Abstract
We study the generation of magnetic fields in the Higgs inflation model with the axial coupling in order to break the conformal invariance of the Maxwell action and produce strong enough magnetic fields for observed large-scale magnetic fields. This interaction breaks the parity and enables a production of only one of the polarization states of the electromagnetic field due to axion-like coupling of electromagnetic field to the inflation. Therefore, the produced magnetic fields are helical. In fact,calculations show the mode of one polarization undergoes amplification, while the other one diminishes. We consider radiatively corrected Higgs inflation potential. In comparison to the Starobinsky potential, we obtain an extra term as a one loop correction and determine the spectrum of generalized electromagnetic fields. The effect of quantum correction modifies potential so that in some certain conditions when back reaction is weak the observed large-scale magnetic field can be explained by our modified potential. We should emphasize in this model we only consider linear approximation for electromagnetic field so that the theory does not contain higher-order derivatives and the so-called ghost degrees of freedom. Therefore, the theory is consistent with cosmology. In addition,the magnetic field generated in this model has very small correlation length. It is impossible to explain within this model both the strength of magnetic field and its large coherence length. Due to the nontrivial helicity, the produced magnetic fields undergo the inverse cascade process in the turbulent plasma which can strongly increase their correlation length. We find that, for two values of coupling parameter \(\chi _{1}=5\times 10^{9}M_{p}^{-2}\) and \(\chi _{1}=7.5\times 10^{9}M_{p}^{-2}\), the back-reaction is weak and our analysis is valid.
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References
Ade, P.A.R., et al.: (Planck Collaboration): Planck 2015 results. XIX. Constraints on primordial magnetic fields. Astron. Astrophys. 594, A19 (2016)
Aghanim, N. et al. (Planck Collaboration): Planck 2018 results. VI. Cosmological parameters. arXiv:1807.06209v1
Barvinsky, A., Kamenshchik, A.Y., Starobinsky, A.: Inflation scenario via the standard model Higgs boson and LHC. JCAP 0811, 021 (2008)
Barvinsky, A.O., Kamenshchik, A.Y., Kiefer, C., Starobinsky, A.A., Steinwachs, C.: Asymptotic freedom in inflationary cosmology with a non-minimal coupled Higgs field. JCAP 0912, 003 (2009)
Barvinsky, A.O., Shaposhnikov, M.: Standard Model Higgs boson mass from inflation: two loop analysis. JHEP 07, 089 (2009)
Barvinsky, A.O., Kamenshchik, A.Y., Kiefer, C., Starobinsky, A.A., Steinwachs, C.F.: Higgs boson, renormalization group, and naturalness in cosmology. arXiv:0910.1041v3 [hep-ph] (2012)
Bamba, K., Yokoyama, J.: Large scale magnetic fields from inflation in dilaton electromagnetism. Phys. Rev. D 69, 043507 (2004)
Bezrukov, F.L., Shaposhnikov, M.: The standard model Higgs boson as the inflation. Phys. Lett. B 659, 703706 (2008)
Bezrukov, F., Gorbunov, D., Shaposhnikov, M.: On the initial conditions for the Hot Big Bang. JCAP 0906, 029 (2009)
Bezrukov, F., Rubio, J., Shaposhnikov, M.: Living beyond the edge: Higgs inflation and vacuum metastability. Phys. Rev. D 92, 88 (2009)
Bezrukov, F., Shaposhnikov, M.: Standard model Higgs boson mass from inflation: two loop analysis. arXiv:0904.1537v2 [hep-ph] (2009)
Bezrukov, F.L., Magnin, A., Shaposhnikov, M.: Standard model Higgs boson mass from inflation. Phys. Lett. B 675, 703 (2009)
Birrel, N.D., Davies, P.C.W.: Quantum Fields in Curved Space. Cambridge University Press, Cambridge (1982)
Buttazzo, D., Degrassi, G., Giardino, P.P., Giudice, G.F., Sala, F., Salvio, A., Strumia, A.: Investigating the near-criticality of the Higgs boson. JHEP 12(089), 089 (2013)
Caprini, C., Gabici, S.: Gamma-ray observations of blazars and the intergalactic magnetic field spectrum. Phys. Rev. D 91, 123514 (2015)
de Simone, A., Hertzberg, M.P., Wilczek, F.: Running inflation in the standard model. Phys. Lett. B 678, 1 (2008)
Demozzi, V., Mukhanov, V.M., Rubinstein, H.: Magnetic fields from inflation? J. Cosmol. Astropart. Phys. 08, 025 (2009)
Dolgov, A.D.: Breaking of conformal invariance and electromagnetic field generation in the universe. Phys. Rev. D 48, 2499 (1993)
Durrer, R., Neronov, A.: Cosmological magnetic fields: their generation, evolution and observation. Astron. Astrophys. Rev. 21, 62 (2013)
Durrer, R., Hollenstein, L., KumarJain, R.: Can slow roll inflation induce relevant helical magnetic fields. JCAP 03(037), 037 (2011)
Faraoni, V., Gunzig, E., Nardone, P.: Conformal transformations in classical gravitational theories and in cosmology. arXiv:gr-qc/9811047v1
Ferreira, R.J.Z., Jain, R.K., Sloth, M.S.: Inflationary magnetogenesis without the strong coupling problem. J. Cosmol. Astropart. Phys. 10, 004 (2013)
Ferreira, R.J.Z., Jain, R.K., Sloth, M.S.: Inflationary magnetogenesis without the strong coupling problem II: Constraints from CMB anisotropies and B-modes. J. Cosmol. Astropart. Phys. 06, 053 (2014)
Garcia-Bellindo, J., Figueroa, D.G., Rubio, J.: Preheating in the standard model with the Higgs-inflation coupled to gravity. Phys. Rev. D 79, 063531 (2009)
Garretson, W.D., Field, G.B., Carroll, S.M.: Primordial magnetic fields from pseudo Goldstone bosons. Phys. Rev. D 46, 5346 (1992)
Giovannini, M.: On the variation of the gauge couplings during inflation. Phys. Rev. D 64, 061301 (2001)
Giovannini, M.: The magnetized universe. Int. J. Mod. Phys. D 13, 391 (2004)
Gorbunov, D.S., Rubakov, V.A.: Introduction to the Theory of the Early Universe: Cosmological Perturbations and Inflationary Theory. World Scientific Publishing, Singapore (2011)
Grasso, D., Rubinstein, H.R.: Magnetic fields in the early universe. Phys. Rep. 348, 163 (2001)
Guth, A.: The Inflationary Universe: The Quest for a New Theory of Cosmic Origins. Perseus Books (1997)
Jedamzik, K., Saveliev, A.: A stringent limit on primordial magnetic fields from the cosmic microwave backround radiation. arXiv:1804.06115 [astro-ph.CO]
Kandus, A., Kunze, K.E., Tsagas, C.G.: Primordial magnetogenesis. Phys. Rep. 505, 1 (2011)
Kanno, S., Soda, J., Watanabe, M.: Cosmological magnetic fields from inflation and backreaction. J. Cosmol. Astropart. Phys. 12, 009 (2009)
Ketov, S.V.: Modified supergravity and early universe: the meeting point of cosmology and high-energy physics. arXiv:1201.2239v3 [hep-th]
Ketov, S.V., Starobinsky, A.A.: Embedding \( R+R^{2} \) inflation in supergravity. Phys. Rev. D 83, 063512 (2011)
Kronberg, P.P.: Extragalactic magnetic fields. Rep. Prog. Phys. 57, 325 (1994)
Liddle, A.R., Parsons, P., Barrow, J.D.: Formalizing the slow roll approximation in inflation. Phys. Rev. D 50, 7222 (1994)
Linde, A.: Particle physics and inflationary cosmology. Contemp. Concepts Phys. 5, 1 (2005)
Lyth, D., Liddle, A.: The Primordial Density Perturbation. Cambridge University Press, Cambridge (2009)
Maeda, K.I.: Towards the Einstein–Hilbert action via conformal transformation. Phys. Rev. D 39, 3159 (1989)
Martin, J., Ringeval, C., Vennin, V.: Encyclopædia inflationaris. Phys. Dark Univ. 75, 5–6 (2014)
Martin, J., Yokoyama, J.: Generation of large-scale magnetic fields in single-field inflation. JCAP 01, 025 (2008)
Mukhanov, V.: Physical Foundations of Cosmology. Cambridge University Press, Cambridge (2005)
Neronov, A., Vovk, I.: Evidence for strong extragalactic magnetic fields from Fermi observations of TeV blazars. Science 328, 73 (2010)
Parker, L.: Particle creation in expanding universes. Phys. Rev. Lett. 21, 562 (1968)
Ratra, B.: Cosmological ‘seed’ magnetic field from inflation. Astrophys. J. 391, L1 (1992)
Savchenko, O., Shtanov, Y.: Magnetogenesis by non-minimal coupling to gravity in the Starobinsky inflationary model. arXiv:1808.06193v1
Sobol, O.O., Gorbar, E.V., Vilchinskii, S.I.: Backreaction of electromagnetic fields and the Schwinger effect in pseudoscalar inflation magnetogenesis. Phys. Rev. D 100, 063523 (2019)
Sobol, O.O., Gorbar, E.V., Kamarpour, M., Vilchinskii, S.I.: Influence of back-reaction of electric fields and the Schwinger effect on inflationary magnetogenesis. Phys. Rev. D 98, 063534 (2018)
Spokoiny, B.L.: Inflation and generation of perturbations in broken-symmetric theory of gravity. Phys. Lett. B 147, 39 (1984)
Steinwachs, C.F., Kamenshchik, A.Y.: Non-minimal Higgs inflation and frame dependence in cosmology. arXiv:1301.5543
Starobinsky, A.A.: A new type of isotropic cosmological models without singularity. Phys. Lett. B 91, 99–102 (1980)
Subramanian, K.: The origin, evolution and signatures of primordial magnetic fields. Rep. Prog. Phys. 79, 076901 (2016)
Sutton, D.R., Feng, C., Reichardt, C.L.: Current and future constraints on primordial magnetic fields. Astrophys. J. 846, 164 (2017)
Synge, J.L.: Relativity: The General Theory. North Holland, Amsterdam (1955)
Tavecchio, F., Ghisellini, G., Foschini, L., Bonnoli, G., Ghirlanda, G., Coppi, P.: The intergalactic magnetic field constrained by Fermi/LAT observations of the TeV blazar 1ES 0229+200. Mon. Not. R. Astron. Soc. 406, L70 (2010)
Taylor, A.M., Vovk, I., Neronov, A.: Extragalactic magnetic fields constraints from simultaneous GeV-TeV observations of blazars. Astron. Astrophys. 529, A144 (2011)
Turner, M.S., Widrow, L.M.: Inflation-produced, large-scale magnetic fields. Phys. Rev. D 37, 2743 (1988)
Vachaspati, T.: Progress on cosmological magnetic fields. arXiv:2010.10525v1 [astro-ph.CO] (2020)
Vilchinskii, S., Sobol, O., Gorbar, E.V., Rudennok, I.: Magnetogenesis during inflation and preheating in the Starobinsky model. Phys. Rev. D 95, 083509 (2017)
Wald, R.M.: General Relativity. Chicago University Press, Chicago (1984)
Widrow, L.M.: Origin of galactic and extragalactic magnetic fields. Rev. Mod. Phys. 74, 775 (2002)
Acknowledgements
The author is thankful to S. Vilchinskii, E.V. Gorbar, and O. Sobol for critical comments and useful discussions during the preparation of manuscript. The author is also thankful to O. Sobol for his assistance in plotting figures.
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Kamarpour, M. Magnetogenesis in Higgs inflation. Gen Relativ Gravit 53, 53 (2021). https://doi.org/10.1007/s10714-021-02824-0
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DOI: https://doi.org/10.1007/s10714-021-02824-0