Abstract
We study I-balls/oscillons, which are long-lived, quasi-periodic, and spatially localized solutions in real scalar field theories. Contrary to the case of Q-balls, there is no evident conserved charge that stabilizes the localized configuration. Nevertheless, in many classical numerical simulations, it has been shown that they are extremely long-lived. In this paper, we clarify the reason for the longevity, and show how the exponential separation of time scales emerges dynamically. Those solutions are time-periodic with a typical frequency of a mass scale of a scalar field. This observation implies that they can be understood by the effective theory after integrating out relativistic modes. We find that the resulting effective theory has an approximate global U(1) symmetry reflecting an approximate number conservation in the non-relativistic regime. As a result, the profile of those solutions is obtained via the bounce method, just like Q-balls, as long as the breaking of the U(1) symmetry is small enough. We then discuss the decay processes of the I-ball/oscillon by the breaking of the U(1) symmetry, namely the production of relativistic modes via number violating processes. We show that the imaginary part is exponentially suppressed, which explains the extraordinary longevity of I-ball/oscillon. In addition, we find that there are some attractor behaviors during the evolution of I-ball/oscillon that further enhance the lifetime. The validity of our effective theory is confirmed by classical numerical simulations. Our formalism may also be useful to study condensates of ultra light bosonic dark matter, such as fuzzy dark matter, and axion stars, for instance.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A.H. Guth, The Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems, Phys. Rev. D 23 (1981) 347 [INSPIRE].
A.D. Linde, A New Inflationary Universe Scenario: A Possible Solution of the Horizon, Flatness, Homogeneity, Isotropy and Primordial Monopole Problems, Phys. Lett. B 108 (1982) 389 [INSPIRE].
Planck collaboration, P.A.R. Ade et al., Planck 2013 results. XVI. Cosmological parameters, Astron. Astrophys. 571 (2014) A16 [arXiv:1303.5076] [INSPIRE].
K. Enqvist and M.S. Sloth, Adiabatic CMB perturbations in pre-big-bang string cosmology, Nucl. Phys. B 626 (2002) 395 [hep-ph/0109214] [INSPIRE].
D.H. Lyth and D. Wands, Generating the curvature perturbation without an inflaton, Phys. Lett. B 524 (2002) 5 [hep-ph/0110002] [INSPIRE].
T. Moroi and T. Takahashi, Effects of cosmological moduli fields on cosmic microwave background, Phys. Lett. B 522 (2001) 215 [Erratum ibid. B 539 (2002) 303] [hep-ph/0110096] [INSPIRE].
R.D. Peccei and H.R. Quinn, CP Conservation in the Presence of Instantons, Phys. Rev. Lett. 38 (1977) 1440 [INSPIRE].
S. Weinberg, A New Light Boson?, Phys. Rev. Lett. 40 (1978) 223 [INSPIRE].
J. Preskill, M.B. Wise and F. Wilczek, Cosmology of the Invisible Axion, Phys. Lett. B 120 (1983) 127 [INSPIRE].
L.F. Abbott and P. Sikivie, A Cosmological Bound on the Invisible Axion, Phys. Lett. B 120 (1983) 133 [INSPIRE].
M. Dine and W. Fischler, The Not So Harmless Axion, Phys. Lett. B 120 (1983) 137 [INSPIRE].
I. Affleck and M. Dine, A New Mechanism for Baryogenesis, Nucl. Phys. B 249 (1985) 361 [INSPIRE].
H. Murayama and T. Yanagida, Leptogenesis in supersymmetric standard model with right-handed neutrino, Phys. Lett. B 322 (1994) 349 [hep-ph/9310297] [INSPIRE].
M. Dine, L. Randall and S.D. Thomas, Baryogenesis from flat directions of the supersymmetric standard model, Nucl. Phys. B 458 (1996) 291 [hep-ph/9507453] [INSPIRE].
Ya.B. Zeldovich, I.Yu. Kobzarev and L.B. Okun, Cosmological Consequences of the Spontaneous Breakdown of Discrete Symmetry, Zh. Eksp. Teor. Fiz. 67 (1974) 3 [INSPIRE].
P. Sikivie, Of Axions, Domain Walls and the Early Universe, Phys. Rev. Lett. 48 (1982) 1156 [INSPIRE].
A. Vilenkin and A.E. Everett, Cosmic Strings and Domain Walls in Models with Goldstone and PseudoGoldstone Bosons, Phys. Rev. Lett. 48 (1982) 1867 [INSPIRE].
S.R. Coleman, Q Balls, Nucl. Phys. B 262 (1985) 263 [Erratum ibid. B 269 (1986) 744] [INSPIRE].
A. Kusenko and M.E. Shaposhnikov, Supersymmetric Q balls as dark matter, Phys. Lett. B 418 (1998) 46 [hep-ph/9709492] [INSPIRE].
K. Enqvist and J. McDonald, Q balls and baryogenesis in the MSSM, Phys. Lett. B 425 (1998) 309 [hep-ph/9711514] [INSPIRE].
K. Enqvist and J. McDonald, B-ball baryogenesis and the baryon to dark matter ratio, Nucl. Phys. B 538 (1999) 321 [hep-ph/9803380] [INSPIRE].
S. Kasuya and M. Kawasaki, Q ball formation through Affleck-Dine mechanism, Phys. Rev. D 61 (2000) 041301 [hep-ph/9909509] [INSPIRE].
S. Kasuya and M. Kawasaki, Q ball formation in the gravity mediated SUSY breaking scenario, Phys. Rev. D 62 (2000) 023512 [hep-ph/0002285] [INSPIRE].
S. Kasuya and M. Kawasaki, Q ball formation: Obstacle to Affleck-Dine baryogenesis in the gauge mediated SUSY breaking?, Phys. Rev. D 64 (2001) 123515 [hep-ph/0106119] [INSPIRE].
I.L. Bogolyubsky and V.G. Makhankov, On the Pulsed Soliton Lifetime in Two Classical Relativistic Theory Models, JETP Lett. 24 (1976) 12 [INSPIRE].
H. Segur and M.D. Kruskal, Nonexistence of Small Amplitude Breather Solutions in ϕ 4 Theory, Phys. Rev. Lett. 58 (1987) 747 [INSPIRE].
M. Gleiser, Pseudostable bubbles, Phys. Rev. D 49 (1994) 2978 [hep-ph/9308279] [INSPIRE].
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].
M. Gleiser and A. Sornborger, Longlived localized field configurations in small lattices: application to oscillons, Phys. Rev. E 62 (2000) 1368 [patt-sol/9909002] [INSPIRE].
E.P. Honda and M.W. Choptuik, Fine structure of oscillons in the spherically symmetric phi**4 Klein-Gordon model, Phys. Rev. D 65 (2002) 084037 [hep-ph/0110065] [INSPIRE].
S. Kasuya, M. Kawasaki and F. Takahashi, I-balls, Phys. Lett. B 559 (2003) 99 [hep-ph/0209358] [INSPIRE].
M. Gleiser, d-dimensional oscillating scalar field lumps and the dimensionality of space, Phys. Lett. B 600 (2004) 126 [hep-th/0408221] [INSPIRE].
G. Fodor, P. Forgacs, P. Grandclement and I. Racz, Oscillons and Quasi-breathers in the ϕ 4 Klein-Gordon model, Phys. Rev. D 74 (2006) 124003 [hep-th/0609023] [INSPIRE].
M. Hindmarsh and P. Salmi, Numerical investigations of oscillons in 2 dimensions, Phys. Rev. D 74 (2006) 105005 [hep-th/0606016] [INSPIRE].
P.M. Saffin and A. Tranberg, Oscillons and quasi-breathers in D+1 dimensions, JHEP 01 (2007) 030 [hep-th/0610191] [INSPIRE].
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].
M. Gleiser and D. Sicilia, Analytical Characterization of Oscillon Energy and Lifetime, Phys. Rev. Lett. 101 (2008) 011602 [arXiv:0804.0791] [INSPIRE].
G. Fodor, P. Forgacs, Z. Horvath and M. Mezei, Radiation of scalar oscillons in 2 and 3 dimensions, Phys. Lett. B 674 (2009) 319 [arXiv:0903.0953] [INSPIRE].
M. Gleiser and D. Sicilia, A General Theory of Oscillon Dynamics, Phys. Rev. D 80 (2009) 125037 [arXiv:0910.5922] [INSPIRE].
M.A. Amin and D. Shirokoff, Flat-top oscillons in an expanding universe, Phys. Rev. D 81 (2010) 085045 [arXiv:1002.3380] [INSPIRE].
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].
P. Salmi and M. Hindmarsh, Radiation and Relaxation of Oscillons, Phys. Rev. D 85 (2012) 085033 [arXiv:1201.1934] [INSPIRE].
E.A. Andersen and A. Tranberg, Four results on ϕ 4 oscillons in D+1 dimensions, JHEP 12 (2012) 016 [arXiv:1210.2227] [INSPIRE].
K.D. Lozanov and M.A. Amin, End of inflation, oscillons and matter-antimatter asymmetry, Phys. Rev. D 90 (2014) 083528 [arXiv:1408.1811] [INSPIRE].
P.M. Saffin, P. Tognarelli and A. Tranberg, Oscillon Lifetime in the Presence of Quantum Fluctuations, JHEP 08 (2014) 125 [arXiv:1401.6168] [INSPIRE].
K. Mukaida and M. Takimoto, Correspondence of I- and Q-balls as Non-relativistic Condensates, JCAP 08 (2014) 051 [arXiv:1405.3233] [INSPIRE].
M. Kawasaki, F. Takahashi and N. Takeda, Adiabatic Invariance of Oscillons/I-balls, Phys. Rev. D 92 (2015) 105024 [arXiv:1508.01028] [INSPIRE].
J. Berges and J. Jaeckel, Far from equilibrium dynamics of Bose-Einstein condensation for Axion Dark Matter, Phys. Rev. D 91 (2015) 025020 [arXiv:1402.4776] [INSPIRE].
S. Davidson, Axions: Bose Einstein Condensate or Classical Field?, Astropart. Phys. 65 (2015) 101 [arXiv:1405.1139] [INSPIRE].
E. Braaten, A. Mohapatra and H. Zhang, Nonrelativistic Effective Field Theory for Axions, Phys. Rev. D 94 (2016) 076004 [arXiv:1604.00669] [INSPIRE].
G.D. Moore, Condensates in Relativistic Scalar Theories, Phys. Rev. D 93 (2016) 065043 [arXiv:1511.00697] [INSPIRE].
M.P. Hertzberg, Quantum Radiation of Oscillons, Phys. Rev. D 82 (2010) 045022 [arXiv:1003.3459] [INSPIRE].
M. Kawasaki and M. Yamada, Decay rates of Gaussian-type-I-balls and Bose-enhancement effects in 3+1 dimensions, JCAP 02 (2014) 001 [arXiv:1311.0985] [INSPIRE].
P.M. Saffin, Recrudescence of massive fermion production by oscillons, arXiv:1612.02014 [INSPIRE].
A. Kusenko, Small Q balls, Phys. Lett. B 404 (1997) 285 [hep-th/9704073] [INSPIRE].
K. Enqvist and M. Laine, Q-ball dynamics from atomic Bose-Einstein condensates, JCAP 08 (2003) 003 [cond-mat/0304355] [INSPIRE].
S.R. Coleman, V. Glaser and A. Martin, Action Minima Among Solutions to a Class of Euclidean Scalar Field Equations, Commun. Math. Phys. 58 (1978) 211 [INSPIRE].
I.E. Gulamov, E. Ya. Nugaev and M.N. Smolyakov, Theory of U(1) gauged Q-balls revisited, Phys. Rev. D 89 (2014) 085006 [arXiv:1311.0325] [INSPIRE].
R. Friedberg, T.D. Lee and A. Sirlin, A Class of Scalar-Field Soliton Solutions in Three Space Dimensions, Phys. Rev. D 13 (1976) 2739 [INSPIRE].
T.D. Lee and Y. Pang, Nontopological solitons, Phys. Rept. 221 (1992) 251 [INSPIRE].
M.I. Tsumagari, The Physics of Q-Balls, PhD thesis, Nottingham University, Nottingham U.K. (2009), arXiv:0910.3845 [INSPIRE].
J. Eby, P. Suranyi and L.C.R. Wijewardhana, The Lifetime of Axion Stars, Mod. Phys. Lett. A 31 (2016) 1650090 [arXiv:1512.01709] [INSPIRE].
R. Ruffini and S. Bonazzola, Systems of selfgravitating particles in general relativity and the concept of an equation of state, Phys. Rev. 187 (1969) 1767 [INSPIRE].
C.J. Hogan and M.J. Rees, Axion miniclusters, Phys. Lett. B 205 (1988) 228 [INSPIRE].
E.W. Kolb and I.I. Tkachev, Axion miniclusters and Bose stars, Phys. Rev. Lett. 71 (1993) 3051 [hep-ph/9303313] [INSPIRE].
E. Seidel and W.-M. Suen, Formation of solitonic stars through gravitational cooling, Phys. Rev. Lett. 72 (1994) 2516 [gr-qc/9309015] [INSPIRE].
W. Hu, R. Barkana and A. Gruzinov, Cold and fuzzy dark matter, Phys. Rev. Lett. 85 (2000) 1158 [astro-ph/0003365] [INSPIRE].
F.S. Guzman and L.A. Urena-Lopez, Gravitational cooling of self-gravitating Bose-Condensates, Astrophys. J. 645 (2006) 814 [astro-ph/0603613] [INSPIRE].
P. Sikivie and Q. Yang, Bose-Einstein Condensation of Dark Matter Axions, Phys. Rev. Lett. 103 (2009) 111301 [arXiv:0901.1106] [INSPIRE].
J. Barranco and A. Bernal, Self-gravitating system made of axions, Phys. Rev. D 83 (2011) 043525 [arXiv:1001.1769] [INSPIRE].
O. Erken, P. Sikivie, H. Tam and Q. Yang, Cosmic axion thermalization, Phys. Rev. D 85 (2012) 063520 [arXiv:1111.1157] [INSPIRE].
P.H. Chavanis and L. Delfini, Mass-radius relation of Newtonian self-gravitating Bose-Einstein condensates with short-range interactions: II. Numerical results, Phys. Rev. D 84 (2011) 043532 [arXiv:1103.2054] [INSPIRE].
J. Eby, P. Suranyi, C. Vaz and L.C.R. Wijewardhana, Axion Stars in the Infrared Limit, JHEP 03 (2015) 080 [Erratum ibid. 1611 (2016) 134] [arXiv:1412.3430] [INSPIRE].
A.H. Guth, M.P. Hertzberg and C. Prescod-WEinstein, Do Dark Matter Axions Form a Condensate with Long-Range Correlation?, Phys. Rev. D 92 (2015) 103513 [arXiv:1412.5930] [INSPIRE].
E. Braaten, A. Mohapatra and H. Zhang, Dense Axion Stars, Phys. Rev. Lett. 117 (2016) 121801 [arXiv:1512.00108] [INSPIRE].
L. Hui, J.P. Ostriker, S. Tremaine and E. Witten, Ultralight scalars as cosmological dark matter, Phys. Rev. D 95 (2017) 043541 [arXiv:1610.08297] [INSPIRE].
J. Eby, M. Leembruggen, P. Suranyi and L.C.R. Wijewardhana, Collapse of Axion Stars, JHEP 12 (2016) 066 [arXiv:1608.06911] [INSPIRE].
J. Ellis, TikZ-Feynman: Feynman diagrams with TikZ, Comput. Phys. Commun. 210 (2017) 103 [arXiv:1601.05437] [INSPIRE].
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
Additional information
ArXiv ePrint: 1612.07750
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), 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.
About this article
Cite this article
Mukaida, K., Takimoto, M. & Yamada, M. On longevity of I-ball/oscillon. J. High Energ. Phys. 2017, 122 (2017). https://doi.org/10.1007/JHEP03(2017)122
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2017)122