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Impact of CMB low-ℓ EE polarization data on dark energy parametrizations

Shubham Barua* and Shantanu Desai†

  • Department of Physics, IIT Hyderabad, Kandi, Telangana 502284, India

  • *Contact author: ph24resch01006@iith.ac.in
  • †Contact author: shntn05@gmail.com
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Phys. Rev. D 114, 043556 – Published 31 August, 2026

DOI: https://doi.org/10.1103/lr47-j87b

Abstract

Measurement of the optical depth to reionization (τreio) is largely driven by the large-scale EE polarization data of cosmic microwave background (CMB) (ℓ<30). Removing the low-ℓ EE data potentially alleviates various cosmological tensions. In this work, we study the effect of the low-ℓ EE polarization measurements on the Chevallier-Polarski-Linder (CPL), Jassal-Bagla-Padmanabhan (JBP), and Barboza-Alcaniz (BA) dark energy parametrizations using CMB data from Planck and Atacama Cosmology Telescope Data Release 6, combined with a Dark Energy Spectroscopic Instrument baryon acoustic oscillation and PantheonPlus compilation of type Ia supernovae. We find that excluding low-ℓ EE data shifts τreio and As to higher values through the unbroken As−τreio degeneracy with a ∼(1.4–1.8)σ shift in As for ΛCDM (cold dark matter) and JBP, and a milder ∼1σ shift for CPL and BA. The equation of state (EOS) for all three parametrizations moves toward the quintessence regime [w(z)>−1] upon exclusion of low-ℓ EE data, driven primarily by the strengthening of the wa−As and the wa−τreio correlations, with a small effect from the correlations of w0 with As and τreio. The most prominent effect occurs in JBP, where the EOS lies entirely within the quintessence regime at 1σ when excluding low-ℓ EE data. Model comparison through the Akaike information criterion shows positive evidence in favor of CPL and BA and weak evidence in favor of JBP, robust to the inclusion of low-ℓ EE data and CMB data used. The deviance information criterion model comparison shows strong evidence in favor of CPL and BA when low-ℓ EE data are included, and positive evidence when they are excluded. For JBP, we get positive (weak) evidence when including (excluding) low-ℓ EE data over ΛCDM.

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References (83)

  1. B. E. Robertson, R. S. Ellis, J. S. Dunlop, R. J. McLure, and D. P. Stark, Nature (London) 468, 49 (2010).
  2. A. Loeb and R. Barkana, Annu. Rev. Astron. Astrophys. 39, 19 (2001).
  3. T. R. Choudhury, Gen. Relativ. Gravit. 54, 102 (2022).
  4. A. Mesinger and Z. Haiman, Astrophys. J. 660, 923 (2007).
  5. F. B. Davies, J. F. Hennawi, E. Bañados, Z. Lukić, R. Decarli, X. Fan, E. P. Farina, C. Mazzucchelli, H.-W. Rix, B. P. Venemans et al., Astrophys. J. 864, 142 (2018).
  6. C. A. Mason, T. Treu, M. Dijkstra, A. Mesinger, M. Trenti, L. Pentericci, S. de Barros, and E. Vanzella, Astrophys. J. 856, 2 (2018).
  7. B. Greig, A. Mesinger, F. B. Davies, F. Wang, J. Yang, and J. F. Hennawi, Mon. Not. R. Astron. Soc. 512, 5390 (2022).
  8. H. Umeda, M. Ouchi, K. Nakajima, Y. Harikane, Y. Ono, Y. Xu, Y. Isobe, and Y. Zhang, Astrophys. J. 971, 124 (2024).
  9. W. Elbers, arXiv:2508.21069.
  10. X. Jin, J. Yang, X. Fan, F. Wang, E. Bañados, F. Bian, F. B. Davies, A.-C. Eilers, E. P. Farina, J. F. Hennawi et al., Astrophys. J. 942, 59 (2023).
  11. I. D. McGreer, A. Mesinger, and V. D’Odorico, Mon. Not. R. Astron. Soc. 447, 499 (2015).
  12. E. Sobacchi and A. Mesinger, Mon. Not. R. Astron. Soc. 453, 1843 (2015).
  13. M. Ouchi, K. Shimasaku, H. Furusawa, T. Saito, M. Yoshida, M. Akiyama, Y. Ono, T. Yamada, K. Ota, N. Kashikawa et al., Astrophys. J. 723, 869 (2010).
  14. O. Zahn, C. L. Reichardt, L. Shaw, A. Lidz, K. A. Aird, B. A. Benson, L. E. Bleem, J. E. Carlstrom, C. L. Chang, H. M. Cho et al., Astrophys. J. 756, 65 (2012).
  15. K. M. Smith and S. Ferraro, Phys. Rev. Lett. 119, 021301 (2017).
  16. S. Raghunathan, P. Ade, A. Anderson, B. Ansarinejad, M. Archipley, J. Austermann, L. Balkenhol, J. Beall, K. Benabed, A. Bender et al., Phys. Rev. Lett. 133, 121004 (2024).
  17. R. Cen, P. McDonald, H. Trac, and A. Loeb, Astrophys. J. 706, L164 (2009).
  18. Z. Abdurashidova, J. E. Aguirre, P. Alexander, Z. S. Ali, Y. Balfour, A. P. Beardsley, G. Bernardi, T. S. Billings, J. D. Bowman, R. F. Bradley et al., Astrophys. J. 925, 221 (2022).
  19. R. Ghara, S. Zaroubi, B. Ciardi, G. Mellema, S. K. Giri, F. Mertens, M. Mevius, L. Koopmans, I. Iliev, A. Acharya et al., Astron. Astrophys. 699, A109 (2025).
  20. P. Jakobsen, P. Ferruit, C. Alves de Oliveira, S. Arribas, G. Bagnasco, R. Barho, T. L. Beck, S. Birkmann, T. Böker, A. J. Bunker et al., Astron. Astrophys. 661, A80 (2022).
  21. G. S. Wright, G. H. Rieke, A. Glasse, M. Ressler, M. García Marín, J. Aguilar, S. Alberts, J. Álvarez-Márquez, I. Argyriou, K. Banks et al., Publ. Astron. Soc. Pac. 135, 048003 (2023).
  22. T. Louis, A. La Posta, Z. Atkins, H. T. Jense, I. Abril-Cabezas, G. E. Addison, P. A. R. Ade, S. Aiola, T. Alford, D. Alonso et al., J. Cosmol. Astropart. Phys. 11 (2025) 062.
  23. N. MacCrann, B. D. Sherwin, F. J. Qu, T. Namikawa, M. S. Madhavacheril, I. Abril-Cabezas, R. An, J. E. Austermann, N. Battaglia, E. S. Battistelli et al., Astrophys. J. 966, 138 (2024).
  24. F. J. Qu, B. D. Sherwin, M. S. Madhavacheril, D. Han, K. T. Crowley, I. Abril-Cabezas, P. A. Ade, S. Aiola, T. Alford, M. Amiri et al., Astrophys. J. 962, 112 (2024).
  25. M. S. Madhavacheril, F. J. Qu, B. D. Sherwin, N. MacCrann, Y. Li, I. Abril-Cabezas, P. A. Ade, S. Aiola, T. Alford, M. Amiri et al., Astrophys. J. 962, 113 (2024).
  26. E. Camphuis, W. Quan, L. Balkenhol, A. R. Khalife, F. Ge, F. Guidi, N. Huang, G. P. Lynch, Y. Omori, C. Trendafilova et al., Phys. Rev. D 113, 083504 (2026).
  27. J. Carlstrom, P. A. Ade, K. Aird, B. Benson, L. Bleem, S. Busetti, C. Chang, E. Chauvin, H.-M. Cho, T. Crawford et al., Publ. Astron. Soc. Pac. 123, 568 (2011).
  28. N. Aghanim, Y. Akrami, M. Ashdown, J. Aumont, C. Baccigalupi, M. Ballardini, A. J. Banday, R. B. Barreiro, N. Bartolo et al. (Planck Collaboration), Astron. Astrophys. 641, A6 (2020).
  29. F. J. Qu, F. Ge, W. K. Wu, I. Abril-Cabezas, M. S. Madhavacheril, M. Millea, Z. Ahmed, E. Anderes, A. J. Anderson, B. Ansarinejad et al., Phys. Rev. Lett. 136, 021001 (2026).
  30. J. B. Muñoz, J. Mirocha, J. Chisholm, S. R. Furlanetto, and C. Mason, Mon. Not. R. Astron. Soc. 535, L37 (2024).
  31. E. Curtis-Lake, S. Carniani, A. Cameron, S. Charlot, P. Jakobsen, R. Maiolino, A. Bunker, J. Witstok, R. Smit, J. Chevallard et al., Nat. Astron. 7, 622 (2023).
  32. M. Llerena, L. Pentericci, L. Napolitano, S. Mascia, R. Amorín, A. Calabrò, M. Castellano, N. Cleri, M. Giavalisco, N. Grogin et al., Astron. Astrophys. 698, A302 (2025).
  33. H. Umeda, M. Ouchi, Y. Kageura, Y. Harikane, M. Nakane, T. T. Thai, and K. Nakajima, Astrophys. J. 997, 86 (2026).
  34. J. Cohon, C. Cain, R. Windhorst, A. D’Aloisio, T. Carleton, and Y. Zhu, Publ. Astron. Soc. Aust. 43, e046 (2026).
  35. W. Giarè, E. Di Valentino, and A. Melchiorri, Phys. Rev. D 109, 103519 (2024).
  36. R. Endsley, D. P. Stark, L. Whitler, M. W. Topping, B. D. Johnson, B. Robertson, S. Tacchella, S. Alberts, W. M. Baker, R. Bhatawdekar et al., Mon. Not. R. Astron. Soc. 533, 1111 (2024).
  37. C. Simmonds, S. Tacchella, K. Hainline, B. Johnson, W. McClymont, B. Robertson, A. Saxena, F. Sun, C. Witten, W. M. Baker et al., Mon. Not. R. Astron. Soc. 527, 6139 (2024).
  38. M. McQuinn, Annu. Rev. Astron. Astrophys. 54, 313 (2016).
  39. B. E. Robertson, R. S. Ellis, S. R. Furlanetto, and J. S. Dunlop, Astrophys. J. Lett. 802, L19 (2015).
  40. M. Abdul Karim, J. Aguilar, S. Ahlen, S. Alam, L. Allen, C. Allende Prieto, O. Alves, A. Anand, U. Andrade, E. Armengaud et al., Phys. Rev. D 112, 083515 (2025).
  41. C. Garcia-Quintero, H. E. Noriega, A. de Mattia, A. Aviles, K. Lodha, D. Chebat, J. Rohlf, S. Nadathur, W. Elbers, J. Aguilar et al., Phys. Rev. D 112, 083529 (2025).
  42. W. Yang, S. Pan, E. Di Valentino, and E. N. Saridakis, Universe 5, 219 (2019).
  43. T.-N. Li, P.-J. Wu, G.-H. Du, S.-J. Jin, H.-L. Li, J.-F. Zhang, and X. Zhang, Astrophys. J. 976, 1 (2024).
  44. S. Roy Choudhury, Astrophys. J. Lett. 986, L31 (2025).
  45. S. Roy Choudhury and T. Okumura, Astrophys. J. Lett. 976, L11 (2024).
  46. S. Roy Choudhury, T. Okumura, and K. Umetsu, Astrophys. J. Lett. 994, L26 (2025).
  47. C.-G. Park, J. d. C. Perez, and B. Ratra, Phys. Rev. D 110, 123533 (2024).
  48. L. Herold and T. Karwal, Phys. Rev. D 113, 123551 (2026).
  49. C.-G. Park and B. Ratra, Int. J. Mod. Phys. D 34, 2550061 (2025).
  50. J. d. C. Pérez, C.-G. Park, and B. Ratra, Phys. Rev. D 110, 023506 (2024).
  51. T.-N. Li, G.-H. Du, H. Wang, Y.-H. Li, J.-F. Zhang, and X. Zhang, Res. Astron. Astrophys. 26, 084002 (2026).
  52. M. Chevallier and D. Polarski, Int. J. Mod. Phys. D 10, 213 (2001).
  53. E. V. Linder, Phys. Rev. Lett. 90, 091301 (2003).
  54. N. Sailer, G. S. Farren, S. Ferraro, and M. White, Phys. Rev. Lett. 136, 081002 (2026).
  55. T. Jhaveri, T. Karwal, and W. Hu, Phys. Rev. D 112, 043541 (2025).
  56. U. Upadhyay, Y. Tiwari, and T. Souradeep, J. Cosmol. Astropart. Phys. 06 (2026) 019.
  57. I. J. Allali, P. Singh, J. Fan, and L. Li, J. Cosmol. Astropart. Phys. 08 (2025) 082.
  58. H. K. Jassal, J. S. Bagla, and T. Padmanabhan, Phys. Rev. D 72, 103503 (2005).
  59. E. M. Barboza and J. S. Alcaniz, Phys. Lett. B 666, 415 (2008).
  60. J. Zheng, D.-C. Qiang, and Z.-Q. You, J. Cosmol. Astropart. Phys. 08 (2025) 056.
  61. D. Scolnic, D. Brout, A. Carr, A. G. Riess, T. M. Davis, A. Dwomoh, D. O. Jones, N. Ali, P. Charvu, R. Chen et al., Astrophys. J. 938, 113 (2022).
  62. D. Brout, D. Scolnic, B. Popovic, A. G. Riess, A. Carr, J. Zuntz, R. Kessler, T. M. Davis, S. Hinton, D. Jones et al., Astrophys. J. 938, 110 (2022).
  63. Y. Akrami, F. Arroja, M. Ashdown, J. Aumont, C. Baccigalupi, M. Ballardini, A. Banday, R. Barreiro, N. Bartolo, S. Basak et al., Astron. Astrophys. 641, A1 (2020).
  64. E. Calabrese, J. C. Hill, H. T. Jense, A. La Posta, I. Abril-Cabezas, G. E. Addison, P. A. Ade, S. Aiola, T. Alford, D. Alonso et al., J. Cosmol. Astropart. Phys. 11 (2025) 063.
  65. N. Aghanim, Y. Akrami, M. Ashdown, J. Aumont, C. Baccigalupi, M. Ballardini, A. J. Banday, R. Barreiro, N. Bartolo, S. Basak et al., Astron. Astrophys. 641, A5 (2020).
  66. G. Efstathiou and S. Gratton, arXiv:1910.00483.
  67. E. Rosenberg, S. Gratton, and G. Efstathiou, Mon. Not. R. Astron. Soc. 517, 4620 (2022).
  68. J.-M. Delouis, L. Pagano, S. Mottet, J.-L. Puget, and L. Vibert, Astron. Astrophys. 629, A38 (2019).
  69. L. Pagano, J.-M. Delouis, S. Mottet, J.-L. Puget, and L. Vibert, Astron. Astrophys. 635, A99 (2020).
  70. J. Carron, M. Mirmelstein, and A. Lewis, J. Cosmol. Astropart. Phys. 09 (2022) 039.
  71. J. Lesgourgues, arXiv:1104.2932.
  72. D. Blas, J. Lesgourgues, and T. Tram, J. Cosmol. Astropart. Phys. 07 (2011) 034.
  73. A. Mead, Mon. Not. R. Astron. Soc. 459, 1468 (2016).
  74. J. Torrado and A. Lewis, J. Cosmol. Astropart. Phys. 05 (2021) 057.
  75. A. Lewis, J. Cosmol. Astropart. Phys. 08 (2025) 025.
  76. M. Kunz, R. Trotta, and D. R. Parkinson, Phys. Rev. D 74, 023503 (2006).
  77. M. Biesiada, J. Cosmol. Astropart. Phys. 02 (2007) 003.
  78. A. R. Liddle, Mon. Not. R. Astron. Soc. 377, L74 (2007).
  79. A. Krishak and S. Desai, J. Cosmol. Astropart. Phys. 07 (2020) 006.
  80. B. Popovic, P. Shah, W. Kenworthy, R. Kessler, T. Davis, A. Goobar, D. Scolnic, M. Vincenzi, P. Wiseman, R. Chen et al., Mon. Not. R. Astron. Soc. 548, stag632 (2026).
  81. D. C. T. Abbott, M. Acevedo, M. Aguena, A. Alarcon, S. Allam, O. Alves, A. Amon, F. Andrade-Oliveira, J. Annis, P. Armstrong et al., Astrophys. J. Lett. 973, L14 (2024).
  82. Y. Dai and W. Liao, arXiv:2605.10116.
  83. J. M. Sullivan, R. de Belsunce, and M. M. Ivanov, arXiv:2606.30903.

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Phys. Rev. D 114, 043556– Published 31 August, 2026
  • Received 21 June 2026
  • Accepted 30 July 2026
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