Abstract
We study the system of axion strings that forms in the early Universe if the Peccei-Quinn symmetry is restored after inflation. Using numerical simulations, we establish the existence of an asymptotic solution to which the system is attracted independently of the initial conditions. We study in detail the properties of this solution, including the average number of strings per Hubble patch, the distribution of loops and long strings, the way that different types of radiation are emitted, and the shape of the spectrum of axions produced. We find clear evidence of logarithmic violations of the scaling properties of the attractor solution. We also find that, while most of the axions are emitted with momenta of order Hubble, most of the axion energy density is contained in axions with energy of order the string core scale, at least in the parameter range available in the simulation. While such a spectrum would lead to a negligible number density of relic axions from strings when extrapolated to the physical parameter region, we show that the presence of small logarithmic corrections to the spectrum shape could completely alter such a conclusion. A detailed understanding of the evolution of the axion spectrum is therefore crucial for a reliable estimate of the relic axion abundance from strings.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
R.D. Peccei and H.R. Quinn, CP conservation in the presence of instantons, Phys. Rev. Lett. 38 (1977) 1440 [INSPIRE].
F. Wilczek, Problem of strong p and t invariance in the presence of instantons, Phys. Rev. Lett. 40 (1978) 279 [INSPIRE].
S. Weinberg, A new light boson?, Phys. Rev. Lett. 40 (1978) 223 [INSPIRE].
J.E. Kim, Weak interaction singlet and strong CP invariance, Phys. Rev. Lett. 43 (1979) 103 [INSPIRE].
M.A. Shifman, A.I. Vainshtein and V.I. Zakharov, Can confinement ensure natural CP invariance of strong interactions?, Nucl. Phys. B 166 (1980) 493 [INSPIRE].
A.R. Zhitnitsky, On possible suppression of the axion hadron interactions, Sov. J. Nucl. Phys. 31 (1980) 260 [Yad. Fiz. 31 (1980) 497] [INSPIRE].
M. Dine, W. Fischler and M. Srednicki, A simple solution to the strong CP problem with a harmless axion, Phys. Lett. B 104 (1981) 199 [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].
P.W. Graham, I.G. Irastorza, S.K. Lamoreaux, A. Lindner and K.A. van Bibber, Experimental searches for the axion and axion-like particles, Ann. Rev. Nucl. Part. Sci. 65 (2015) 485 [arXiv:1602.00039] [INSPIRE].
I.G. Irastorza and J. Redondo, New experimental approaches in the search for axion-like particles, Prog. Part. Nucl. Phys. 102 (2018) 89 [arXiv:1801.08127] [INSPIRE].
P. Sikivie, Axion cosmology, Lect. Notes Phys. 741 (2008) 19 [astro-ph/0610440] [INSPIRE].
D.J.E. Marsh, Axion cosmology, Phys. Rept. 643 (2016) 1 [arXiv:1510.07633] [INSPIRE].
D.H. Lyth, A limit on the inflationary energy density from axion isocurvature fluctuations, Phys. Lett. B 236 (1990) 408 [INSPIRE].
M.S. Turner and F. Wilczek, Inflationary axion cosmology, Phys. Rev. Lett. 66 (1991) 5 [INSPIRE].
A.D. Linde, Axions in inflationary cosmology, Phys. Lett. B 259 (1991) 38 [INSPIRE].
A. Vilenkin and A.E. Everett, Cosmic strings and domain walls in models with Goldstone and pseudo-Goldstone bosons, Phys. Rev. Lett. 48 (1982) 1867 [INSPIRE].
P. Sikivie, Of axions, domain walls and the early universe, Phys. Rev. Lett. 48 (1982) 1156 [INSPIRE].
A. Vilenkin, Cosmic strings and domain walls, Phys. Rept. 121 (1985) 263 [INSPIRE].
R.L. Davis, Goldstone bosons in string models of galaxy formation, Phys. Rev. D 32 (1985) 3172 [INSPIRE].
R.L. Davis, Cosmic axions from cosmic strings, Phys. Lett. B 180 (1986) 225 [INSPIRE].
T.W.B. Kibble, Topology of cosmic domains and strings, J. Phys. A 9 (1976) 1387 [INSPIRE].
T.W.B. Kibble, Some implications of a cosmological phase transition, Phys. Rept. 67 (1980) 183 [INSPIRE].
A. Vilenkin, Cosmic strings, Phys. Rev. D 24 (1981) 2082 [INSPIRE].
A. Albrecht and N. Turok, Evolution of cosmic strings, Phys. Rev. Lett. 54 (1985) 1868 [INSPIRE].
D.P. Bennett and F.R. Bouchet, Evidence for a scaling solution in cosmic string evolution, Phys. Rev. Lett. 60 (1988) 257 [INSPIRE].
B. Allen and E.P.S. Shellard, Cosmic string evolution: a numerical simulation, Phys. Rev. Lett. 64 (1990) 119 [INSPIRE].
G.R. Vincent, M. Hindmarsh and M. Sakellariadou, Scaling and small scale structure in cosmic string networks, Phys. Rev. D 56 (1997) 637 [astro-ph/9612135] [INSPIRE].
C.J. A.P. Martins and E.P.S. Shellard, Extending the velocity dependent one scale string evolution model, Phys. Rev. D 65 (2002) 043514 [hep-ph/0003298] [INSPIRE].
A. Vilenkin and E.P.S. Shellard, Cosmic strings and other topological defects, Cambridge University Press, Cambridge, U.K., (2000) [INSPIRE].
A. Vilenkin and T. Vachaspati, Radiation of Goldstone bosons from cosmic strings, Phys. Rev. D 35 (1987) 1138 [INSPIRE].
R.L. Davis and E.P.S. Shellard, Do axions need inflation?, Nucl. Phys. B 324 (1989) 167 [INSPIRE].
A. Dabholkar and J.M. Quashnock, Pinning down the axion, Nucl. Phys. B 333 (1990) 815 [INSPIRE].
R.A. Battye and E.P.S. Shellard, Global string radiation, Nucl. Phys. B 423 (1994) 260 [astro-ph/9311017] [INSPIRE].
R.A. Battye and E.P.S. Shellard, Axion string constraints, Phys. Rev. Lett. 73 (1994) 2954 [Erratum ibid. 76 (1996) 2203] [astro-ph/9403018] [INSPIRE].
M. Yamaguchi, M. Kawasaki and J. Yokoyama, Evolution of axionic strings and spectrum of axions radiated from them, Phys. Rev. Lett. 82 (1999) 4578 [hep-ph/9811311] [INSPIRE].
M. Yamaguchi, Scaling property of the global string in the radiation dominated universe, Phys. Rev. D 60 (1999) 103511 [hep-ph/9907506] [INSPIRE].
C. Hagmann, S. Chang and P. Sikivie, Axion radiation from strings, Phys. Rev. D 63 (2001) 125018 [hep-ph/0012361] [INSPIRE].
H. Georgi and M.B. Wise, Hiding the invisible axion, Phys. Lett. B 116 (1982) 123 [INSPIRE].
S. Chang, C. Hagmann and P. Sikivie, Studies of the motion and decay of axion walls bounded by strings, Phys. Rev. D 59 (1999) 023505 [hep-ph/9807374] [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 [Sov. Phys. JETP 40 (1974) 1] [INSPIRE].
G.B. Gelmini, M. Gleiser and E.W. Kolb, Cosmology of biased discrete symmetry breaking, Phys. Rev. D 39 (1989) 1558 [INSPIRE].
S.E. Larsson, S. Sarkar and P.L. White, Evading the cosmological domain wall problem, Phys. Rev. D 55 (1997) 5129 [hep-ph/9608319] [INSPIRE].
T. Hiramatsu, M. Kawasaki, K. Saikawa and T. Sekiguchi, Axion cosmology with long-lived domain walls, JCAP 01 (2013) 001 [arXiv:1207.3166] [INSPIRE].
L. Di Luzio, E. Nardi and L. Ubaldi, Accidental Peccei-Quinn symmetry protected to arbitrary order, Phys. Rev. Lett. 119 (2017) 011801 [arXiv:1704.01122] [INSPIRE].
C. Hagmann and P. Sikivie, Computer simulations of the motion and decay of global strings, Nucl. Phys. B 363 (1991) 247 [INSPIRE].
L. Visinelli and P. Gondolo, Axion cold dark matter in view of BICEP2 results, Phys. Rev. Lett. 113 (2014) 011802 [arXiv:1403.4594] [INSPIRE].
D. Harari and P. Sikivie, On the evolution of global strings in the early universe, Phys. Lett. B 195 (1987) 361 [INSPIRE].
T. Hiramatsu, M. Kawasaki, T. Sekiguchi, M. Yamaguchi and J. Yokoyama, Improved estimation of radiated axions from cosmological axionic strings, Phys. Rev. D 83 (2011) 123531 [arXiv:1012.5502] [INSPIRE].
V.B. Klaer and G.D. Moore, How to simulate global cosmic strings with large string tension, JCAP 10 (2017) 043 [arXiv:1707.05566] [INSPIRE].
M. Yamaguchi, J. Yokoyama and M. Kawasaki, Numerical analysis of formation and evolution of global strings in (2 + 1)-dimensions, Prog. Theor. Phys. 100 (1998) 535 [hep-ph/9808326] [INSPIRE].
L. Fleury and G.D. Moore, Axion dark matter: strings and their cores, JCAP 01 (2016) 004 [arXiv:1509.00026] [INSPIRE].
M. Hindmarsh, J. Lizarraga, J. Urrestilla, D. Daverio and M. Kunz, Scaling from gauge and scalar radiation in Abelian Higgs string networks, Phys. Rev. D 96 (2017) 023525 [arXiv:1703.06696] [INSPIRE].
M. Hindmarsh, S. Stuckey and N. Bevis, Abelian Higgs cosmic strings: small scale structure and loops, Phys. Rev. D 79 (2009) 123504 [arXiv:0812.1929] [INSPIRE].
C. Hagmann, S. Chang and P. Sikivie, Axions from string decay, Nucl. Phys. Proc. Suppl. 72 (1999) 81 [hep-ph/9807428] [INSPIRE].
V.B. Klaer and G.D. Moore, The dark-matter axion mass, JCAP 11 (2017) 049 [arXiv:1708.07521] [INSPIRE].
K. Clough, P. Figueras, H. Finkel, M. Kunesch, E.A. Lim and S. Tunyasuvunakool, GRChombo: numerical relativity with adaptive mesh refinement, Class. Quant. Grav. 32 (2015) 245011 [arXiv:1503.03436] [INSPIRE].
L.M. Fleury and G.D. Moore, Axion string dynamics I: 2 + 1D, JCAP 05 (2016) 005 [arXiv:1602.04818] [INSPIRE].
R.J. LeVeque, Finite difference methods for ordinary and partial differential equations, Cambridge University Press, Cambridge, U.K., (2007).
WMAP collaboration, G. Hinshaw et al., First year Wilkinson Microwave Anisotropy Probe (WMAP) observations: the angular power spectrum, Astrophys. J. Suppl. 148 (2003) 135 [astro-ph/0302217] [INSPIRE].
R.L. Davis and E.P.S. Shellard, Antisymmetric tensors and spontaneous symmetry breaking, Phys. Lett. B 214 (1988) 219 [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: 1806.04677
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, 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 licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Gorghetto, M., Hardy, E. & Villadoro, G. Axions from strings: the attractive solution. J. High Energ. Phys. 2018, 151 (2018). https://doi.org/10.1007/JHEP07(2018)151
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2018)151