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Schwinger effect in 4D de Sitter space and constraints on magnetogenesis in the early universe. (English) Zbl 1333.83272
Summary: We investigate pair creation by an electric field in four-dimensional de Sitter space. The expectation value of the induced current is computed, using the method of adiabatic regularization. Under strong electric fields the behavior of the current is similar to that in flat space, while under weak electric fields the current becomes inversely proportional to the mass squared of the charged field. Thus we find that the de Sitter space obtains a large conductivity under weak electric fields in the presence of a charged field with a tiny mass. We then apply the results to constrain electromagnetic fields in the early universe. In particular, we study cosmological scenarios for generating large-scale magnetic fields during the inflationary era. Electric fields generated along with the magnetic fields can induce sufficiently large conductivity to terminate the phase of magnetogenesis. For inflationary magnetogenesis models with a modified Maxwell kinetic term, the generated magnetic fields cannot exceed 10-30G on Mpc scales in the present epoch, when a charged field carrying an elementary charge with mass of order the Hubble scale or smaller exists in the Lagrangian. Similar constraints from the Schwinger effect apply for other magnetogenesis mechanisms.

##### MSC:
 83F05 Cosmology
DLMF
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##### References:
 [1] Sauter, F., Uber das verhalten eines elektrons im homogenen elektrischen feld nach der relativistischen theorie diracs, Z. Phys., 69, 742, (1931) [2] Heisenberg, W.; Euler, H., Consequences of dirac’s theory of positrons, Z. Phys., 98, 714, (1936) [3] Schwinger, JS, On gauge invariance and vacuum polarization, Phys. Rev., 82, 664, (1951) [4] Nikishov, AI, Barrier scattering in field theory removal of Klein paradox, Nucl. Phys., B 21, 346, (1970) [5] Narozhnyi, NB; Nikishov, AI, The simplist processes in the pair creating electric field, Yad. Fiz., 11, 1072, (1970) [6] Martin, J., Inflationary perturbations: the cosmological Schwinger effect, Lect. Notes Phys., 738, 193, (2008) [7] Fröb, MB; Garriga, J.; Kanno, S.; Sasaki, M.; Soda, J.; etal., Schwinger effect in de Sitter space, JCAP, 04, 009, (2014) [8] Garriga, J., Pair production by an electric field in (1+1)-dimensional de Sitter space, Phys. Rev., D 49, 6343, (1994) [9] Cooper, F.; Mottola, E., Quantum back reaction in scalar QED as an initial value problem, Phys. Rev., D 40, 456, (1989) [10] Kluger, Y.; Eisenberg, JM; Svetitsky, B.; Cooper, F.; Mottola, E., Pair production in a strong electric field, Phys. Rev. Lett., 67, 2427, (1991) [11] Kluger, Y.; Eisenberg, JM; Svetitsky, B.; Cooper, F.; Mottola, E., Fermion pair production in a strong electric field, Phys. Rev., D 45, 4659, (1992) [12] Cooper, F.; Eisenberg, JM; Kluger, Y.; Mottola, E.; Svetitsky, B., Particle production in the central rapidity region, Phys. Rev., D 48, 190, (1993) [13] Anderson, PR; Mottola, E., On the instability of global de Sitter space to particle creation, Phys. Rev., D 89, 104038, (2014) [14] Anderson, PR; Mottola, E., Quantum vacuum instability of ‘eternal’ de Sitter space, Phys. Rev., D 89, 104039, (2014) [15] Parker, L.; Fulling, SA, Adiabatic regularization of the energy momentum tensor of a quantized field in homogeneous spaces, Phys. Rev., D 9, 341, (1974) [16] Fulling, SA; Parker, L., Renormalization in the theory of a quantized scalar field interacting with a Robertson-Walker spacetime, Annals Phys., 87, 176, (1974) [17] Fulling, SA; Parker, L.; Hu, BL, Conformal energy-momentum tensor in curved spacetime: adiabatic regularization and renormalization, Phys. Rev., D 10, 3905, (1974) [18] Bunch, TS, Calculation of the renormalized quantum stress tensor by adiabatic regularization in two-dimensional and four-dimensional Robertson-Walker space-times, J. Phys., A 11, 603, (1978) [19] Bunch, TS, Adiabatic regularization for scalar fields with arbitrary coupling to the scalar curvature, J. Phys., A 13, 1297, (1980) [20] Anderson, PR; Parker, L., Adiabatic regularization in closed Robertson-Walker universes, Phys. Rev., D 36, 2963, (1987) [21] Turner, MS; Widrow, LM, Inflation produced, large scale magnetic fields, Phys. Rev., D 37, 2743, (1988) [22] Ratra, B., Cosmological ‘seed’ magnetic field from inflation, Astrophys. J., 391, l1, (1992) [23] Bamba, K.; Yokoyama, J., Large scale magnetic fields from inflation in Dilaton electromagnetism, Phys. Rev., D 69, 043507, (2004) [24] Demozzi, V.; Mukhanov, V.; Rubinstein, H., Magnetic fields from inflation?, JCAP, 08, 025, (2009) [25] S. Kanno, J. Soda and M.-a. Watanabe, Cosmological Magnetic Fields from Inflation and Backreaction, JCAP12 (2009) 009 [arXiv:0908.3509] [INSPIRE]. [26] Fujita, T.; Mukohyama, S., Universal upper limit on inflation energy scale from cosmic magnetic field, JCAP, 10, 034, (2012) [27] Kobayashi, T., Primordial magnetic fields from the post-inflationary universe, JCAP, 05, 040, (2014) [28] Tavecchio, F.; Ghisellini, G.; Foschini, L.; Bonnoli, G.; Ghirlanda, G.; etal., The intergalactic magnetic field constrained by Fermi/LAT observations of the TeV blazar 1ES 0229+200, Mon. Not. Roy. Astron. Soc., 406, l70, (2010) [29] Neronov, A.; Vovk, I., Evidence for strong extragalactic magnetic fields from Fermi observations of TeV blazars, Science, 328, 73, (2010) [30] Ando, S.; Kusenko, A., Evidence for gamma-ray halos around active galactic nuclei and the first measurement of intergalactic magnetic fields, Astrophys. J., 722, l39, (2010) [31] Taylor, AM; Vovk, I.; Neronov, A., Extragalactic magnetic fields constraints from simultaneous gev-TeV observations of blazars, Astron. Astrophys., 529, a144, (2011) [32] Takahashi, K.; Mori, M.; Ichiki, K.; Inoue, S.; Takami, H., Lower bounds on magnetic fields in intergalactic voids from long-term gev-TeV light curves of the blazar mrk 421, Astrophys. J., 771, l42, (2013) [33] Fermi-LAT collaboration, J. Finke, L. Reyes and M. Georganopoulos, Constraints on the Intergalactic Magnetic Field from Gamma-Ray Observations of Blazars, eConfC 121028 (2012) 365 [arXiv:1303.5093] [INSPIRE]. [34] H. Tashiro, W. Chen, F. Ferrer and T. Vachaspati, Search for CP-violating Signature of Intergalactic Magnetic Helicity in the Gamma Ray Sky, arXiv:1310.4826 [INSPIRE]. [35] Stewart, ED, Inflation, supergravity and superstrings, Phys. Rev., D 51, 6847, (1995) [36] Dine, M.; Randall, L.; Thomas, SD, Supersymmetry breaking in the early universe, Phys. Rev. Lett., 75, 398, (1995) [37] Starobinsky, AA; Yokoyama, J., Equilibrium state of a selfinteracting scalar field in the de Sitter background, Phys. Rev., D 50, 6357, (1994) [38] Woodard, RP, Generalizing starobinskii’s formalism to Yukawa theory & to scalar QED, J. Phys. Conf. Ser., 68, 012032, (2007) [39] Burgess, CP; Holman, R.; Leblond, L.; Shandera, S., Breakdown of semiclassical methods in de Sitter space, JCAP, 10, 017, (2010) [40] Serreau, J., Effective potential for quantum scalar fields on a de Sitter geometry, Phys. Rev. Lett., 107, 191103, (2011) [41] Boyanovsky, D., Condensates and quasiparticles in inflationary cosmology: mass generation and decay widths, Phys. Rev., D 85, 123525, (2012) [42] Garretson, WD; Field, GB; Carroll, SM, Primordial magnetic fields from pseudogoldstone bosons, Phys. Rev., D 46, 5346, (1992) [43] Gasperini, M.; Giovannini, M.; Veneziano, G., Primordial magnetic fields from string cosmology, Phys. Rev. Lett., 75, 3796, (1995) [44] Giovannini, M.; Shaposhnikov, ME, Primordial magnetic fields from inflation?, Phys. Rev., D 62, 103512, (2000) [45] Davis, A-C; Dimopoulos, K.; Prokopec, T.; Tornkvist, O., Primordial spectrum of gauge fields from inflation, Phys. Lett., B 501, 165, (2001) [46] Anber, MM; Sorbo, L., N-flationary magnetic fields, JCAP, 10, 018, (2006) [47] Martin, J.; Yokoyama, J., Generation of large-scale magnetic fields in single-field inflation, JCAP, 01, 025, (2008) [48] Bamba, K.; Odintsov, SD, Inflation and late-time cosmic acceleration in non-minimal Maxwell-F(R) gravity and the generation of large-scale magnetic fields, JCAP, 04, 024, (2008) [49] Emami, R.; Firouzjahi, H.; Movahed, MS, Inflation from charged scalar and primordial magnetic fields?, Phys. Rev., D 81, 083526, (2010) [50] Durrer, R.; Hollenstein, L.; Jain, RK, Can slow roll inflation induce relevant helical magnetic fields?, JCAP, 03, 037, (2011) [51] Ferreira, RJZ; Jain, RK; Sloth, MS, Inflationary magnetogenesis without the strong coupling problem, JCAP, 10, 004, (2013) [52] Ferreira, RJZ; Jain, RK; Sloth, MS, Inflationary magnetogenesis without the strong coupling problem II: constraints from CMB anisotropies and B-modes, JCAP, 06, 053, (2014) [53] Dvali, G.; Pujolàs, O.; Redi, M., Consistent Lorentz violation in flat and curved space, Phys. Rev., D 76, 044028, (2007) [54] Himmetoglu, B.; Contaldi, CR; Peloso, M., Ghost instabilities of cosmological models with vector fields nonminimally coupled to the curvature, Phys. Rev., D 80, 123530, (2009) [55] BICEP2 collaboration; Ade, PAR; etal., Detection of B-mode polarization at degree angular scales by BICEP2, Phys. Rev. Lett., 112, 241101, (2014) [56] Broderick, AE; Chang, P.; Pfrommer, C., The cosmological impact of luminous TeV blazars I: implications of plasma instabilities for the intergalactic magnetic field and extragalactic gamma-ray background, Astrophys. J., 752, 22, (2012) [57] Miniati, F.; Elyiv, A., Relaxation of blazar induced pair beams in cosmic voids: measurement of magnetic field in voids and thermal history of the IGM, Astrophys. J., 770, 54, (2013) [58] Durrer, R.; Neronov, A., Cosmological magnetic fields: their generation, evolution and observation, Astron. Astrophys. Rev., 21, 62, (2013) [59] Kawasaki, M.; Kohri, K.; Sugiyama, N., Mev scale reheating temperature and thermalization of neutrino background, Phys. Rev., D 62, 023506, (2000) [60] Hannestad, S., What is the lowest possible reheating temperature?, Phys. Rev., D 70, 043506, (2004) [61] Bezrukov, FL; Shaposhnikov, M., The standard model Higgs boson as the inflaton, Phys. Lett., B 659, 703, (2008) [62] Vachaspati, T., Magnetic fields from cosmological phase transitions, Phys. Lett., B 265, 258, (1991) [63] Cornwall, JM, Speculations on primordial magnetic helicity, Phys. Rev., D 56, 6146, (1997) [64] Vachaspati, T., Magnetic fields in the aftermath of phase transitions, Phil. Trans. Roy. Soc. Lond., A 366, 2915, (2008) [65] F.W. J. Olver, D.W. Lozier, R.F. Boisvert and C.W. Clark, NIST Handbook of Mathematical Functions, Cambridge University Press, 2010.
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