- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Letters

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

  • Open Access

Pion Condensation in the Early Universe at Nonvanishing Lepton Flavor Asymmetry and Its Gravitational Wave Signatures

Volodymyr Vovchenko1, Bastian B. Brandt2, Francesca Cuteri3, Gergely Endrődi2, Fazlollah Hajkarim3,4, and Jürgen Schaffner-Bielich3

  • 1Nuclear Science Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720, USA
  • 2Fakultät für Physik, Universität Bielefeld, D-33615 Bielefeld, Germany
  • 3Institut für Theoretische Physik, Goethe Universität Frankfurt, Max-von-Laue-Strasse 1, D-60438 Frankfurt am Main, Germany
  • 4Dipartimento di Fisica e Astronomia, Università degli Studi di Padova, Via Marzolo 8, 35131 Padova, Italy

PDF

Phys. Rev. Lett. 126, 012701 – Published 6 January, 2021

DOI: https://doi.org/10.1103/PhysRevLett.126.012701

Abstract

We investigate the possible formation of a Bose-Einstein condensed phase of pions in the early Universe at nonvanishing values of lepton flavor asymmetries. A hadron resonance gas model with pion interactions, based on first-principle lattice QCD simulations at nonzero isospin density, is used to evaluate cosmic trajectories at various values of electron, muon, and tau lepton asymmetries that satisfy the available constraints on the total lepton asymmetry. The cosmic trajectory can pass through the pion condensed phase if the combined electron and muon asymmetry is sufficiently large: |le+lμ|≳0.1, with little sensitivity to the difference le−lμ between the individual flavor asymmetries. Future constraints on the values of the individual lepton flavor asymmetries will thus be able to either confirm or rule out the condensation of pions during the cosmic QCD epoch. We demonstrate that the pion condensed phase leaves an imprint both on the spectrum of primordial gravitational waves and on the mass distribution of primordial black holes at the QCD scale, e.g., the black hole binary of recent LIGO event GW190521 can be formed in that phase.

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (92)

  1. A. Riotto and M. Trodden, Annu. Rev. Nucl. Part. Sci. 49, 35 (1999).
  2. J. M. Cline, arXiv:hep-ph/0609145.
  3. S. Davidson, E. Nardi, and Y. Nir, Phys. Rep. 466, 105 (2008).
  4. M. Flanz, E. A. Paschos, and U. Sarkar, Phys. Lett. B 345, 248 (1995); 384, 487 (1996); 382, 447 (1996).
  5. B. Abbott et al. (LIGO Scientific and Virgo Collaborations), Phys. Rev. Lett. 116, 061102 (2016).
  6. B. Abbott et al. (LIGO Scientific and Virgo Collaborations), Astrophys. J. Lett. 818, L22 (2016).
  7. C. Caprini and D. G. Figueroa, Classical Quantum Gravity 35, 163001 (2018).
  8. L. Grishchuk, Zh. Eksp. Teor. Fiz. 67, 825 (1974) [Sov. Phys. JETP 40, 409 (1975)].
  9. A. A. Starobinsky, JETP Lett. 30, 682 (1979) [ 30, 682 (1979)].
  10. V. F. Mukhanov, H. Feldman, and R. H. Brandenberger, Phys. Rep. 215, 203 (1992).
  11. Y. Watanabe and E. Komatsu, Phys. Rev. D 73, 123515 (2006).
  12. N. Bernal and F. Hajkarim, Phys. Rev. D 100, 063502 (2019).
  13. F. Hajkarim, J. Schaffner-Bielich, S. Wystub, and M. M. Wygas, Phys. Rev. D 99, 103527 (2019).
  14. S. Schettler, T. Boeckel, and J. Schaffner-Bielich, Phys. Rev. D 83, 064030 (2011).
  15. B. J. Carr, Astrophys. J. 201, 1 (1975).
  16. B. J. Carr and S. Hawking, Mon. Not. R. Astron. Soc. 168, 399 (1974).
  17. S. Bird, I. Cholis, J. B. Muñoz, Y. Ali-Haïmoud, M. Kamionkowski, E. D. Kovetz, A. Raccanelli, and A. G. Riess, Phys. Rev. Lett. 116, 201301 (2016).
  18. M. Y. Khlopov, Res. Astron. Astrophys. 10, 495 (2010).
  19. M. Sasaki, T. Suyama, T. Tanaka, and S. Yokoyama, Classical Quantum Gravity 35, 063001 (2018).
  20. B. Carr, F. Kuhnel, and M. Sandstad, Phys. Rev. D 94, 083504 (2016).
  21. J. A. Harvey and M. S. Turner, Phys. Rev. D 42, 3344 (1990).
  22. I. M. Oldengott and D. J. Schwarz, Europhys. Lett. 119, 29001 (2017).
  23. M. M. Wygas, I. M. Oldengott, D. Bödeker, and D. J. Schwarz, Phys. Rev. Lett. 121, 201302 (2018).
  24. M. M. Middeldorf-Wygas, I. M. Oldengott, D. Bödeker, and D. J. Schwarz, arXiv:2009.00036.

  25. In contrast to Refs. [23, 24], where the equation of state is based on Taylor expansion around zero chemical potentials, here we explicitly include a pion-condensed phase at large μQ via an effective mass model matched to lattice data.

  26. B. B. Brandt, G. Endrődi, and S. Schmalzbauer, Phys. Rev. D 97, 054514 (2018).
  27. B. B. Brandt, G. Endrődi, E. S. Fraga, M. Hippert, J. Schaffner-Bielich, and S. Schmalzbauer, Phys. Rev. D 98, 094510 (2018).

  28. We discuss the distinction between μI and μQ in Section 2 of the Supplemental Material.

  29. H. Abuki, T. Brauner, and H. J. Warringa, Eur. Phys. J. C 64, 123 (2009).
  30. S. Borsányi, Z. Fodor, S. D. Katz, S. Krieg, C. Ratti, and K. Szabó, J. High Energy Phys. 01 (2012) 138.
  31. A. Bazavov et al. (HotQCD Collaboration), Phys. Rev. D 86, 034509 (2012).
  32. O. Savchuk, Y. Bondar, O. Stashko, R. V. Poberezhnyuk, V. Vovchenko, M. I. Gorenstein, and H. Stoecker, Phys. Rev. C 102, 035202 (2020).
  33. D. T. Son and M. A. Stephanov, Phys. Rev. Lett. 86, 592 (2001).
  34. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevLett.126.012701 for details on the effective mass model and the comparison to chiral perturbation theory and other model approaches, which includes references to Refs. [35–42], on the lattice simulations and comparisons between the effective mass model and lattice data, which includes references to Refs. [43–46], and for details of the primordial black holes population calculation, which includes references to Refs. [47–52].
  35. H. W. Barz, B. L. Friman, J. Knoll, and H. Schulz, Phys. Rev. D 40, 157 (1989).
  36. P. Adhikari and J. O. Andersen, Phys. Lett. B 804, 135352 (2020).
  37. P. Adhikari and J. O. Andersen, J. High Energy Phys. 06 (2020b) 170.
  38. P. Adhikari and J. O. Andersen, arXiv:2003.12567.
  39. P. Adhikari, J. O. Andersen, and M. A. Mojahed, arXiv:2010.13655.
  40. L.-y. He, M. Jin, and P.-f. Zhuang, Phys. Rev. D 71, 116001 (2005).
  41. P. Adhikari, J. O. Andersen, and P. Kneschke, Phys. Rev. D 98, 074016 (2018).
  42. A. Folkestad and J. O. Andersen, Phys. Rev. D 99, 054006 (2019).
  43. B. B. Brandt and G. Endrődi, Phys. Rev. D 99, 014518 (2019).
  44. S. Borsányi, G. Endrődi, Z. Fodor, A. Jakovác, S. D. Katz, S. Krieg, C. Ratti, and K. K. Szabó, J. High Energy Phys. 11 (2010) 077.
  45. B. B. Brandt and G. Endrődi, Proc. Sci., LATTICE2016 (2016) 039 [arXiv:1611.06758].
  46. M. Mannarelli, Particles 2, 411 (2019).
  47. C. R. Evans and J. S. Coleman, Phys. Rev. Lett. 72, 1782 (1994).
  48. T. Koike, T. Hara, and S. Adachi, Phys. Rev. Lett. 74, 5170 (1995).
  49. I. Musco, J. C. Miller, and A. G. Polnarev, Classical Quantum Gravity 26, 235001 (2009).
  50. I. Musco, J. C. Miller, and L. Rezzolla, Classical Quantum Gravity 22, 1405 (2005).
  51. T. Harada, C.-M. Yoo, and K. Kohri, Phys. Rev. D 88, 084051 (2013); 89, 029903(E) (2014).
  52. A. Escrivà, C. Germani, and R. K. Sheth, Phys. Rev. D 101, 044022 (2020).
  53. K. Olive et al. (Particle Data Group), Chin. Phys. C 38, 090001 (2014).
  54. C. G. Broyden, Math. Comput. 19, 577 (1965).
  55. V. Vovchenko and H. Stoecker, Comput. Phys. Commun. 244, 295 (2019).
  56. I. Affleck and M. Dine, Nucl. Phys. B249, 361 (1985).
  57. M. Stuke, D. J. Schwarz, and G. Starkman, J. Cosmol. Astropart. Phys. 03 (2012) 040.
  58. A. Casas, W. Y. Cheng, and G. Gelmini, Nucl. Phys. B538, 297 (1999).
  59. J. McDonald, Phys. Rev. Lett. 84, 4798 (2000).
  60. K. Abazajian, N. F. Bell, G. M. Fuller, and Y. Y. Y. Wong, Phys. Rev. D 72, 063004 (2005).
  61. K. Ichikawa, M. Kawasaki, and F. Takahashi, Phys. Lett. B 597, 1 (2004).
  62. F. Hajkarim and J. Schaffner-Bielich, Phys. Rev. D 101, 043522 (2020).
  63. K. Saikawa and S. Shirai, J. Cosmol. Astropart. Phys. 05 (2018) 035.
  64. V. Mukhanov, Physical Foundations of Cosmology (Cambridge University Press, Oxford, 2005).
  65. Y. Akrami et al. (Planck Collaboration), Astron. Astrophys. 641, A10 (2020).
  66. N. Aghanim et al. (Planck Collaboration), Astron. Astrophys. 641, A6 (2020).

  67. The initial conditions that we consider at superhorizon scale (k≪aH) are X(k,0)=1 and X′(k,0)=0.

  68. M. Drees, F. Hajkarim, and E. R. Schmitz, J. Cosmol. Astropart. Phys. 06 (2015) 025.
  69. G. Janssen et al., Proc. Sci., AASKA14 (2015) 037 [arXiv:1501.00127].
  70. A. Weltman et al., Pub. Astron. Soc. Aust. 37, e002 (2020).
  71. P. Amaro-Seoane et al. (LISA Collaboration), arXiv:1702.00786.
  72. C. T. Byrnes, M. Hindmarsh, S. Young, and M. R. S. Hawkins, J. Cosmol. Astropart. Phys. 08 (2018) 041.
  73. P. Widerin and C. Schmid, arXiv:astro-ph/9808142.
  74. J. Sobrinho, P. Augusto, and A. Gonçalves, Mon. Not. R. Astron. Soc. 463, 2348 (2016).
  75. K. Jedamzik, Phys. Rev. D 55, R5871 (1997).
  76. C. Schmid, D. J. Schwarz, and P. Widerin, Phys. Rev. D 59, 043517 (1999).
  77. J. C. Niemeyer and K. Jedamzik, Phys. Rev. Lett. 80, 5481 (1998).
  78. J. C. Niemeyer and K. Jedamzik, Phys. Rev. D 59, 124013 (1999).

  79. Other experiments can put stronger bounds on fPBH in a narrower range of masses which we do not consider here (see Refs. [20, 80, 81]).

  80. B. Carr and F. Kuhnel, arXiv:2006.02838.
  81. B. Carr, K. Kohri, Y. Sendouda, and J. Yokoyama, arXiv:2002.12778.
  82. H. Niikura et al., Nat. Astron. 3, 524 (2019ba).
  83. H. Niikura, M. Takada, S. Yokoyama, T. Sumi, and S. Masaki, Phys. Rev. D 99, 083503 (2019).
  84. P. Tisserand et al. (EROS-2 Collaboration), Astron. Astrophys. 469, 387 (2007).
  85. C. Alcock et al. (Macho Collaboration), Astrophys. J. Lett. 550, L169 (2001).
  86. M. Oguri, J. M. Diego, N. Kaiser, P. L. Kelly, and T. Broadhurst, Phys. Rev. D 97, 023518 (2018).
  87. S. Wang, T. Terada, and K. Kohri, Phys. Rev. D 99, 103531 (2019); 101, 069901(E) (2020).
  88. N. Bartolo, V. De Luca, G. Franciolini, M. Peloso, D. Racco, and A. Riotto, Phys. Rev. D 99, 103521 (2019).
  89. R. Abbott et al. (LIGO Scientific and Virgo Collaborations), Astrophys. J. Lett. 900, L13 (2020).
  90. R. Abbott et al. (LIGO Scientific and Virgo Collaborations), Phys. Rev. Lett. 125, 101102 (2020).
  91. S. Carignano, L. Lepori, A. Mammarella, M. Mannarelli, and G. Pagliaroli, Eur. Phys. J. A 53, 35 (2017).
  92. J. O. Andersen and P. Kneschke, arXiv:1807.08951.

Outline

Information

Phys. Rev. Lett. 126, 012701– Published 6 January, 2021
  • Received 17 September 2020
  • Revised 2 November 2020
  • Accepted 7 December 2020
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation