Abstract
In this work, we assess the sensitivity reach of pulsar timing array (PTA) measurements to probe pointlike primordial black holes (PBHs), with an extended mass distribution, which originate from collapsed Fermi balls that are formed through the aggregation of asymmetric U(1) dark fermions trapped within false vacuum bubbles during a dark first order phase transition (FOPT). The PBH formation scenario is mainly characterized by the dark asymmetry, strength of the FOPT, rate of FOPT, and the percolation temperature. Meanwhile, for PBH masses of interest lying within 10−10M⊙ − 102M⊙, the relevant signal for PTA measurements is the Doppler phase shift in the timing signal, due to the velocity change induced by transiting PBHs on pulsars. Taking the dark asymmetry parameter to be 10−4 and 10−5, we find that percolation temperatures within the 0.1 − 10 keV range, FOPT rates above 103 times the Hubble parameter at percolation, and FOPT strengths within 10−6 − 0.1 can give rise to PBHs that can be probed by an SKA-like PTA observation. On the other hand, the accompanying gravitational wave (GW) signal from the FOPT can be used as a complementary probe, assuming that the peak frequency lies within the 𝒪(10−10) − 𝒪(10−7) Hz range, and the peak GW abundance is above the peak-integrated sensitivity curves associated with pulsar timing observations that search for stochastic GWs. At the fundamental level, a quartic effective potential for a dark scalar field can trigger the FOPT. By performing a parameter scan, we obtained the class of effective potentials that lead to FOPT scenarios that can be probed by SKA through pulsar timing and GW observations.
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S. Hawking, Gravitationally collapsed objects of very low mass, Mon. Not. Roy. Astron. Soc. 152 (1971) 75 [INSPIRE].
G.F. Chapline, Cosmological effects of primordial black holes, Nature 253 (1975) 251 [INSPIRE].
M.Y. Khlopov, Primordial Black Holes, Res. Astron. Astrophys. 10 (2010) 495 [arXiv:0801.0116] [INSPIRE].
B. Carr, F. Kuhnel and M. Sandstad, Primordial Black Holes as Dark Matter, Phys. Rev. D 94 (2016) 083504 [arXiv:1607.06077] [INSPIRE].
B. Carr, K. Kohri, Y. Sendouda and J. Yokoyama, Constraints on primordial black holes, Rept. Prog. Phys. 84 (2021) 116902 [arXiv:2002.12778] [INSPIRE].
B. Carr and F. Kuhnel, Primordial Black Holes as Dark Matter: Recent Developments, Ann. Rev. Nucl. Part. Sci. 70 (2020) 355 [arXiv:2006.02838] [INSPIRE].
A.M. Green and B.J. Kavanagh, Primordial Black Holes as a dark matter candidate, J. Phys. G 48 (2021) 043001 [arXiv:2007.10722] [INSPIRE].
B.J. Carr and S.W. Hawking, Black holes in the early Universe, Mon. Not. Roy. Astron. Soc. 168 (1974) 399 [INSPIRE].
M. Sasaki, T. Suyama, T. Tanaka and S. Yokoyama, Primordial black holes — perspectives in gravitational wave astronomy, Class. Quant. Grav. 35 (2018) 063001 [arXiv:1801.05235] [INSPIRE].
S.W. Hawking, I.G. Moss and J.M. Stewart, Bubble Collisions in the Very Early Universe, Phys. Rev. D 26 (1982) 2681 [INSPIRE].
H. Kodama, M. Sasaki and K. Sato, Abundance of Primordial Holes Produced by Cosmological First Order Phase Transition, Prog. Theor. Phys. 68 (1982) 1979 [INSPIRE].
I.G. Moss, Singularity formation from colliding bubbles, Phys. Rev. D 50 (1994) 676 [INSPIRE].
R.V. Konoplich, S.G. Rubin, A.S. Sakharov and M.Y. Khlopov, Formation of black holes in first-order phase transitions as a cosmological test of symmetry-breaking mechanisms, Phys. Atom. Nucl. 62 (1999) 1593 [INSPIRE].
M.J. Baker, M. Breitbach, J. Kopp and L. Mittnacht, Primordial Black Holes from First-Order Cosmological Phase Transitions, arXiv:2105.07481 [INSPIRE].
C. Gross, G. Landini, A. Strumia and D. Teresi, Dark Matter as dark dwarfs and other macroscopic objects: multiverse relics?, JHEP 09 (2021) 033 [arXiv:2105.02840] [INSPIRE].
K. Kawana and K.-P. Xie, Primordial black holes from a cosmic phase transition: The collapse of Fermi-balls, Phys. Lett. B 824 (2022) 136791 [arXiv:2106.00111] [INSPIRE].
D. Marfatia and P.-Y. Tseng, Correlated signals of first-order phase transitions and primordial black hole evaporation, JHEP 08 (2022) 001 [Erratum ibid. 08 (2022) 249] [arXiv:2112.14588] [INSPIRE].
D. Croon, D. McKeen, N. Raj and Z. Wang, Subaru-HSC through a different lens: Microlensing by extended dark matter structures, Phys. Rev. D 102 (2020) 083021 [arXiv:2007.12697] [INSPIRE].
D. Croon, D. McKeen and N. Raj, Gravitational microlensing by dark matter in extended structures, Phys. Rev. D 101 (2020) 083013 [arXiv:2002.08962] [INSPIRE].
A.N. Lommen, Pulsar timing arrays: the promise of gravitational wave detection, Rept. Prog. Phys. 78 (2015) 124901 [INSPIRE].
C. Tiburzi, Pulsars probe the low-frequency gravitational sky: Pulsar Timing Arrays basics and recent results, Publ. Astron. Soc. Austral. 35 (2018) e013 [arXiv:1802.05076] [INSPIRE].
K. Kashiyama and N. Seto, Enhanced exploration for primordial black holes using pulsar timing arrays, Mon. Not. Roy. Astron. Soc. 426 (2012) 1369 [arXiv:1208.4101] [INSPIRE].
K. Schutz and A. Liu, Pulsar timing can constrain primordial black holes in the LIGO mass window, Phys. Rev. D 95 (2017) 023002 [arXiv:1610.04234] [INSPIRE].
J.A. Dror, H. Ramani, T. Trickle and K.M. Zurek, Pulsar Timing Probes of Primordial Black Holes and Subhalos, Phys. Rev. D 100 (2019) 023003 [arXiv:1901.04490] [INSPIRE].
H. Ramani, T. Trickle and K.M. Zurek, Observability of Dark Matter Substructure with Pulsar Timing Correlations, JCAP 12 (2020) 033 [arXiv:2005.03030] [INSPIRE].
V.S.H. Lee, A. Mitridate, T. Trickle and K.M. Zurek, Probing Small-Scale Power Spectra with Pulsar Timing Arrays, JHEP 06 (2021) 028 [arXiv:2012.09857] [INSPIRE].
T. Liu, X. Lou and J. Ren, Pulsar Polarization Arrays, Phys. Rev. Lett. 130 (2023) 121401 [arXiv:2111.10615] [INSPIRE].
G. Janssen et al., Gravitational wave astronomy with the SKA, PoS AASKA14 (2015) 037 [arXiv:1501.00127] [INSPIRE].
Theia collaboration, Theia: Faint objects in motion or the new astrometry frontier, arXiv:1707.01348 [INSPIRE].
A. Sesana et al., Unveiling the gravitational universe at μ-Hz frequencies, Exper. Astron. 51 (2021) 1333 [arXiv:1908.11391] [INSPIRE].
K. Schmitz, New Sensitivity Curves for Gravitational-Wave Signals from Cosmological Phase Transitions, JHEP 01 (2021) 097 [arXiv:2002.04615] [INSPIRE].
P.A. Rosado, A. Sesana and J. Gair, Expected properties of the first gravitational wave signal detected with pulsar timing arrays, Mon. Not. Roy. Astron. Soc. 451 (2015) 2417 [arXiv:1503.04803] [INSPIRE].
P. Lu, K. Kawana and K.-P. Xie, Old phase remnants in first-order phase transitions, Phys. Rev. D 105 (2022) 123503 [arXiv:2202.03439] [INSPIRE].
X. Wang, F.P. Huang and X. Zhang, Phase transition dynamics and gravitational wave spectra of strong first-order phase transition in supercooled universe, JCAP 05 (2020) 045 [arXiv:2003.08892] [INSPIRE].
G.D. Moore and T. Prokopec, How fast can the wall move? A Study of the electroweak phase transition dynamics, Phys. Rev. D 52 (1995) 7182 [hep-ph/9506475] [INSPIRE].
G.D. Moore and T. Prokopec, Bubble wall velocity in a first order electroweak phase transition, Phys. Rev. Lett. 75 (1995) 777 [hep-ph/9503296] [INSPIRE].
M. Hindmarsh, S.J. Huber, K. Rummukainen and D.J. Weir, Numerical simulations of acoustically generated gravitational waves at a first order phase transition, Phys. Rev. D 92 (2015) 123009 [arXiv:1504.03291] [INSPIRE].
B. Laurent and J.M. Cline, First principles determination of bubble wall velocity, Phys. Rev. D 106 (2022) 023501 [arXiv:2204.13120] [INSPIRE].
M.S. Turner, E.J. Weinberg and L.M. Widrow, Bubble nucleation in first order inflation and other cosmological phase transitions, Phys. Rev. D 46 (1992) 2384 [INSPIRE].
D. Chway, T.H. Jung and C.S. Shin, Dark matter filtering-out effect during a first-order phase transition, Phys. Rev. D 101 (2020) 095019 [arXiv:1912.04238] [INSPIRE].
P. Asadi et al., Thermal squeezeout of dark matter, Phys. Rev. D 104 (2021) 095013 [arXiv:2103.09827] [INSPIRE].
M.D. Rintoul and S. Torquato, Precise determination of the critical threshold and exponents in a three-dimensional continuum percolation model, J. Phys. A 30 (1997) L585.
J.-P. Hong, S. Jung and K.-P. Xie, Fermi-ball dark matter from a first-order phase transition, Phys. Rev. D 102 (2020) 075028 [arXiv:2008.04430] [INSPIRE].
P. Huang and K.-P. Xie, Primordial black holes from an electroweak phase transition, Phys. Rev. D 105 (2022) 115033 [arXiv:2201.07243] [INSPIRE].
M. Drees, F. Hajkarim and E.R. Schmitz, The Effects of QCD Equation of State on the Relic Density of WIMP Dark Matter, JCAP 06 (2015) 025 [arXiv:1503.03513] [INSPIRE].
F. Iocco et al., Primordial Nucleosynthesis: from precision cosmology to fundamental physics, Phys. Rept. 472 (2009) 1 [arXiv:0809.0631] [INSPIRE].
P.J. Steinhardt, Relativistic Detonation Waves and Bubble Growth in False Vacuum Decay, Phys. Rev. D 25 (1982) 2074 [INSPIRE].
M. Laine, Bubble growth as a detonation, Phys. Rev. D 49 (1994) 3847 [hep-ph/9309242] [INSPIRE].
J.R. Espinosa, T. Konstandin, J.M. No and G. Servant, Energy Budget of Cosmological First-order Phase Transitions, JCAP 06 (2010) 028 [arXiv:1004.4187] [INSPIRE].
A. Megevand and A.D. Sanchez, Supercooling and phase coexistence in cosmological phase transitions, Phys. Rev. D 77 (2008) 063519 [arXiv:0712.1031] [INSPIRE].
E. Witten, Cosmic Separation of Phases, Phys. Rev. D 30 (1984) 272 [INSPIRE].
Y. Bai, A.J. Long and S. Lu, Dark Quark Nuggets, Phys. Rev. D 99 (2019) 055047 [arXiv:1810.04360] [INSPIRE].
P. Lu, K. Kawana and A. Kusenko, Late-forming primordial black holes: Beyond the CMB era, Phys. Rev. D 107 (2023) 103037 [arXiv:2210.16462] [INSPIRE].
D. Marfatia and P.-Y. Tseng, Correlated gravitational wave and microlensing signals of macroscopic dark matter, JHEP 11 (2021) 068 [arXiv:2107.00859] [INSPIRE].
M. Fairbairn, E. Hardy and A. Wickens, Hearing without seeing: gravitational waves from hot and cold hidden sectors, JHEP 07 (2019) 044 [arXiv:1901.11038] [INSPIRE].
Y. Nakai, M. Suzuki, F. Takahashi and M. Yamada, Gravitational Waves and Dark Radiation from Dark Phase Transition: Connecting NANOGrav Pulsar Timing Data and Hubble Tension, Phys. Lett. B 816 (2021) 136238 [arXiv:2009.09754] [INSPIRE].
L.G. Book and E.E. Flanagan, Astrometric Effects of a Stochastic Gravitational Wave Background, Phys. Rev. D 83 (2011) 024024 [arXiv:1009.4192] [INSPIRE].
J. Garcia-Bellido, H. Murayama and G. White, Exploring the early Universe with Gaia and Theia, JCAP 12 (2021) 023 [arXiv:2104.04778] [INSPIRE].
R. Hellings and G. Downs, Upper limits on the isotropic gravitational radiation background from pulsar timing analysis, Astrophys. J. Lett. 265 (1983) L39 [INSPIRE].
NANOGrav collaboration, The NANOGrav 15 yr Data Set: Evidence for a Gravitational-wave Background, Astrophys. J. Lett. 951 (2023) L8 [arXiv:2306.16213] [INSPIRE].
NANOGrav collaboration, The NANOGrav 15 yr Data Set: Detector Characterization and Noise Budget, Astrophys. J. Lett. 951 (2023) L10 [arXiv:2306.16218] [INSPIRE].
J. Yokoyama, Implication of pulsar timing array experiments on cosmological gravitational wave detection, AAPPS Bull. 31 (2021) 17 [arXiv:2105.07629] [INSPIRE].
F.C. Adams, General solutions for tunneling of scalar fields with quartic potentials, Phys. Rev. D 48 (1993) 2800 [hep-ph/9302321] [INSPIRE].
S.R. Coleman, The Fate of the False Vacuum. 1. Semiclassical Theory, Phys. Rev. D 15 (1977) 2929 [Erratum ibid. 16 (1977) 1248] [INSPIRE].
Acknowledgments
We acknowledge the kind support of the National Science and Technology Council of the Republic of China (formerly the Ministry of Science and Technology), with grant number NSTC 111-2811-M-007-018-MY2. This work used high-performance computing facilities operated by the Center for Informatics and Computation in Astronomy (CICA) at National Tsing Hua University. This equipment was funded by the Ministry of Education of Taiwan, the National Science and Technology Council of Taiwan, and National Tsing Hua University. The authors would like to thank Reginald Bernardo, Thong Tran Quang Nguyen, Martin Spinrath, and Yu-Min Yeh for the helpful discussions and comments.
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Acuña, J.T., Tseng, PY. Probing primordial black holes from a first order phase transition through pulsar timing and gravitational wave signals. J. High Energ. Phys. 2023, 117 (2023). https://doi.org/10.1007/JHEP08(2023)117
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DOI: https://doi.org/10.1007/JHEP08(2023)117