• [1]

    G. F. R. Ellis and J. E. Baldwin, MNRAS 206, 377 (1984)

  • [2]

    J. J. Condon, W. D. Cotton, E. W. Greisen et al, Astrophys. J. 115, 1693 (1998)

  • [3]

    R. Maartens, C. Clarkson and S. Chen, JCAP 2018, 013 (2018)

  • [4]

    T. Nadolny, R. Durrer, M. Kunz et al., JCAP 2021, 009 (2021)

  • [5]

    C. Gibelyou and D. Huterer, MNRAS 427, 1994 (2012)

  • [6]

    T. Mauch, T. Murphy, H. J. Buttery et al, MNRAS 342, 1117 (2003)

  • [7]

    Y. Itoh, K. Yahata, and M. Takada, Phys. Rev. D 82, 043530 (2010)

  • [8]

    A. K. Singal, Astrophys. J. 742, L23 (2011)

  • [9]

    M. Rubart and D. J. Schwarz, A & A 555, A117 (2013)

  • [10]

    P. Tiwari and A. Nusser, JCAP 2016, 062 (2016)

  • [11]

    A. K. Singal, Phys. Rev. D 100, 063501 (2019)

  • [12]

    T. M. Siewert, M. Schmidt-Rubart, and D. J. Schwarz, A & A 653, A9 (2021)

  • [13]

    N. Secrest, S. v. Hausegger, M. Rameez et al., Astrophys. J. Lett. 908, L51 (2021)

  • [14]

    N. Secrest, S. v. Hausegger, M. Rameez et al., Astrophys. J. Lett. 937, L31 (2022)

  • [15]

    N. Secrest, S. von Hausegger, M. Rameez et al., Rev. Mod. Phys. 97, 041001 (2025)

  • [16]

    P. K. Aluri, P. Cea, P. Chingangbam et al, Class. Quant. Grav. 40, 094001 (2023)

  • [17]

    L. Dam, G. F. Lewis, and B. J. Brewer, MNRAS 525, 231 (2023), arXiv: 2212.07733

  • [18]

    O. T. Oayda, V. Mittal, G. F. Lewis et al., MNRAS 531, 4545 (2024), arXiv: 2406.01871

  • [19]

    J. Darling, Astrophys. J. Lett. 931, L14 (2022)

  • [20]

    A. Abghari, E. F. Bunn, L. T. Hergt et al, JCAP 2024, 067 (2024)

  • [21]

    S. Mittal, G. Kulkarni, D. Anstey et al., MNRAS 534, 1317 (2024)

  • [22]

    A. L. Erickcek, C. M. Hirata, and M. Kamionkowski, Phys. Rev. D 80, 083507 (2009)

  • [23]

    G. Domènech, R. Mohayaee, S. P. Patil et al., JCAP 2022, 019 (2022)

  • [24]

    M. S. Turner, Gen. Relativ. Gravit. 24, 1 (1992)

  • [25]

    A. L. Erickcek, S. M. Carroll, and M. Kamionkowski, Phys. Rev. D 78, 083012 (2008)

  • [26]

    K. Tomita, Astrophys. J. 529, 26 (2000)

  • [27]

    Y. Z. Ma, C. Gordon, and H. A. Feldman, Phys. Rev. D 83, 103002 (2011)

  • [28]

    J. Colin, R. Mohayaee, M. Rameez et al., A & A 631, L13 (2019)

  • [29]

    C. T. Byrnes and E. R. M. Tarrant, JCAP 2015, 007 (2015)

  • [30]

    C. Byrnes, G. Domènech, M. Sasaki et al., JCAP 2016, 020 (2016)

  • [31]

    Q. Yang, Y. Liu, and H. Di, Phys. Rev. D 96, 083516 (2017)

  • [32]

    E. Ebrahimian, C. Krishnan, R. Mondol et al., Class. Quant. Grav. 41, 145007 (2024), arXiv: 2305.16177

  • [33]

    C. Han, Phys. Rev. D 108, 015026 (2023)

  • [34]

    R. D. Peccei and H. R. Quinn, Phys. Rev. Lett. 38, 1440 (1977)

  • [35]

    R. D. Peccei and H. R. Quinn, Phys. Rev. D 16, 1791 (1977)

  • [36]

    P. J. Steinhardt and M. S. Turner, Phys. Lett. B 129, 51 (1983)

  • [37]

    J. Preskill, M. B. Wise, and F. Wilczek, Phys. Lett. B 120, 127 (1983)

  • [38]

    M. Dine and W. Fischler, Phys. Lett. B 120, 137 (1983)

  • [39]

    L. F. Abbott and P. Sikivie, Phys. Lett. B 120, 133 (1983)

  • [40]

    D. Seckel and M. S. Turner, Phys. Rev. D 32, 3178 (1985)

  • [41]

    D. H. Lyth, Phys. Lett. B 236, 408 (1990)

  • [42]

    M. S. Turner and F. Wilczek, Phys.l Rev. Lett. 66, 5 (1991)

  • [43]

    A. Linde, Phys. Lett. B 259, 38 (1991)

  • [44]

    J. E. Kim and G. Carosi, Rev. Mod. Phys. 82, 557 (2010), arXiv: 0807.3125

  • [45]

    O. Wantz and E. P. S. Shellard, Phys. Rev. D 82, 123508 (2010)

  • [46]

    D. J. E. Marsh, Phys. Rep. 643, 1 (2016)

  • [47]

    X. Chen, J. Fan, and L. Li, (2024), arXiv: 2303.03406

  • [48]

    N. Aghanim et al. (Planck Collaboration), A & A 641, A6 (2020)

  • [49]

    N. Aghanim et al. (Planck Collaboration), A & A 641, A1 (2020)

  • [50]

    C. Dalang and C. Bonvin, MNRAS 512, 3895 (2022)

  • [51]

    R. Durrer, The Cosmic Microwave Background, Second edition (Cambridge University Press, 2020)

  • [52]

    C. Bonvin and R. Durrer, Phys. Rev. D 84, 063505 (2011)

  • [53]

    A. Challinor and A. Lewis, Phys. Rev. D 84, 043516 (2011)

  • [54]

    J. P. Zibin and D. Scott, Phys. Rev. D 78, 123529 (2008)

  • [55]

    D. Blas, J. Lesgourgues, and T. Tram, JCAP 2011, 034 (2011)

  • [56]

    E. Di Dio, F. Montanari, J. Lesgourgues et al., JCAP 11, 044 (2013)

  • [57]

    N. Aghanim et al. (Planck Collaboration), A & A 641, A10 (2020)