Magnetogenesis in Natural Inflation Model

M. Kamarpour; O. Sobol

doi:10.15407/ujpe63.8.673

Автор(и)

M. Kamarpour Physics Faculty, Taras Shevchenko National University of Kyiv
O. Sobol Physics Faculty, Taras Shevchenko National University of Kyiv, Institute of Physics, ´ Ecole Polytechnique F´ed´erale de Lausanne

DOI:

https://doi.org/10.15407/ujpe63.8.673

Ключові слова:

natural inflation, magnetogenesis, kinetic coupling, large-scale magnetic fields

Анотація

Дослiджено процес iнфляцiйного магнетогенезису у моделi природної iнфляцiї з одним полем, параметри якої вибрано згiдно з даними нещодавнiх спостережень Колаборацiї Planck [1]. Конформну iнварiантнiсть максвеллiвської дiї порушено кiнетичним зв’язком з iнфлатонним полем через функцiю, яка поводить себе як степiнь масштабного фактора, I(ф) ∝ aa, i значення a < 0 використано для того,
щоб уникнути проблеми сильного зв’язку. Для таких значень a електрична компонента густини енергiї домiнує над магнiтною i для a <- −2,2 вона призводить до сильної зворотної реакцiї, що може порушити iнфляцiйну динамiку i припинити пiдсилення магнiтного поля. Показано, що магнiтнi поля, згенерованi без спричинення зворотної реакцiї, не можуть перевищувати в теперiшню епоху ∼ 10−20 Гс, а їхнiй спектр має блакитний ухил.

Посилання

<ol>
<li>P.A.R. Ade et al. (Planck Collaboration). Planck 2015 results. XX. Constraints on inflation. Astron. Astrophys. 594, A20 (2016).
<a href="https://doi.org/10.1051/0004-6361/201525898">https://doi.org/10.1051/0004-6361/201525898</a>">https://doi.org/10.1051/0004-6361/201525898">https://doi.org/10.1051/0004-6361/201525898</a></a>
</li>
<li>P.P. Kronberg. Extragalactic magnetic fields. Rep. Prog. Phys. 57, 325 (1994).
<a href="https://doi.org/10.1088/0034-4885/57/4/001">https://doi.org/10.1088/0034-4885/57/4/001</a>
</li>
<li>D. Grasso, H.R. Rubinstein. Magnetic fields in the early universe. Phys. Rep. 348, 163 (2001).
<a href="https://doi.org/10.1016/S0370-1573(00)00110-1">https://doi.org/10.1016/S0370-1573(00)00110-1</a>
</li>
<li>L.M. Widrow. Origin of galactic and extragalactic magnetic fields. Rev. Mod. Phys. 74, 775 (2002).
<a href="https://doi.org/10.1103/RevModPhys.74.775">https://doi.org/10.1103/RevModPhys.74.775</a>
</li>
<li>M. Giovannini. The magnetized universe. Int. J. Mod. Phys. D 13, 391 (2004).
<a href="https://doi.org/10.1142/S0218271804004530">https://doi.org/10.1142/S0218271804004530</a>
</li>
<li>A. Kandus, K.E. Kunze, C. G. Tsagas. Primordial magnetogenesis. Phys. Rep. 505, 1 (2011).
<a href="https://doi.org/10.1016/j.physrep.2011.03.001">https://doi.org/10.1016/j.physrep.2011.03.001</a>
</li>
<li>R. Durrer, A. Neronov. Cosmological magnetic fields: their generation, evolution and observation. Astron. Astrophys. Rev. 21, 62 (2013).
<a href="https://doi.org/10.1007/s00159-013-0062-7">https://doi.org/10.1007/s00159-013-0062-7</a>
</li>
<li>K. Subramanian. The origin, evolution and signatures of primordial magnetic fields. Rep. Prog. Phys. 79, 076901 (2016).
<a href="https://doi.org/10.1088/0034-4885/79/7/076901">https://doi.org/10.1088/0034-4885/79/7/076901</a>
</li>
<li>D.R. Sutton, C. Feng, C.L. Reichardt. Current and future constraints on primordial magnetic fields. Astrophys. J. 846, 164 (2017).
<a href="https://doi.org/10.3847/1538-4357/aa85e2">https://doi.org/10.3847/1538-4357/aa85e2</a>
</li>
<li> K. Jedamzik, A. Saveliev. A stringent limit on primordial magnetic fields from the cosmic microwave backround radiation. arXiv:1804.06115 [astro-ph.CO].
</li>
<li> A. Neronov, I. Vovk. Evidence for strong extragalactic magnetic fields from Fermi observations of TeV blazars. Science 328, 73 (2010).
<a href="https://doi.org/10.1126/science.1184192">https://doi.org/10.1126/science.1184192</a>
</li>
<li> F. Tavecchio, G. Ghisellini, L. Foschini et al. The intergalactic magnetic field constrained by Fermi/LAT observations of the TeV blazar 1ES 0229+200. Mon. Not. R. Astron. Soc. 406, L70 (2010).
</li>
<li> A.M. Taylor, I. Vovk, A. Neronov. Extragalactic magnetic fields constraints from simultaneous GeV-TeV observations of blazars. Astron. Astrophys. 529, A144 (2011).
<a href="https://doi.org/10.1051/0004-6361/201116441">https://doi.org/10.1051/0004-6361/201116441</a>
</li>
<li> C. Caprini, S. Gabici. Gamma-ray observations of blazars and the intergalactic magnetic field spectrum. Phys. Rev. D 91, 123514 (2015).
<a href="https://doi.org/10.1103/PhysRevD.91.123514">https://doi.org/10.1103/PhysRevD.91.123514</a>
</li>
<li> L. Biermann. ? Uber den ursprung der magnetfelder auf sternen und im interstellaren raum. (About the origin of the magnetic fields on stars and in the interstellar space). Z. Naturforsch. A 5, 65 (1950).
</li>
<li> Ya.B. Zeldovich, A.A. Ruzmaikin, D.D. Sokoloff. Magnetic Fields in Astrophysics (Gordon and Breach, 1990) [ISBN: 978-0677223308].
</li>
<li> H. Lesch, M. Chiba. Protogalactic evolution and magnetic fields. Astron. Astrophys. 297, 305 (1995).
</li>
<li> R. Kulsrud, S.C. Cowley, A.V. Gruzinov et al. Dynamos and cosmic magnetic fields. Phys. Rep. 283, 213 (1997).
<a href="https://doi.org/10.1016/S0370-1573(96)00061-0">https://doi.org/10.1016/S0370-1573(96)00061-0</a>
</li>
<li> S.A. Colgate, H. Li. The origin of the magnetic fields of the universe: The plasma astrophysics of the free energy of the universe. Phys. Plasmas 8, 2425 (2001).
<a href="https://doi.org/10.1063/1.1351827">https://doi.org/10.1063/1.1351827</a>
</li>
<li> M.J. Rees. The origin and cosmogonic implications of seed magnetic fields. Quarterly J. R. Astr. Soc. 28, 197 (1987).
</li>
<li> R.A. Daly, A. Loeb. A possible origin of galactic magnetic fields. Astrophys. J. 364, 451 (1990).
<a href="https://doi.org/10.1086/169429">https://doi.org/10.1086/169429</a>
</li>
<li> T.A. En?lin, P.L. Biermann, P.P. Kronberg et al. Cosmicray protons and magnetic fields in clusters of galaxies and their cosmological consequences. Astrophys. J. 477, 560 (1997).
<a href="https://doi.org/10.1086/303722">https://doi.org/10.1086/303722</a>
</li>
<li> S. Bertone, C. Vogt, T. En?lin. Magnetic field seeding by galactic winds. Mon. Not. R. Astron. Soc. 370, 319 (2006).
<a href="https://doi.org/10.1111/j.1365-2966.2006.10474.x">https://doi.org/10.1111/j.1365-2966.2006.10474.x</a>
</li>
<li> M.S. Turner, L.M. Widrow. Inflation-produced, large-scale magnetic fields. Phys. Rev. D 37, 2743 (1988).
<a href="https://doi.org/10.1103/PhysRevD.37.2743">https://doi.org/10.1103/PhysRevD.37.2743</a>
</li>
<li> B. Ratra. Cosmological "seed" magnetic field from inflation. Astrophys. J. 391, L1 (1992).
<a href="https://doi.org/10.1086/186384">https://doi.org/10.1086/186384</a>
</li>
<li> C.J. Hogan. Magnetohydrodynamic effects of a first-order cosmological phase transition. Phys. Rev. Lett. 51, 1488 (1983).
<a href="https://doi.org/10.1103/PhysRevLett.51.1488">https://doi.org/10.1103/PhysRevLett.51.1488</a>
</li>
<li> J.M. Quashnock, A. Loeb, D.N. Spergel. Magnetic field generation during the cosmological QCD phase transition. Astrophys. J. 344, L49 (1989).
<a href="https://doi.org/10.1086/185528">https://doi.org/10.1086/185528</a>
</li>
<li> T. Vachaspati. Magnetic fields from cosmological phase transitions. Phys. Lett. B 265, 258 (1991).
<a href="https://doi.org/10.1016/0370-2693(91)90051-Q">https://doi.org/10.1016/0370-2693(91)90051-Q</a>
</li>
<li> B.-L. Cheng, A.V. Olinto. Primordial magnetic fields generated in the quark – hadron transition. Phys. Rev. D 50, 2421 (1994).
<a href="https://doi.org/10.1103/PhysRevD.50.2421">https://doi.org/10.1103/PhysRevD.50.2421</a>
</li>
<li> G. Sigl, A.V. Olinto, K. Jedamzik. Primordial magnetic fields from cosmological first order phase transitions. Phys. Rev. D 55, 4582 (1997).
<a href="https://doi.org/10.1103/PhysRevD.55.4582">https://doi.org/10.1103/PhysRevD.55.4582</a>
</li>
<li> J. Ahonen, K. Enqvist. Magnetic field generation in first order phase transition bubble collisions. Phys. Rev. D 57, 664 (1998).
<a href="https://doi.org/10.1103/PhysRevD.57.664">https://doi.org/10.1103/PhysRevD.57.664</a>
</li>
<li> V.F. Mukhanov, G.V. Chibisov. Quantum fluctuations and a nonsingular universe. JETP Lett. 33, 532 (1981).
</li>
<li> S.W. Hawking. The development of irregularities in a single bubble inflationary universe. Phys. Lett. B 115, 295 (1982).
<a href="https://doi.org/10.1016/0370-2693(82)90373-2">https://doi.org/10.1016/0370-2693(82)90373-2</a>
</li>
<li> A.A. Starobinsky. Dynamics of phase transition in the new inflationary universe scenario and generation of perturbations. Phys. Lett. B 117, 175 (1982).
<a href="https://doi.org/10.1016/0370-2693(82)90541-X">https://doi.org/10.1016/0370-2693(82)90541-X</a>
</li>
<li> A.H. Guth, S.Y. Pi. Fluctuations in the new inflationary Universe. Phys. Rev. Lett. 49, 1110 (1982).
<a href="https://doi.org/10.1103/PhysRevLett.49.1110">https://doi.org/10.1103/PhysRevLett.49.1110</a>
</li>
<li> J.M. Bardeen, P.J. Steinhardt, M.S. Turner. Spontaneous creation of almost scale-free density perturbations in an inflationary universe. Phys. Rev. D 28, 679 (1983).
<a href="https://doi.org/10.1103/PhysRevD.28.679">https://doi.org/10.1103/PhysRevD.28.679</a>
</li>
<li> L.P. Grishchuk. Amplification of gravitational waves in an isotropic universe. Sov. Phys. JETP 40, 409 (1975).
</li>
<li> A.A. Starobinsky. Spectrum of relict gravitational radiation and the early state of the Universe. JETP Lett. 30, 682 (1979).
</li>
<li> V.A. Rubakov, M.V. Sazhin, A.V. Veryaskin. Graviton creation in the inflationary Universe and the grand unification scale. Phys. Lett. B 115, 189 (1982).
<a href="https://doi.org/10.1016/0370-2693(82)90641-4">https://doi.org/10.1016/0370-2693(82)90641-4</a>
</li>
<li> L. Parker. Particle creation in expanding universes. Phys. Rev. Lett. 21, 562 (1968).
<a href="https://doi.org/10.1103/PhysRevLett.21.562">https://doi.org/10.1103/PhysRevLett.21.562</a>
</li>
<li> A.D. Dolgov. Breaking of conformal invariance and electromagnetic field generation in the universe. Phys. Rev. D 48, 2499 (1993).
<a href="https://doi.org/10.1103/PhysRevD.48.2499">https://doi.org/10.1103/PhysRevD.48.2499</a>
</li>
<li> M. Gasperini, M. Giovannini, G. Veneziano. Primordial magnetic fields from string cosmology. Phys. Rev. Lett. 75, 3796 (1995).
<a href="https://doi.org/10.1103/PhysRevLett.75.3796">https://doi.org/10.1103/PhysRevLett.75.3796</a>
</li>
<li> M. Giovannini. Magnetogenesis and the dynamics of internal dimensions. Phys. Rev. D 62, 123505 (2000).
<a href="https://doi.org/10.1103/PhysRevD.62.123505">https://doi.org/10.1103/PhysRevD.62.123505</a>
</li>
<li> K. Atmjeet, I. Pahwa, T.R. Seshadri et al. Cosmological magnetogenesis from extra-dimensional Gauss–Bonnet gravity. Phys. Rev. D 89, 063002 (2014).
<a href="https://doi.org/10.1103/PhysRevD.89.063002">https://doi.org/10.1103/PhysRevD.89.063002</a>
</li>
<li> M. Giovannini. On the variation of the gauge couplings during inflation. Phys. Rev. D 64, 061301 (2001).
<a href="https://doi.org/10.1103/PhysRevD.64.061301">https://doi.org/10.1103/PhysRevD.64.061301</a>
</li>
<li> K. Bamba, J. Yokoyama. Large scale magnetic fields from inflation in dilaton electromagnetism. Phys. Rev. D 69, 043507 (2004).
<a href="https://doi.org/10.1103/PhysRevD.69.043507">https://doi.org/10.1103/PhysRevD.69.043507</a>
</li>
<li> J. Martin, J. Yokoyama. Generation of large-scale magnetic fields in single-field inflation. J. Cosmol. Astropart. Phys. 01, 025 (2008).
</li>
<li> V. Demozzi, V.M. Mukhanov, H. Rubinstein. Magnetic fields from inflation. J. Cosmol. Astropart. Phys. 08, 025 (2009).
</li>
<li> S. Kanno, J. Soda, M. Watanabe. Cosmological magnetic fields from inflation and backreaction. J. Cosmol. Astropart. Phys. 12, 009 (2009).
</li>
<li> R.J.Z. Ferreira, R.K. Jain, M.S. Sloth. Inflationary magnetogenesis without the strong coupling problem. J. Cosmol. Astropart. Phys. 10, 004 (2013).
</li>
<li> R.J.Z. Ferreira, R.K. Jain, M.S. Sloth. Inflationary magnetogenesis without the strong coupling problem II: Constraints from CMB anisotropies and B-modes. J. Cosmol. Astropart. Phys. 06, 053 (2014).
</li>
<li> S. Vilchinskii, O. Sobol, E.V. Gorbar et al. Magnetogenesis during inflation and preheating in the Starobinsky model. Phys. Rev. D 95, 083509 (2017).
<a href="https://doi.org/10.1103/PhysRevD.95.083509">https://doi.org/10.1103/PhysRevD.95.083509</a>
</li>
<li> J. Martin, C. Ringeval, V. Vennina. Encyclop?dia inflationaris. Phys. Dark Universe 5–6, 75 (2014).
<a href="https://doi.org/10.1016/j.dark.2014.01.003">https://doi.org/10.1016/j.dark.2014.01.003</a>
</li>
<li> K. Freese, J.A. Frieman, A.V. Olinto. Natural inflation with pseudo Nambu-Goldstone bosons. Phys. Rev. Lett. 65, 3233 (1990).
<a href="https://doi.org/10.1103/PhysRevLett.65.3233">https://doi.org/10.1103/PhysRevLett.65.3233</a>
</li>
<li> F.C. Adams, J.R. Bond, K. Freese et al. Natural inflation: Particle physics models, power-law spectra for large-scale structure, and constraints from the Cosmic Background Explorer. Phys. Rev. D 47, 426 (1993).
<a href="https://doi.org/10.1103/PhysRevD.47.426">https://doi.org/10.1103/PhysRevD.47.426</a>
</li>
<li> J.E. Kim, H.P. Nilles, M. Peloso. Completing natural inflation. J. Cosmol. Astropart. Phys. 01, 005 (2005).
</li>
<li> A.R. Liddle, P. Parsons, J.D. Barrow. Formalizing the slow roll approximation in inflation. Phys. Rev. D 50, 7222 (1994).
<a href="https://doi.org/10.1103/PhysRevD.50.7222">https://doi.org/10.1103/PhysRevD.50.7222</a>
</li>
<li> D.S. Gorbunov, V.A. Rubakov. Introduction to the Theory of the Early Universe: Cosmological Perturbations and Inflationary Theory (World Scientific, 2011) [ISBN 978-981-4322-22-5].
</li>