Skip to main content

Recrudescence of massive fermion production by oscillons

A preprint version of the article is available at arXiv.


We bring together the physics of preheating, following a period of inflation, and the dynamics of non-topological solitons, namely oscillons. We show that the oscillating condensate that makes up an oscillon can be an efficient engine for producing heavy fermions, just as a homogeneous condensate is known for doing the same. This then allows heavy fermions to be produced when the energy scale of the Universe has dropped below the scale naturally associated to the fermions.


  1. A.D. Dolgov and D.P. Kirilova, on particle creation by a time dependent scalar field, Sov. J. Nucl. Phys. 51 (1990) 172 [Yad. Fiz. 51 (1990) 273] [INSPIRE].

  2. J.H. Traschen and R.H. Brandenberger, Particle Production During Out-of-equilibrium Phase Transitions, Phys. Rev. D 42 (1990) 2491 [INSPIRE].

    ADS  Google Scholar 

  3. L. Kofman, A.D. Linde and A.A. Starobinsky, Reheating after inflation, Phys. Rev. Lett. 73 (1994) 3195 [hep-th/9405187] [INSPIRE].

    ADS  Article  Google Scholar 

  4. Y. Shtanov, J.H. Traschen and R.H. Brandenberger, Universe reheating after inflation, Phys. Rev. D 51 (1995) 5438 [hep-ph/9407247] [INSPIRE].

  5. M. Yoshimura, Catastrophic particle production under periodic perturbation, Prog. Theor. Phys. 94 (1995) 873 [hep-th/9506176] [INSPIRE].

    ADS  Article  Google Scholar 

  6. D.I. Kaiser, Post inflation reheating in an expanding universe, Phys. Rev. D 53 (1996) 1776 [astro-ph/9507108] [INSPIRE].

  7. L. Kofman, A.D. Linde and A.A. Starobinsky, Towards the theory of reheating after inflation, Phys. Rev. D 56 (1997) 3258 [hep-ph/9704452] [INSPIRE].

  8. S. Yu. Khlebnikov and I.I. Tkachev, Classical decay of inflaton, Phys. Rev. Lett. 77 (1996) 219 [hep-ph/9603378] [INSPIRE].

  9. S. Yu. Khlebnikov and I.I. Tkachev, The Universe after inflation: The wide resonance case, Phys. Lett. B 390 (1997) 80 [hep-ph/9608458] [INSPIRE].

  10. S. Yu. Khlebnikov and I.I. Tkachev, Resonant decay of Bose condensates, Phys. Rev. Lett. 79 (1997) 1607 [hep-ph/9610477] [INSPIRE].

  11. S.Y. Khlebnikov and I.I. Tkachev, Relic gravitational waves produced after preheating, Phys. Rev. D 56 (1997) 653 [hep-ph/9701423] [INSPIRE].

  12. B. Bassett, The preheating — gravitational wave correspondence: 1., Phys. Rev. D 56 (1997) 3439 [hep-ph/9704399] [INSPIRE].

  13. D. Tilley and R. Maartens, Gravitational waves in preheating, Class. Quant. Grav. 17 (2000) 2875 [gr-qc/0002089] [INSPIRE].

  14. J. García-Bellido and D.G. Figueroa, A stochastic background of gravitational waves from hybrid preheating, Phys. Rev. Lett. 98 (2007) 061302 [astro-ph/0701014] [INSPIRE].

  15. J.F. Dufaux, A. Bergman, G.N. Felder, L. Kofman and J.-P. Uzan, Theory and Numerics of Gravitational Waves from Preheating after Inflation, Phys. Rev. D 76 (2007) 123517 [arXiv:0707.0875] [INSPIRE].

    ADS  Google Scholar 

  16. S.-Y. Zhou, E.J. Copeland, R. Easther, H. Finkel, Z.-G. Mou and P.M. Saffin, Gravitational Waves from Oscillon Preheating, JHEP 10 (2013) 026 [arXiv:1304.6094] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  17. S. Kasuya and M. Kawasaki, Can topological defects be formed during preheating?, Phys. Rev. D 56 (1997) 7597 [hep-ph/9703354] [INSPIRE].

  18. I. Tkachev, S. Khlebnikov, L. Kofman and A.D. Linde, Cosmic strings from preheating, Phys. Lett. B 440 (1998) 262 [hep-ph/9805209] [INSPIRE].

  19. S. Khlebnikov, L. Kofman, A.D. Linde and I. Tkachev, First order nonthermal phase transition after preheating, Phys. Rev. Lett. 81 (1998) 2012 [hep-ph/9804425] [INSPIRE].

  20. I.I. Tkachev, Phase transitions at preheating, Phys. Lett. B 376 (1996) 35 [hep-th/9510146] [INSPIRE].

    ADS  Article  Google Scholar 

  21. L. Kofman, A.D. Linde and A.A. Starobinsky, Nonthermal phase transitions after inflation, Phys. Rev. Lett. 76 (1996) 1011 [hep-th/9510119] [INSPIRE].

    ADS  Article  Google Scholar 

  22. M.A. Amin, Inflaton fragmentation: Emergence of pseudo-stable inflaton lumps (oscillons) after inflation, arXiv:1006.3075 [INSPIRE].

  23. M.A. Amin, R. Easther and H. Finkel, Inflaton Fragmentation and Oscillon Formation in Three Dimensions, JCAP 12 (2010) 001 [arXiv:1009.2505] [INSPIRE].

    ADS  Article  Google Scholar 

  24. M.A. Amin, R. Easther, H. Finkel, R. Flauger and M.P. Hertzberg, Oscillons After Inflation, Phys. Rev. Lett. 108 (2012) 241302 [arXiv:1106.3335] [INSPIRE].

    ADS  Article  Google Scholar 

  25. E.W. Kolb, A.D. Linde and A. Riotto, GUT baryogenesis after preheating, Phys. Rev. Lett. 77 (1996) 4290 [hep-ph/9606260] [INSPIRE].

  26. E.W. Kolb, A. Riotto and I.I. Tkachev, GUT baryogenesis after preheating: Numerical study of the production and decay of X bosons, Phys. Lett. B 423 (1998) 348 [hep-ph/9801306] [INSPIRE].

  27. J. García-Bellido, D. Yu. Grigoriev, A. Kusenko and M.E. Shaposhnikov, Nonequilibrium electroweak baryogenesis from preheating after inflation, Phys. Rev. D 60 (1999) 123504 [hep-ph/9902449] [INSPIRE].

  28. J. García-Bellido and E. Ruiz Morales, Particle production from symmetry breaking after inflation, Phys. Lett. B 536 (2002) 193 [hep-ph/0109230] [INSPIRE].

  29. D. Boyanovsky, M. D’Attanasio, H.J. de Vega, R. Holman and D.S. Lee, Reheating and thermalization: Linear versus nonlinear relaxation, Phys. Rev. D 52 (1995) 6805 [hep-ph/9507414] [INSPIRE].

  30. J. Baacke, K. Heitmann and C. Patzold, Nonequilibrium dynamics of fermions in a spatially homogeneous scalar background field, Phys. Rev. D 58 (1998) 125013 [hep-ph/9806205] [INSPIRE].

  31. P.B. Greene and L. Kofman, Preheating of fermions, Phys. Lett. B 448 (1999) 6 [hep-ph/9807339] [INSPIRE].

  32. I.I. Tkachev, Inflation, Nucl. Phys. Proc. Suppl. 110 (2002) 144 [hep-ph/0112136] [INSPIRE].

  33. G.F. Giudice, M. Peloso, A. Riotto and I. Tkachev, Production of massive fermions at preheating and leptogenesis, JHEP 08 (1999) 014 [hep-ph/9905242] [INSPIRE].

  34. S. Borsányi and M. Hindmarsh, Low-cost fermions in classical field simulations, Phys. Rev. D 79 (2009) 065010 [arXiv:0809.4711] [INSPIRE].

    ADS  Google Scholar 

  35. J. Berges, D. Gelfand and J. Pruschke, Quantum theory of fermion production after inflation, Phys. Rev. Lett. 107 (2011) 061301 [arXiv:1012.4632] [INSPIRE].

    ADS  Article  Google Scholar 

  36. M. Gleiser, Pseudostable bubbles, Phys. Rev. D 49 (1994) 2978 [hep-ph/9308279] [INSPIRE].

  37. A.G. Cohen, S.R. Coleman, H. Georgi and A. Manohar, The Evaporation of Q Balls, Nucl. Phys. B 272 (1986) 301 [INSPIRE].

    ADS  Article  Google Scholar 

  38. T. Multamaki and I. Vilja, Analytical and numerical properties of Q balls, Nucl. Phys. B 574 (2000) 130 [hep-ph/9908446] [INSPIRE].

  39. S.S. Clark, Particle production from Q-balls, Nucl. Phys. B 756 (2006) 38 [hep-ph/0510078] [INSPIRE].

  40. M. Kawasaki and M. Yamada, Q ball Decay Rates into Gravitinos and Quarks, Phys. Rev. D 87 (2013) 023517 [arXiv:1209.5781] [INSPIRE].

    ADS  Google Scholar 

  41. S.R. Coleman, Q Balls, Nucl. Phys. B 262 (1985) 263 [Erratum ibid. B 269 (1986) 744] [INSPIRE].

  42. W. Greiner, Relativistic quantum mechanics, Springer, Berlin, Germany (1990).

    Book  MATH  Google Scholar 

  43. P. Strange, Relativistic Quantum Mechanics: with applications in condensed matter and atomic physics, Cambridge University Press, U.K. (1998).

    Book  Google Scholar 

  44. P.B. Greene, Inflationary reheating and fermions, AIP Conf. Proc. 478 (1999) 72 [hep-ph/9905256] [INSPIRE].

  45. I.L. Bogolyubsky and V.G. Makhankov, On the Pulsed Soliton Lifetime in Two Classical Relativistic Theory Models, JETP Lett. 24 (1976) 12 [INSPIRE].

    ADS  Google Scholar 

  46. E.W. Kolb and I.I. Tkachev, Nonlinear axion dynamics and formation of cosmological pseudosolitons, Phys. Rev. D 49 (1994) 5040 [astro-ph/9311037] [INSPIRE].

  47. E.J. Copeland, M. Gleiser and H.R. Muller, Oscillons: Resonant configurations during bubble collapse, Phys. Rev. D 52 (1995) 1920 [hep-ph/9503217] [INSPIRE].

  48. I. Dymnikova, L. Koziel, M. Khlopov and S. Rubin, Quasilumps from first order phase transitions, Grav. Cosmol. 6 (2000) 311 [hep-th/0010120] [INSPIRE].

    ADS  MATH  Google Scholar 

  49. H. Segur and M.D. Kruskal, Nonexistence of Small Amplitude Breather Solutions in ϕ 4 Theory, Phys. Rev. Lett. 58 (1987) 747 [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  50. G. Fodor, P. Forgacs, Z. Horvath and M. Mezei, Computation of the radiation amplitude of oscillons, Phys. Rev. D 79 (2009) 065002 [arXiv:0812.1919] [INSPIRE].

    ADS  Google Scholar 

  51. M. Gleiser and D. Sicilia, A General Theory of Oscillon Dynamics, Phys. Rev. D 80 (2009) 125037 [arXiv:0910.5922] [INSPIRE].

    ADS  Google Scholar 

  52. P.M. Saffin and A. Tranberg, Oscillons and quasi-breathers in D+1 dimensions, JHEP 01 (2007) 030 [hep-th/0610191] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  53. M. Gleiser, d-dimensional oscillating scalar field lumps and the dimensionality of space, Phys. Lett. B 600 (2004) 126 [hep-th/0408221] [INSPIRE].

  54. M.P. Hertzberg, Quantum Radiation of Oscillons, Phys. Rev. D 82 (2010) 045022 [arXiv:1003.3459] [INSPIRE].

    ADS  Google Scholar 

  55. P.M. Saffin, P. Tognarelli and A. Tranberg, Oscillon Lifetime in the Presence of Quantum Fluctuations, JHEP 08 (2014) 125 [arXiv:1401.6168] [INSPIRE].

    ADS  Article  Google Scholar 

  56. A. Tranberg and D.J. Weir, On the quantum stability of Q-balls, JHEP 04 (2014) 184 [arXiv:1310.7487] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  57. M.A. Amin and D. Shirokoff, Flat-top oscillons in an expanding universe, Phys. Rev. D 81 (2010) 085045 [arXiv:1002.3380] [INSPIRE].

    ADS  Google Scholar 

  58. M. Gleiser and D. Sicilia, Analytical Characterization of Oscillon Energy and Lifetime, Phys. Rev. Lett. 101 (2008) 011602 [arXiv:0804.0791] [INSPIRE].

    ADS  Article  Google Scholar 

Download references

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Paul M. Saffin.

Additional information

ArXiv ePrint: 1612.02014

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Saffin, P.M. Recrudescence of massive fermion production by oscillons. J. High Energ. Phys. 2017, 126 (2017).

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI:


  • Nonperturbative Effects
  • Solitons Monopoles and Instantons