/8. We compute the expectation value of the trace of the energy-momentum tensor in the in-vacuum state and we show that using adiabatic subtraction regularization method the linear ultraviolet divergence is removed and a finite expression obtain. We investigate the behavior of the regularized trace for different intensities of the scalar field mass and the electric field. We show that the trace as a function of the electric field has a discontinuity at which it changes the sign. We show that for the case of a conformally coupled scalar field to the de Sitter spacetime the trace vanishes, and there is no trace anomaly. We discuss the gravitational backreaction effect of the created Schwinger pairs.
 

Keywords

1. F. Sauter, Uber das Verhalten eines Elektrons im homogenen elektrischen Feld nach der relativistischen Theorie Diracs, Z. Phys. 69, (1931) 742.
2. W. Heisenberg and H. Euler, Consequences of Dirac's theory of positrons, Z. Phys. 98, (1936) 714.
3. J. S. Schwinger, On gauge invariance and vacuum polarization, Phys. Rev. 82, (1951) 664.
4. F. Gelis and N. Tanji, Schwinger mechanism revisited, Prog. Part. Nucl. Phys. 87, (2016) 1.
5. A. Di Piazza, C. Muller, K. Z. Hatsagortsyan, C. H. Keitel, Extremely high-intensity laser interactions with fundamental quantum systems, Rev. Mod. Phys. 84 (2012) 1177.
6. E. Mottola, Particle Creation in de Sitter Space, Phys. Rev. D 31 (1985) 754.
7. J. Garriga, Pair production by an electric field in (1+1)-dimensional de Sitter space, Phys. Rev. D 49 (1994) 6343.
8. M. B. Fröb, J. Garriga, S. Kanno, M. Sasaki, J. Soda, T. Tanaka and A. Vilenkin, Schwinger effect in de Sitter space, JCAP 1404 (2014) 009.
9. E. Bavarsad, C. Stahl and S.S. Xue, Scalar current of created pairs by Schwinger mechanism in de Sitter spacetime, Phys. Rev. D 94 (2016) 104011.
10. T. Kobayashi, N. Afshordi, Schwinger Effect in 4D de Sitter Space and Constraints on Magnetogenesis in the Early Universe, JHEP 1410 (2014) 166.
11. C. Stahl, E. Strobel, S.S. Xue, Fermionic current and Schwinger effect in de Sitter spacetime, Phys. Rev. D 93 (2016) 025004.
12. T. Hayashinaka, T. Fujita, J. Yokoyama, Fermionic Schwinger effect and induced current in de Sitter space, JCAP 07 (2016) 010.
13. C. Stahl and S. S. Xue, Schwinger effect and backreaction in de Sitter spacetime, Phys. Lett. B 760 (2016) 288.
14. T. Markkanen, A. Rajantie, Massive scalar field evolution in de Sitter, JHEP 1701 (2017) 133.
15. T. Markkanen, De Sitter Stability and Coarse Graining, arXiv:1703.06898 [gr-qc].
16. L. Parker, S. A. Fulling, Adiabatic regularization of the energy momentum tensor of a quantized field in homogeneous spaces, Phys. Rev. D 9 (1974) 341.
17. S. A. Fulling, L. Parker, Renormalization in the theory of a quantized scalar field interacting with a robertson-walker spacetime, Annals Phys. 87 (1974) 176.
18. J. S. Dowker, R. Critchley, Effective Lagrangian and Energy Momentum Tensor in de Sitter Space, Phys. Rev. D 13 (1976) 3224.
19. S. Habib, C. Molina-Paris, E. Mottola, Energy momentum tensor of particles created in an expanding universe, Phys. Rev. D 61 (1999) 024010.
20. D. Lopez Nacir, F. D. Mazzitelli, Backreaction in trans-Planckian cosmology: Renormalization, trace anomaly and selfconsistent solutions, Phys. Rev. D 76 (2007) 024013.
21. A. Landete, J. Navarro-Salas, F. Torrenti, Adiabatic regularization and particle creation for spin one-half fields, Phys. Rev. D 89 (2014) 044030.
22. A. Landete, J. Navarro-Salas, F. Torrenti, Adiabatic regularization for spin-1/2 fields, Phys. Rev. D 88 (2013) 061501.
23. S. Ghosh, Creation of spin 1/2 particles and renormalization in FLRW spacetime, Phys. Rev. D 91 (2015) 124075.
24. S. Ghosh, Spin 1/2 field and regularization in a de Sitter and radiation dominated universe, Phys. Rev. D 93 (2016) 044032.
27. F. W. J. Olver, D. W. Lozier, R. F. Boisvert, C. W. Clark, NIST Handbook of Mathematical Functions (Cambridge University Press, Cambridge, UK, 2010).
29. L. Parker and D. Toms, Quantum Field Theory in Curved Spacetime: Quantized Fields and Gravity (Cambridge University Press, Cambridge, UK, 2009).
30. N. D. Birrell and P. C. W. Davies, Quantum Fields in Curved Space (Cambridge University Press, Cambridge, UK, 1984).
31. M. J. Duff, Twenty Years of the Weyl Anomaly, Class. Quant. Grav. 11, (1994) 1387.

ارتقاء امنیت وب با وف ایرانی