[1] G. ’t Hooft, Nucl. Phys. B 79, 276 (1974). doi:10.1016/0550-3213(74)90486-6
[2] A. M. Polyakov, JETP Lett. 20, 194 (1974) [Pisma Zh. Eksp. Teor. Fiz. 20, 430 (1974)].
[3] S. Baek, P. Ko and W. I. Park, JCAP 10, 067 (2014) doi:10.1088/1475- 7516/2014/10/067 [arXiv:1311.1035 [hep-ph]].
[4] V. V. Khoze and G. Ro, JHEP 10, 061 (2014) doi:10.1007/JHEP10(2014)061 [arXiv:1406.2291 [hep-ph]].
[5] M. Tanabashi et al. [Particle Data Group], Phys. Rev. D 98, no. 3, 030001 (2018). doi:10.1103/PhysRevD.98.030001
[6] E. Witten, Phys. Lett. B 86, 283 (1979) [Phys. Lett. 86B, 283 (1979)]. doi:10.1016/0370-2693(79)90838-4
[7] G. Aad et al. [ATLAS], Phys. Lett. B 716, 1-29 (2012) doi:10.1016/j.physletb.2012.08.020 [arXiv:1207.7214 [hep-ex]].
[8] S. Chatrchyan et al. [CMS], Phys. Lett. B 716, 30-61 (2012) doi:10.1016/j.physletb.2012.08.021 [arXiv:1207.7235 [hep-ex]].
[9] N. Aghanim et al. [Planck], [arXiv:1807.06209 [astro-ph.CO]].
[10] B. Abbott et al. [LIGO Scientific and Virgo], Phys. Rev. Lett. 116, no.6, 061102 (2016) doi:10.1103/PhysRevLett.116.061102 [arXiv:1602.03837 [gr-qc]].
[11] F. Englert and R. Brout, Phys. Rev. Lett. 13, 321 (1964). doi:10.1103/PhysRevLett.13.321
[12] P. W. Higgs, Phys. Rev. 145, 1156 (1966). doi:10.1103/PhysRev.145.1156
[13] G. S. Guralnik, C. R. Hagen and T. W. B. Kibble, Phys. Rev. Lett. 13, 585 (1964). doi:10.1103/PhysRevLett.13.585
[14] J. Christenson, J. Cronin, V. Fitch and R. Turlay, Phys. Rev. Lett. 13, 138-140 (1964) doi:10.1103/PhysRevLett.13.138
[15] M. Kobayashi and T. Maskawa, Prog. Theor. Phys. 49, 652-657 (1973) doi:10.1143/PTP.49.652
[16] B. Pontecorvo, Sov. Phys. JETP 7, 172-173 (1958)
[17] Z. Maki, M. Nakagawa and S. Sakata, Prog. Theor. Phys. 28, 870-880 (1962) doi:10.1143/PTP.28.870
[18] P.A. Zyla et al. (Particle Data Group), to be published in Prog. Theor. Exp. Phys. 2020, 083C01 (2020).
[19] E. W. Kolb and M. S. Turner, Front. Phys. 69, 1-547 (1990)
[20] P. F. de Salas and S. Pastor, JCAP 07, 051 (2016) doi:10.1088/1475- 7516/2016/07/051 [arXiv:1606.06986 [hep-ph]].
[21] T. Yanagida, Prog. Theor. Phys. 64, 1103 (1980) doi:10.1143/PTP.64.1103
[22] A. Sakharov, Sov. Phys. Usp. 34, no.5, 392-393 (1991) doi:10.1070/PU1991v034n05ABEH002497
[23] M. B. Gavela, P. Hernandez, J. Orloff and O. Pene, Mod. Phys. Lett. A 9, 795-810 (1994) doi:10.1142/S0217732394000629 [arXiv:hep-ph/9312215 [hep-ph]].
[24] M. B. Gavela, P. Hernandez, J. Orloff, O. Pene and C. Quimbay, Nucl. Phys. B 430, 382-426 (1994) doi:10.1016/0550-3213(94)00410-2 [arXiv:hep-ph/9406289 [hep-ph]].
[25] P. Huet and E. Sather, Phys. Rev. D 51, 379-394 (1995) doi:10.1103/PhysRevD.51.379 [arXiv:hep-ph/9404302 [hep-ph]].
[26] V. A. Kuzmin, V. A. Rubakov and M. E. Shaposhnikov, Phys. Lett. B 155, 36 (1985) doi:10.1016/0370-2693(85)91028-7
[27] W. Buchmuller, R. Peccei and T. Yanagida, Ann. Rev. Nucl. Part. Sci. 55, 311- 355 (2005) doi:10.1146/annurev.nucl.55.090704.151558 [arXiv:hep-ph/0502169 [hep- ph]].
[28] M. Fukugita and T. Yanagida, Phys. Lett. B 174, 45-47 (1986) doi:10.1016/0370-2693(86)91126-3
[29] V. Rubakov and M. Shaposhnikov, Usp. Fiz. Nauk 166, 493-537 (1996) doi:10.1070/PU1996v039n05ABEH000145 [arXiv:hep-ph/9603208 [hep-ph]].
[30] B. Graner, Y. Chen, E. Lindahl and B. Heckel, Phys. Rev. Lett. 116, no.16, 161601 (2016) doi:10.1103/PhysRevLett.116.161601 [arXiv:1601.04339 [physics.atom-ph]].
[31] R. Peccei and H. R. Quinn, Phys. Rev. Lett. 38, 1440-1443 (1977) doi:10.1103/PhysRevLett.38.1440
[32] R. Peccei and H. R. Quinn, Phys. Rev. D 16, 1791-1797 (1977) doi:10.1103/PhysRevD.16.1791
[33] G. Jungman, M. Kamionkowski and K. Griest, Phys. Rept. 267, 195-373 (1996) doi:10.1016/0370-1573(95)00058-5 [arXiv:hep-ph/9506380 [hep-ph]].
[34] N. Arkani-Hamed, A. Cohen, E. Katz and A. Nelson, JHEP 07, 034 (2002) doi:10.1088/1126-6708/2002/07/034 [arXiv:hep-ph/0206021 [hep-ph]].
[35] E. W. Kolb and R. Slansky, Phys. Lett. B 135, 378 (1984) doi:10.1016/0370- 2693(84)90298-3
[36] C. Amole et al. [PICO Collaboration], Phys. Rev. D 100, no. 2, 022001 (2019) doi:10.1103/PhysRevD.100.022001 [arXiv:1902.04031 [astro-ph.CO]].
[37] S. Weinberg, Phys. Rev. Lett. 40, 223-226 (1978) doi:10.1103/PhysRevLett.40.223
[38] F. Wilczek, Phys. Rev. Lett. 40, 279-282 (1978) doi:10.1103/PhysRevLett.40.279
[39] S. Borsanyi et al., Nature 539, no. 7627, 69 (2016) [arXiv:1606.07494 [hep-lat]].
[40] E. Berkowitz, M. I. Buchoff and E. Rinaldi, Phys. Rev. D 92, no. 3, 034507 (2015) [arXiv:1505.07455 [hep-ph]].
[41] P. Petreczky, H. P. Schadler and S. Sharma, Phys. Lett. B 762, 498 (2016) [arXiv:1606.03145 [hep-lat]].
[42] J. Frison, R. Kitano, H. Matsufuru, S. Mori and N. Yamada, JHEP 1609, 021 (2016) [arXiv:1606.07175 [hep-lat]].
[43] Y. Taniguchi, K. Kanaya, H. Suzuki and T. Umeda, Phys. Rev. D 95, no. 5, 054502 (2017) [arXiv:1611.02411 [hep-lat]].
[44] G. Grilli di Cortona, E. Hardy, J. Pardo Vega and G. Villadoro, The QCD axion, precisely, JHEP 1601, 034 (2016) doi:10.1007/JHEP01(2016)034 [arXiv:1511.02867 [hep-ph]].
[45] J. Preskill, M. B. Wise and F. Wilczek, Phys. Lett. B 120, 127 (1983).
[46] L. F. Abbott and P. Sikivie, Phys. Lett. B 120, 133 (1983).
[47] M. Dine and W. Fischler, Phys. Lett. B 120, 137 (1983).
[48] T. Hiramatsu, M. Kawasaki, K. Saikawa and T. Sekiguchi, Phys. Rev. D 85, 105020 (2012) Erratum: [Phys. Rev. D 86, 089902 (2012)] [arXiv:1202.5851 [hep-ph]].
[49] M. Kawasaki, K. Saikawa and T. Sekiguchi, Phys. Rev. D 91, no. 6, 065014 (2015) [arXiv:1412.0789 [hep-ph]].
[50] L. Fleury and G. D. Moore, JCAP 1601, 004 (2016) [arXiv:1509.00026 [hep-ph]].
[51] V. B. Klaer and G. D. Moore, JCAP 1711, no. 11, 049 (2017) [arXiv:1708.07521 [hep-ph]].
[52] M. Gorghetto, E. Hardy and G. Villadoro, JHEP 1807, 151 (2018) [arXiv:1806.04677 [hep-ph]].
[53] M. Kawasaki, T. Sekiguchi, M. Yamaguchi and J. Yokoyama, arXiv:1806.05566 [hep-ph].
[54] G. Ballesteros, J. Redondo, A. Ringwald and C. Tamarit, JCAP 1708, no. 08, 001 (2017) [arXiv:1610.01639 [hep-ph]].
[55] R. Mayle, J. R. Wilson, J. R. Ellis, K. A. Olive, D. N. Schramm and G. Steigman, Phys. Lett. B 203, 188 (1988).
[56] G. Raffelt and D. Seckel, Phys. Rev. Lett. 60, 1793 (1988).
[57] M. S. Turner, Phys. Rev. Lett. 60, 1797 (1988).
[58] T. Kobayashi, R. Kurematsu and F. Takahashi, JCAP 1309, 032 (2013) [arXiv:1304.0922 [hep-ph]].
[59] A. Arvanitaki, S. Dimopoulos, S. Dubovsky, N. Kaloper and J. March-Russell, Phys. Rev. D 81, 123530 (2010) [arXiv:0905.4720 [hep-th]].
[60] B. S. Acharya, K. Bobkov and P. Kumar, JHEP 1011, 105 (2010) [arXiv:1004.5138 [hep-th]].
[61] M. Cicoli, M. Goodsell and A. Ringwald, JHEP 1210, 146 (2012) [arXiv:1206.0819 [hep-th]].
[62] T. Higaki and F. Takahashi, JHEP 1407, 074 (2014) [arXiv:1404.6923 [hep-th]].
[63] T. Higaki and F. Takahashi, Phys. Lett. B 744, 153 (2015) [arXiv:1409.8409 [hep- ph]].
[64] N. Kitajima and F. Takahashi, JCAP 1501, no. 01, 032 (2015) [arXiv:1411.2011 [hep-ph]].
[65] D. Cadamuro and J. Redondo, JCAP 1202, 032 (2012) [arXiv:1110.2895 [hep-ph]].
[66] P. Arias, D. Cadamuro, M. Goodsell, J. Jaeckel, J. Redondo and A. Ringwald, JCAP 1206, 013 (2012) [arXiv:1201.5902 [hep-ph]].
[67] S. J. Asztalos et al. [ADMX Collaboration], Phys. Rev. D 69, 011101 (2004) [astro- ph/0310042].
[68] S. J. Asztalos et al. [ADMX Collaboration], Phys. Rev. Lett. 104, 041301 (2010) [arXiv:0910.5914 [astro-ph.CO]].
[69] G. Carosi, A. Friedland, M. Giannotti, M. J. Pivovaroff, J. Ruz and J. K. Vogel, arXiv:1309.7035 [hep-ph].
[70] V. Anastassopoulos et al. [CAST Collaboration], Nature Phys. 13 (2017) 584 [arXiv:1705.02290 [hep-ex]].
[71] https://indico.in2p3.fr/event/16579/contributions/60840/attachments/47276/59399/Moriond.pdf
[72] E. Petrakou [CAPP/IBS Collaboration], EPJ Web Conf. 164, 01012 (2017) [arXiv:1702.03664 [physics.ins-det]].
[73] A. Caldwell et al. [MADMAX Working Group], Phys. Rev. Lett. 118, no. 9, 091801 (2017) [arXiv:1611.05865 [physics.ins-det]].
[74] Y. Kahn, B. R. Safdi and J. Thaler, Phys. Rev. Lett. 117, no. 14, 141801 (2016) [arXiv:1602.01086 [hep-ph]].
[75] R. B¨ahre et al., JINST 8, T09001 (2013) [arXiv:1302.5647 [physics.ins-det]].
[76] E. Armengaud et al., JINST 9, T05002 (2014) [arXiv:1401.3233 [physics.ins-det]].
[77] A. Ayala, I. Dom´ınguez, M. Giannotti, A. Mirizzi and O. Straniero, Phys. Rev. Lett. 113, no. 19, 191302 (2014) [arXiv:1406.6053 [astro-ph.SR]].
[78] J. E. Kim, Phys. Rev. Lett. 43, 103 (1979).
[79] M. A. Shifman, A. I. Vainshtein and V. I. Zakharov, Nucl. Phys. B 166, 493 (1980).
[80] M. Dine, W. Fischler and M. Srednicki, Phys. Lett. 104B, 199 (1981).
[81] A. R. Zhitnitsky, Sov. J. Nucl. Phys. 31, 260 (1980) [Yad. Fiz. 31, 497 (1980)].
[82] S. Y. Ho, K. Saikawa and F. Takahashi, JCAP 10, 042 (2018) doi:10.1088/1475- 7516/2018/10/042 [arXiv:1806.09551 [hep-ph]].
[83] S. Y. Ho, F. Takahashi and W. Yin, JHEP 04, 149 (2019) doi:10.1007/JHEP04(2019)149 [arXiv:1901.01240 [hep-ph]].
[84] Y. Hochberg, E. Kuflik, T. Volansky and J. G. Wacker, Phys. Rev. Lett. 113, 171301 (2014) doi:10.1103/PhysRevLett.113.171301 [arXiv:1402.5143 [hep-ph]].
[85] S. Y. Ho, T. Toma and K. Tsumura, JHEP 07, 101 (2017) doi:10.1007/JHEP07(2017)101 [arXiv:1705.00592 [hep-ph]].
[86] P. Hut and K. A. Olive, Phys. Lett. 87B, 144 (1979). doi:10.1016/0370- 2693(79)90039-X
[87] S. Nussinov, Phys. Lett. 165B, 55 (1985). doi:10.1016/0370-2693(85)90689-6
[88] K. M. Zurek, Phys. Rept. 537, 91-121 (2014) doi:10.1016/j.physrep.2013.12.001 [arXiv:1308.0338 [hep-ph]].
[89] Ya.B. Zel’dovich and I.D. Novikov, Sov. Astron. 10, 602 (1967).
[90] S.W. Hawking, Nature (London) 248, 30 (1974).
[91] T. Harada, C. M. Yoo and K. Kohri, Phys. Rev. D 88, no.8, 084051 (2013) doi:10.1103/PhysRevD.88.084051 [arXiv:1309.4201 [astro-ph.CO]].
[92] B. Carr, K. Kohri, Y. Sendouda and J. Yokoyama, [arXiv:2002.12778 [astro-ph.CO]].
[93] H. Niikura, M. Takada, N. Yasuda, R. H. Lupton, T. Sumi, S. More, T. Kurita, S. Sugiyama, A. More, M. Oguri and M. Chiba, Nature Astron. 3, no.6, 524-534 (2019) doi:10.1038/s41550-019-0723-1 [arXiv:1701.02151 [astro-ph.CO]].
[94] W. Hu, R. Barkana and A. Gruzinov, Phys. Rev. Lett. 85, 1158-1161 (2000) doi:10.1103/PhysRevLett.85.1158 [arXiv:astro-ph/0003365 [astro-ph]].
[95] T. W. B. Kibble, J. Phys. A 9, 1387 (1976). doi:10.1088/0305-4470/9/8/029
[96] E. J. Weinberg, doi:10.1017/CBO9781139017787
[97] P. Goddard and D. I. Olive, Rept. Prog. Phys. 41, 1357 (1978). doi:10.1088/0034- 4885/41/9/001
[98] L. H. Ryder, Quantum Field Theory
[99] E. B. Bogomolny, Sov. J. Nucl. Phys. 24, 449 (1976) [Yad. Fiz. 24, 861 (1976)].
[100] M. Prasad and C. M. Sommerfield, Phys. Rev. Lett. 35, 760-762 (1975) doi:10.1103/PhysRevLett.35.760
[101] J. S. Schwinger, Science 165, 757 (1969). doi:10.1126/science.165.3895.757
[102] W. Fischler and J. Preskill, Phys. Lett. 125B, 165 (1983). doi:10.1016/0370- 2693(83)91260-1
[103] W. H. Zurek, Nature 317, 505 (1985). doi:10.1038/317505a0
[104] H. Murayama and J. Shu, Phys. Lett. B 686, 162 (2010) doi:10.1016/j.physletb.2010.02.037 [arXiv:0905.1720 [hep-ph]].
[105] G. Belanger, F. Boudjema, A. Pukhov and A. Semenov, Comput. Phys. Commun. 180, 747 (2009) doi:10.1016/j.cpc.2008.11.019 [arXiv:0803.2360 [hep-ph]].
[106] F. Brummer and J. Jaeckel, Phys. Lett. B 675, 360 (2009) doi:10.1016/j.physletb.2009.04.041 [arXiv:0902.3615 [hep-ph]].
[107] F. Brummer, J. Jaeckel and V. V. Khoze, JHEP 0906, 037 (2009) doi:10.1088/1126- 6708/2009/06/037 [arXiv:0905.0633 [hep-ph]].
[108] K. Kadota, T. Sekiguchi and H. Tashiro, arXiv:1602.04009 [astro-ph.CO].
[109] A. Stebbins and G. Krnjaic, arXiv:1908.05275 [astro-ph.CO].
[110] B. von Harling and K. Petraki, JCAP 12, 033 (2014) doi:10.1088/1475- 7516/2014/12/033 [arXiv:1407.7874 [hep-ph]].
[111] M. A. Buen-Abad and J. Fan, JHEP 12, 161 (2019) doi:10.1007/JHEP12(2019)161 [arXiv:1911.05737 [hep-ph]].
[112] D. E. Kaplan and R. Rattazzi, Phys. Rev. D 93, no.8, 085007 (2016) doi:10.1103/PhysRevD.93.085007 [arXiv:1511.01827 [hep-ph]].
[113] M. E. Peskin and D. V. Schroeder, An Introduction to quantum field theory,
[114] K. R. Dienes, J. Kumar, B. Thomas and D. Yaylali, Phys. Rev. D 90, no. 1, 015012 (2014) doi:10.1103/PhysRevD.90.015012 [arXiv:1312.7772 [hep-ph]].
[115] E. Behnke et al. [COUPP Collaboration], Phys. Rev. D 86, no. 5, 052001 (2012) Erratum: [Phys. Rev. D 90, no. 7, 079902 (2014)] doi:10.1103/PhysRevD.86.052001, 10.1103/PhysRevD.90.079902 [arXiv:1204.3094 [astro-ph.CO]].
[116] https://indico.cern.ch/event/660187/contributions/2888067/attachments/1624996/2587371/Aspen2018LevinePICO.pdf
[117] F. Bergsma et al. [CHARM], Phys. Lett. B 157, 458-462 (1985) doi:10.1016/0370-2693(85)90400-9
[118] S. Alekhin, et al. [SHiP], Rept. Prog. Phys. 79, no.12, 124201 (2016) doi:10.1088/0034-4885/79/12/124201 [arXiv:1504.04855 [hep-ph]]. LaTeX (US)
[119] M. J. Dolan, F. Kahlhoefer, C. McCabe and K. Schmidt-Hoberg, JHEP 1503, 171 (2015) Erratum: [JHEP 1507, 103 (2015)] doi:10.1007/JHEP07(2015)103,10.1007/JHEP03(2015)171 [arXiv:1412.5174 [hep-ph]].
[120] A. Djouadi, Phys. Rept. 457, 1 (2008) doi:10.1016/j.physrep.2007.10.004 [hep- ph/0503172].
[121] R. Ammar et al. [CLEO Collaboration], Phys. Rev. Lett. 87, 271801 (2001) doi:10.1103/PhysRevLett.87.271801 [hep-ex/0106038].
[122] G. G. Raffelt, Phys. Rept. 198, 1 (1990). doi:10.1016/0370-1573(90)90054-6
[123] G. G. Raffelt, Lect. Notes Phys. 741, 51 (2008) [hep-ph/0611350].
[124] N. Bar, K. Blum and G. D’amico, arXiv:1907.05020 [hep-ph].
[125] F. D’Eramo, R. Z. Ferreira, A. Notari and J. L. Bernal, JCAP 1811, 014 (2018) doi:10.1088/1475-7516/2018/11/014 [arXiv:1808.07430 [hep-ph]].
[126] A. G. Riess, S. Casertano, W. Yuan, L. M. Macri and D. Scolnic, Astrophys. J. 876, no. 1, 85 (2019) doi:10.3847/1538-4357/ab1422 [arXiv:1903.07603 [astro-ph.CO]].
[127] F. Takahashi and M. Yamada, JCAP 1907, no. 07, 001 (2019) doi:10.1088/1475- 7516/2019/07/001 [arXiv:1904.12864 [astro-ph.CO]].
[128] J. Preskill, Ann. Rev. Nucl. Part. Sci. 34, 461 (1984). doi:10.1146/annurev.ns.34.120184.002333