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Constraining the inflaton potential with gravitational waves from oscillons

Kaloian D. Lozanov1,2,3, Misao Sasaki2,3,4,5, and Jan Tränkle6,*

  • *Contact author: jan.traenkle@itp.uni-hannover.de
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Phys. Rev. D 113, 123507 – Published 3 June, 2026

DOI: https://doi.org/10.1103/p16t-xz3k

Abstract

Under certain conditions, the oscillating inflaton condensate filling the Universe after inflation can fragment and form so-called oscillons. These long-lived solitonlike field configurations can dominate the Universe for several e-folds of expansion, leading to an early matter-dominated phase preceding the standard radiation era. In this paper we show how the rapid final decay of the oscillons leads to an enhanced production of induced gravitational waves, whose energy density can saturate the observational bound on the effective number of relativistic species. We leverage this bound to constrain the inflaton mass, cubic, and quartic self-coupling in generic models that admit oscillon formation, providing novel and complementary constraints in regions of parameter space that are inaccessible with cosmic microwave background observations alone.

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References (102)

  1. A. A. Starobinsky, A new type of isotropic cosmological models without singularity, Phys. Lett. 91B, 99 (1980).
  2. D. Kazanas, Dynamics of the universe and spontaneous symmetry breaking, Astrophys. J. Lett. 241, L59 (1980).
  3. A. H. Guth, The inflationary universe: A possible solution to the horizon and flatness problems, Phys. Rev. D 23, 347 (1981).
  4. A. D. Linde, A new inflationary universe scenario: A possible solution of the horizon, flatness, homogeneity, isotropy and primordial monopole problems, Phys. Lett. 108B, 389 (1982).
  5. A. Albrecht and P. J. Steinhardt, Cosmology for grand unified theories with radiatively induced symmetry breaking, Phys. Rev. Lett. 48, 1220 (1982).
  6. N. Aghanim et al. (Planck Collaboration), Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys. 641, A6 (2020); 652, C4(E) (2021).
  7. Y. Akrami et al. (Planck Collaboration), Planck 2018 results. X. Constraints on inflation, Astron. Astrophys. 641, A10 (2020).
  8. T. Louis et al. (Atacama Cosmology Telescope Collaboration), The Atacama Cosmology Telescope: DR6 power spectra, likelihoods and ΛCDM parameters, J. Cosmol. Astropart. Phys. 11 (2025) 062.
  9. E. Calabrese et al. (Atacama Cosmology Telescope Collaboration), The Atacama Cosmology Telescope: DR6 constraints on extended cosmological models, J. Cosmol. Astropart. Phys. 11 (2025) 063.
  10. V. F. Mukhanov and G. V. Chibisov, Quantum fluctuations and a nonsingular universe, JETP Lett. 33, 532 (1981).
  11. H. Kodama and M. Sasaki, Cosmological perturbation theory, Prog. Theor. Phys. Suppl. 78, 1 (1984).
  12. M. Sasaki, Large scale quantum fluctuations in the inflationary universe, Prog. Theor. Phys. 76, 1036 (1986).
  13. V. F. Mukhanov, H. A. Feldman, and R. H. Brandenberger, Theory of cosmological perturbations. Part 1. Classical perturbations. Part 2. Quantum theory of perturbations. Part 3. Extensions, Phys. Rep. 215, 203 (1992).
  14. A. R. Liddle and D. H. Lyth, Cosmological Inflation and Large-Scale Structure (Cambridge University Press, Cambridge, England, 2000), 10.1017/CBO9781139175180.
  15. D. Baumann, Inflation, in Physics of the Large and the Small (World Scientific, Singapore, 2011), pp. 523–686.
  16. J. Martin, C. Ringeval, and V. Vennin, Encyclopædia inflationaris: Opiparous edition, Phys. Dark Universe 5–6, 75 (2014).
  17. R. Allahverdi et al., The first three seconds: A review of possible expansion histories of the early universe, Open J. Astrophys. 4 (2021).
  18. S. Choudhury, G. Bauyrzhan, S. K. Singh, and K. Yerzhanov, What new physics can we extract from inflation using the ACT DR6 and DESI DR2 observations?, arXiv:2506.15407.
  19. E. J. Copeland, M. Gleiser, and H. R. Muller, Oscillons: Resonant configurations during bubble collapse, Phys. Rev. D 52, 1920 (1995).
  20. S. Kasuya, M. Kawasaki, and F. Takahashi, I-balls, Phys. Lett. B 559, 99 (2003).
  21. M. A. Amin and D. Shirokoff, Flat-top oscillons in an expanding universe, Phys. Rev. D 81, 085045 (2010).
  22. M. A. Amin, Inflaton fragmentation: Emergence of pseudo-stable inflaton lumps (oscillons) after inflation, arXiv:1006.3075.
  23. M. A. Amin, R. Easther, and H. Finkel, Inflaton fragmentation and oscillon formation in three dimensions, J. Cosmol. Astropart. Phys. 12 (2010) 001.
  24. M. A. Amin, R. Easther, H. Finkel, R. Flauger, and M. P. Hertzberg, Oscillons after inflation, Phys. Rev. Lett. 108, 241302 (2012).
  25. M. Gleiser and D. Sicilia, Analytical characterization of oscillon energy and lifetime, Phys. Rev. Lett. 101, 011602 (2008).
  26. M. P. Hertzberg, Quantum radiation of oscillons, Phys. Rev. D 82, 045022 (2010).
  27. P. Salmi and M. Hindmarsh, Radiation and relaxation of oscillons, Phys. Rev. D 85, 085033 (2012).
  28. P. M. Saffin, P. Tognarelli, and A. Tranberg, Oscillon lifetime in the presence of quantum fluctuations, J. High Energy Phys. 08 (2014) 125.
  29. M. Kawasaki, F. Takahashi, and N. Takeda, Adiabatic invariance of Oscillons/I-balls, Phys. Rev. D 92, 105024 (2015).
  30. M. Ibe, M. Kawasaki, W. Nakano, and E. Sonomoto, Decay of I-ball/oscillon in classical field theory, J. High Energy Phys. 04 (2019) 030.
  31. M. Gleiser and M. Krackow, Resonant configurations in scalar field theories: Can some oscillons live forever?, Phys. Rev. D 100, 116005 (2019).
  32. H.-Y. Zhang, M. A. Amin, E. J. Copeland, P. M. Saffin, and K. D. Lozanov, Classical decay rates of oscillons, J. Cosmol. Astropart. Phys. 07 (2020) 055.
  33. E. Cotner, A. Kusenko, and V. Takhistov, Primordial black holes from inflaton fragmentation into oscillons, Phys. Rev. D 98, 083513 (2018).
  34. E. Cotner, A. Kusenko, M. Sasaki, and V. Takhistov, Analytic description of primordial black hole formation from scalar field fragmentation, J. Cosmol. Astropart. Phys. 10 (2019) 077.
  35. S. Y. Khlebnikov and I. I. Tkachev, Relic gravitational waves produced after preheating, Phys. Rev. D 56, 653 (1997).
  36. R. Easther and E. A. Lim, Stochastic gravitational wave production after inflation, J. Cosmol. Astropart. Phys. 04 (2006) 010.
  37. S.-Y. Zhou, E. J. Copeland, R. Easther, H. Finkel, Z.-G. Mou, and P. M. Saffin, Gravitational waves from oscillon preheating, J. High Energy Phys. 10 (2013) 026.
  38. S. Antusch, F. Cefala, and S. Orani, Gravitational waves from oscillons after inflation, Phys. Rev. Lett. 118, 011303 (2017); 120, 219901(E) (2018).
  39. S. Antusch, F. Cefala, and S. Orani, What can we learn from the stochastic gravitational wave background produced by oscillons?, J. Cosmol. Astropart. Phys. 03 (2017) 032.
  40. K. D. Lozanov and M. A. Amin, Gravitational perturbations from oscillons and transients after inflation, Phys. Rev. D 99, 123504 (2019).
  41. T. Hiramatsu, E. I. Sfakianakis, and M. Yamaguchi, Gravitational wave spectra from oscillon formation after inflation, J. High Energy Phys. 03 (2020) 021.
  42. K. D. Lozanov, M. Sasaki, and V. Takhistov, Universal gravitational wave signatures of cosmological solitons, J. Cosmol. Astropart. Phys. 01 (2023) 094.
  43. K. D. Lozanov, M. Sasaki, and V. Takhistov, Universal gravitational waves from interacting and clustered solitons, Phys. Lett. B 848, 138392 (2024).
  44. K. D. Lozanov and M. A. Amin, Equation of state and duration to radiation domination after inflation, Phys. Rev. Lett. 119, 061301 (2017).
  45. K. D. Lozanov and M. A. Amin, Self-resonance after inflation: Oscillons, transients and radiation domination, Phys. Rev. D 97, 023533 (2018).
  46. T. Jia, Y. Sang, and X. Zhang, Nonlinear dynamics of oscillons and transients during preheating after single field inflation, Phys. Rev. D 111, 083531 (2025).
  47. J. Ollé, O. Pujolàs, and F. Rompineve, Oscillons and dark matter, J. Cosmol. Astropart. Phys. 02 (2019) 006.
  48. K. Inomata, K. Kohri, T. Nakama, and T. Terada, Enhancement of gravitational waves induced by scalar perturbations due to a sudden transition from an early matter era to the radiation era, Phys. Rev. D 100, 043532 (2019); 108, 049901(E) (2023).
  49. K. D. Lozanov and V. Takhistov, Enhanced gravitational waves from inflaton oscillons, Phys. Rev. Lett. 130, 181002 (2023).
  50. X.-B. Sui, J. Liu, and R.-G. Cai, Enhancement of small-scale induced gravitational waves from solitons and oscillons, Phys. Rev. D 111, 123503 (2025).
  51. B. A. Bassett, S. Tsujikawa, and D. Wands, Inflation dynamics and reheating, Rev. Mod. Phys. 78, 537 (2006).
  52. K. D. Lozanov, Lectures on reheating after inflation, arXiv:1907.04402.
  53. M. A. G. Garcia, M. Gross, Y. Mambrini, K. A. Olive, M. Pierre, and J.-H. Yoon, Effects of fragmentation on post-inflationary reheating, J. Cosmol. Astropart. Phys. 12 (2023) 028.
  54. I. Dymnikova, L. Koziel, M. Khlopov, and S. Rubin, Quasilumps from first order phase transitions, Gravitation Cosmol. 6, 311 (2000).
  55. S. Antusch and S. Orani, Impact of other scalar fields on oscillons after hilltop inflation, J. Cosmol. Astropart. Phys. 03 (2015) 026.
  56. M. Shafi, E. J. Copeland, R. Mahbub, S. S. Mishra, and S. Basak, Formation and decay of oscillons after inflation in the presence of an external coupling. Part I. Lattice simulations, J. Cosmol. Astropart. Phys. 10 (2024) 082.
  57. S. Li, M. Yamaguchi, and Y.-l. Zhang, Decay and lifetime of oscillons coupled to an external scalar field: Insights from instability band analysis, J. Cosmol. Astropart. Phys. 12 (2025) 028.
  58. S. Li, Oscillon decay via parametric resonance: The case of three-point scalar interactions, arXiv:2511.03501.
  59. J. Kim and J. McDonald, Inflaton condensate fragmentation: Analytical conditions and application to α-attractor models, Phys. Rev. D 95, 123537 (2017).
  60. J. Kim and J. McDonald, General analytical conditions for inflaton fragmentation: Quick and easy tests for its occurrence, Phys. Rev. D 105, 063508 (2022).
  61. M. A. Amin and P. Mocz, Formation, gravitational clustering, and interactions of nonrelativistic solitons in an expanding universe, Phys. Rev. D 100, 063507 (2019).
  62. S. Antusch, F. Cefalà, and F. Torrentí, Properties of oscillons in hilltop potentials: Energies, shapes, and lifetimes, J. Cosmol. Astropart. Phys. 10 (2019) 002.
  63. R. Kallosh and A. Linde, Universality class in conformal inflation, J. Cosmol. Astropart. Phys. 07 (2013) 002.
  64. R. Kallosh, A. Linde, and D. Roest, Superconformal inflationary α-attractors, J. High Energy Phys. 11 (2013) 198.
  65. E. Silverstein and A. Westphal, Monodromy in the CMB: Gravity waves and string inflation, Phys. Rev. D 78, 106003 (2008).
  66. L. McAllister, E. Silverstein, and A. Westphal, Gravity waves and linear inflation from axion monodromy, Phys. Rev. D 82, 046003 (2010).
  67. L. McAllister, E. Silverstein, A. Westphal, and T. Wrase, The powers of monodromy, J. High Energy Phys. 09 (2014) 123.
  68. L. Boubekeur and D. H. Lyth, Hilltop inflation, J. Cosmol. Astropart. Phys. 07 (2005) 010.
  69. M. Lynker and R. Schimmrigk, ACT implications for Hilltop inflation, arXiv:2507.15076.
  70. R. Mahbub and S. S. Mishra, Oscillon formation from preheating in asymmetric inflationary potentials, Phys. Rev. D 108, 063524 (2023).
  71. N. Takeda and Y. Watanabe, No quasistable scalaron lump forms after R2 inflation, Phys. Rev. D 90, 023519 (2014).
  72. P. Ade et al. (Simons Observatory Collaboration), The Simons Observatory: Science goals and forecasts, J. Cosmol. Astropart. Phys. 02 (2018) 056.
  73. E. Allys et al. (LiteBIRD Collaboration), Probing cosmic inflation with the LiteBIRD cosmic microwave background polarization survey, Prog. Theor. Exp. Phys. 2023, 042F01 (2023).
  74. T. Papanikolaou, V. Vennin, and D. Langlois, Gravitational waves from a universe filled with primordial black holes, J. Cosmol. Astropart. Phys. 03 (2020) 053.
  75. D. Baumann, Cosmology (Cambridge University Press, Cambridge, England, 2022).
  76. K. Tomita, Non-Linear theory of gravitational instability in the expanding universe, Prog. Theor. Phys. 37, 831 (1967).
  77. S. Matarrese, O. Pantano, and D. Saez, A general relativistic approach to the nonlinear evolution of collisionless matter, Phys. Rev. D 47, 1311 (1993).
  78. K. N. Ananda, C. Clarkson, and D. Wands, The cosmological gravitational wave background from primordial density perturbations, Phys. Rev. D 75, 123518 (2007).
  79. D. Baumann, P. J. Steinhardt, K. Takahashi, and K. Ichiki, Gravitational wave spectrum induced by primordial scalar perturbations, Phys. Rev. D 76, 084019 (2007).
  80. K. Kohri and T. Terada, Semianalytic calculation of gravitational wave spectrum nonlinearly induced from primordial curvature perturbations, Phys. Rev. D 97, 123532 (2018).
  81. G. Domènech, Scalar induced gravitational waves review, Universe 7, 398 (2021).
  82. K. Inomata, K. Kohri, and T. Terada, The poltergeist mechanism—enhancement of scalar-induced gravitational waves with early matter-dominated era, arXiv:2511.07266.
  83. K. Imagawa, M. Kawasaki, K. Murai, H. Nakatsuka, and E. Sonomoto, Free streaming length of axion-like particle after oscillon/I-ball decays, J. Cosmol. Astropart. Phys. 02 (2021) 024.
  84. G. Domènech, C. Lin, and M. Sasaki, Gravitational wave constraints on the primordial black hole dominated early universe, J. Cosmol. Astropart. Phys. 04 (2021) 062; 11 (2021) E01.
  85. G. Domènech and J. Tränkle, From formation to evaporation: Induced gravitational wave probes of the primordial black hole reheating scenario, Phys. Rev. D 111, 063528 (2025).
  86. K. Inomata, M. Kawasaki, K. Mukaida, T. Terada, and T. T. Yanagida, Gravitational wave production right after a primordial black hole evaporation, Phys. Rev. D 101, 123533 (2020).
  87. G. Domènech, V. Takhistov, and M. Sasaki, Exploring evaporating primordial black holes with gravitational waves, Phys. Lett. B 823, 136722 (2021).
  88. N. Herman, L. Lehoucq, and A. Fúzfa, Electromagnetic antennas for the resonant detection of the stochastic gravitational wave background, Phys. Rev. D 108, 124009 (2023).
  89. N. Aggarwal et al., Challenges and opportunities of gravitational-wave searches at MHz to GHz frequencies, Living Rev. Relativity 24, 4 (2021).
  90. A. Berlin, D. Blas, R. Tito D’Agnolo, S. A. R. Ellis, R. Harnik, Y. Kahn, and J. Schütte-Engel, Detecting high-frequency gravitational waves with microwave cavities, Phys. Rev. D 105, 116011 (2022).
  91. V. Domcke, C. Garcia-Cely, and N. L. Rodd, Novel search for high-frequency gravitational waves with low-mass axion haloscopes, Phys. Rev. Lett. 129, 041101 (2022).
  92. Y. He, S. K. Giri, R. Sharma, S. Mtchedlidze, and I. Georgiev, Inverse gertsenshtein effect as a probe of high-frequency gravitational waves, J. Cosmol. Astropart. Phys. 05 (2023) 051.
  93. N. Aggarwal et al., Challenges and opportunities of gravitational wave searches above 10 kHz, Living Rev. Relativity 28, 10 (2025).
  94. C. Caprini and D. G. Figueroa, Cosmological backgrounds of gravitational waves, Classical Quantum Gravity 35, 163001 (2018).
  95. K. Inomata, K. Kohri, T. Nakama, and T. Terada, Gravitational waves induced by scalar perturbations during a gradual transition from an early matter era to the radiation era, J. Cosmol. Astropart. Phys. 10 (2019) 071; 08 (2023) E01.
  96. M. Pearce, L. Pearce, G. White, and C. Balazs, Gravitational wave signals from early matter domination: Interpolating between fast and slow transitions, J. Cosmol. Astropart. Phys. 06 (2023) 021.
  97. M. Pearce, L. Pearce, G. White, and C. Balázs, Using gravitational wave signals to disentangle early matter dominated epochs, J. Cosmol. Astropart. Phys. 11 (2025) 004.
  98. M. Kawasaki and K. Murai, Enhancement of gravitational waves at Q-ball decay including non-linear density perturbations, J. Cosmol. Astropart. Phys. 01 (2023) 050.
  99. N. Fernandez, J. W. Foster, B. Lillard, and J. Shelton, Stochastic gravitational waves from early structure formation, Phys. Rev. Lett. 133, 111002 (2024).
  100. K. A. Malik and D. Wands, Cosmological perturbations, Phys. Rep. 475, 1 (2009).
  101. H. Kodama and M. Sasaki, Evolution of isocurvature perturbations. I. Photon—baryon universe, Int. J. Mod. Phys. A 01, 265 (1986).
  102. H. Kodama and M. Sasaki, Evolution of isocurvature perturbations. II. Radiation dust universe, Int. J. Mod. Phys. A 02, 491 (1987).

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Phys. Rev. D 113, 123507– Published 3 June, 2026
  • Received 28 January 2026
  • Accepted 11 May 2026
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