Magnetogenesis in Natural Inflation Model
DOI:
https://doi.org/10.15407/ujpe63.8.673Keywords:
natural inflation, magnetogenesis, kinetic coupling, large-scale magnetic fieldsAbstract
We study the process of inflationary magnetogenesis in the natural single-field inflation model, whose parameters are chosen in accordance with the recent observations by the Planck collaboration [1]. The conformal invariance of the Maxwell action is broken by a kinetic coupling with the inflaton field by means of the coupling function as a power of the scale factor, I(ф) ∝ aa, and a < 0 is used in order to avoid the strong coupling problem. For such a, the electric component of the energy density dominates over the magnetic one and, for a <- −2.2, it causes a strong back-reaction, which can spoil inflation and terminate the enhancement of the magnetic field. It is found that the magnetic fields generated without back-reaction problem cannot exceed ∼10−20G at the present epoch, and their spectrum has a blue tilt.
References
<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>
Downloads
Published
How to Cite
Issue
Section
License
Copyright Agreement
License to Publish the Paper
Kyiv, Ukraine
The corresponding author and the co-authors (hereon referred to as the Author(s)) of the paper being submitted to the Ukrainian Journal of Physics (hereon referred to as the Paper) from one side and the Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, represented by its Director (hereon referred to as the Publisher) from the other side have come to the following Agreement:
1. Subject of the Agreement.
The Author(s) grant(s) the Publisher the free non-exclusive right to use the Paper (of scientific, technical, or any other content) according to the terms and conditions defined by this Agreement.
2. The ways of using the Paper.
2.1. The Author(s) grant(s) the Publisher the right to use the Paper as follows.
2.1.1. To publish the Paper in the Ukrainian Journal of Physics (hereon referred to as the Journal) in original language and translated into English (the copy of the Paper approved by the Author(s) and the Publisher and accepted for publication is a constitutive part of this License Agreement).
2.1.2. To edit, adapt, and correct the Paper by approval of the Author(s).
2.1.3. To translate the Paper in the case when the Paper is written in a language different from that adopted in the Journal.
2.2. If the Author(s) has(ve) an intent to use the Paper in any other way, e.g., to publish the translated version of the Paper (except for the case defined by Section 2.1.3 of this Agreement), to post the full Paper or any its part on the web, to publish the Paper in any other editions, to include the Paper or any its part in other collections, anthologies, encyclopaedias, etc., the Author(s) should get a written permission from the Publisher.
3. License territory.
The Author(s) grant(s) the Publisher the right to use the Paper as regulated by sections 2.1.1–2.1.3 of this Agreement on the territory of Ukraine and to distribute the Paper as indispensable part of the Journal on the territory of Ukraine and other countries by means of subscription, sales, and free transfer to a third party.
4. Duration.
4.1. This Agreement is valid starting from the date of signature and acts for the entire period of the existence of the Journal.
5. Loyalty.
5.1. The Author(s) warrant(s) the Publisher that:
– he/she is the true author (co-author) of the Paper;
– copyright on the Paper was not transferred to any other party;
– the Paper has never been published before and will not be published in any other media before it is published by the Publisher (see also section 2.2);
– the Author(s) do(es) not violate any intellectual property right of other parties. If the Paper includes some materials of other parties, except for citations whose length is regulated by the scientific, informational, or critical character of the Paper, the use of such materials is in compliance with the regulations of the international law and the law of Ukraine.
6. Requisites and signatures of the Parties.
Publisher: Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine.
Address: Ukraine, Kyiv, Metrolohichna Str. 14-b.
Author: Electronic signature on behalf and with endorsement of all co-authors.