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  • Open Access

Generalized neutrino isocurvature

Christopher Gerlach1,*, Wolfram Ratzinger2,†, and Pedro Schwaller1,‡

  • *Contact author: cgerlach@uni-mainz.de
  • †Contact author: wolfram.ratzinger@weizmann.ac.il
  • ‡Contact author: pedro.schwaller@uni-mainz.de

Phys. Rev. D 113, 083526 – Published 21 April, 2026

DOI: https://doi.org/10.1103/9wh7-9d7h

Abstract

Searches for neutrino isocurvature usually constrain a specific linear combination of isocurvature perturbations. In this work, we discuss realistic cosmological scenarios giving rise to neutrino isocurvature. We show that in general both neutrino and matter isocurvature perturbations are generated, whose ratio we parametrize by a newly introduced mixing angle. We obtain the first limits on this new mixing angle from PLANCK data, and discuss novel insights into the early Universe that could be provided by future measurements.

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References (55)

  1. J. M. Bardeen, Gauge invariant cosmological perturbations, Phys. Rev. D 22, 1882 (1980).
  2. S. Weinberg, Must cosmological perturbations remain non-adiabatic after multi-field inflation?, Phys. Rev. D 70, 083522 (2004).
  3. S. Weinberg, Can non-adiabatic perturbations arise after single-field inflation?, Phys. Rev. D 70, 043541 (2004).
  4. M. Bucher, K. Moodley, and N. Turok, The general primordial cosmic perturbation, Phys. Rev. D 62, 083508 (2000).
  5. The correlation matrix has to be kept positive definite. See Ref. [6] for details on how to ensure this constraint.

  6. P. A. R. Ade et al. (Planck Collaboration), Planck 2013 results. XXII. Constraints on inflation, Astron. Astrophys. 571, A22 (2014).
  7. M. Bucher, K. Moodley, and N. Turok, Constraining isocurvature perturbations with CMB polarization, Phys. Rev. Lett. 87, 191301 (2001).
  8. M. Bucher, J. Dunkley, P. G. Ferreira, K. Moodley, and C. Skordis, The initial conditions of the universe: How much isocurvature is allowed?, Phys. Rev. Lett. 93, 081301 (2004).
  9. K. Moodley, M. Bucher, J. Dunkley, P. G. Ferreira, and C. Skordis, Constraints on isocurvature models from the WMAP first-year data, Phys. Rev. D 70, 103520 (2004).
  10. R. Bean, J. Dunkley, and E. Pierpaoli, Constraining isocurvature initial conditions with WMAP 3-year data, Phys. Rev. D 74, 063503 (2006).
  11. Y. Akrami et al. (Planck Collaboration), Planck 2018 results. X. Constraints on inflation, Astron. Astrophys. 641, A10 (2020).
  12. P. A. R. Ade et al. (Planck Collaboration), Planck 2015 results. XX. Constraints on inflation, Astron. Astrophys. 594, A20 (2016).
  13. J. Preskill, M. B. Wise, and F. Wilczek, Cosmology of the invisible axion, Phys. Lett. 120B, 127 (1983).
  14. L. F. Abbott and P. Sikivie, A cosmological bound on the invisible axion, Phys. Lett. 120B, 133 (1983).
  15. M. Dine and W. Fischler, The not so harmless axion, Phys. Lett. 120B, 137 (1983).
  16. A. D. Linde, Generation of isothermal density perturbations in an inflationary universe, ZhETF Pisma Redaktsiiu 40, 496 (1984).
  17. J. Hamann, S. Hannestad, G. G. Raffelt, and Y. Y. Y. Wong, Isocurvature forecast in the anthropic axion window, J. Cosmol. Astropart. Phys. 06 (2009) 022.
  18. A. Caputo, M. Geller, and G. Rossi, New source for light dark matter isocurvature in low scale inflation, Phys. Rev. D 110, 055027 (2024).
  19. J. Lesgourgues and S. Pastor, Massive neutrinos and cosmology, Phys. Rep. 429, 307 (2006).
  20. M. Lattanzi and M. Gerbino, Status of neutrino properties and future prospects—Cosmological and astrophysical constraints, Front. Phys. 5, 70 (2018).
  21. P. F. De Salas, S. Gariazzo, O. Mena, C. A. Ternes, and M. Tórtola, Neutrino mass ordering from oscillations and beyond: 2018 status and future prospects, Front. Astron. Space Sci. 5, 36 (2018).
  22. C. Gerlach, W. Ratzinger, and P. Schwaller, Superhorizon isocurvature as a window into dark matter production, arXiv:2510.21917.
  23. D. Wands, K. A. Malik, D. H. Lyth, and A. R. Liddle, A new approach to the evolution of cosmological perturbations on large scales, Phys. Rev. D 62, 043527 (2000).
  24. D. H. Lyth and D. Wands, Conserved cosmological perturbations, Phys. Rev. D 68, 103515 (2003).
  25. D. H. Lyth and Y. Rodríguez, Inflationary prediction for primordial non-gaussianity, Phys. Rev. Lett. 95, 121302 (2005).
  26. D. Artigas, J. Grain, and V. Vennin, Hamiltonian formalism for cosmological perturbations: The separate-universe approach, J. Cosmol. Astropart. Phys. 02 (2022) 001.
  27. M. Cirelli, A. Strumia, and J. Zupan, Dark matter, arXiv:2406.01705.
  28. M. Dine and A. Kusenko, The origin of the matter—antimatter asymmetry, Rev. Mod. Phys. 76, 1 (2003).
  29. D. H. Lyth, C. Ungarelli, and D. Wands, The primordial density perturbation in the curvaton scenario, Phys. Rev. D 67, 023503 (2003).
  30. D. H. Lyth and D. Wands, The CDM isocurvature perturbation in the curvaton scenario, Phys. Rev. D 68, 103516 (2003).
  31. P. Adshead, G. Holder, and P. Ralegankar, BBN constraints on dark radiation isocurvature, J. Cosmol. Astropart. Phys. 09 (2020) 016.
  32. N. Aghanim et al. (Planck Collaboration), Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys. 641, A6 (2020); 652, C4(E) (2021).
  33. E. Di Valentino, M. Lattanzi, G. Mangano, A. Melchiorri, and P. Serpico, Future constraints on neutrino isocurvature perturbations in the curvaton scenario, Phys. Rev. D 85, 043511 (2012).
  34. J. A. Harvey and M. S. Turner, Cosmological baryon and lepton number in the presence of electroweak fermion number violation, Phys. Rev. D 42, 3344 (1990).
  35. V. Domcke, M. Escudero, M. Fernandez Navarro, and S. Sandner, A limit on the total lepton number in the Universe from BBN and the CMB, J. Cosmol. Astropart. Phys. 02 (2025) 017.
  36. D. Grin, O. Dore, and M. Kamionkowski, Compensated isocurvature perturbations and the cosmic microwave background, Phys. Rev. D 84, 123003 (2011).
  37. D. Grin, O. Dore, and M. Kamionkowski, Do baryons trace dark matter in the early universe?, Phys. Rev. Lett. 107, 261301 (2011).
  38. N. Lee and Y. Ali-Haïmoud, Probing small-scale baryon and dark matter isocurvature perturbations with cosmic microwave background anisotropies, Phys. Rev. D 104, 103509 (2021).
  39. A. Barreira, Constraints on compensated isocurvature perturbations from BOSS DR12 galaxy data, J. Cosmol. Astropart. Phys. 08 (2023) 051.
  40. M. Kawasaki, K. Miyamoto, K. Nakayama, and T. Sekiguchi, Isocurvature perturbations in extra radiation, J. Cosmol. Astropart. Phys. 02 (2012) 022.
  41. E. Kawakami, M. Kawasaki, K. Miyamoto, K. Nakayama, and T. Sekiguchi, Non-Gaussian isocurvature perturbations in dark radiation, J. Cosmol. Astropart. Phys. 07 (2012) 037.
  42. S. Ghosh, S. Kumar, and Y. Tsai, Free-streaming and coupled dark radiation isocurvature perturbations: Constraints and application to the Hubble tension, J. Cosmol. Astropart. Phys. 05 (2022) 014.
  43. D. Blas, J. Lesgourgues, and T. Tram, The Cosmic Linear Anisotropy Solving System (CLASS) II: Approximation schemes, J. Cosmol. Astropart. Phys. 07 (2011) 034.
  44. N. Aghanim et al. (Planck Collaboration), Planck 2018 results. V. CMB power spectra and likelihoods, Astron. Astrophys. 641, A5 (2020).
  45. S. Alam et al. (BOSS Collaboration), The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: Cosmological analysis of the DR12 galaxy sample, Mon. Not. R. Astron. Soc. 470, 2617 (2017).
  46. A. J. Ross, L. Samushia, C. Howlett, W. J. Percival, A. Burden, and M. Manera, The clustering of the SDSS DR7 main Galaxy sample—I. A 4 per cent distance measure at z=0.15, Mon. Not. R. Astron. Soc. 449, 835 (2015).
  47. F. Beutler, C. Blake, M. Colless, D. H. Jones, L. Staveley-Smith, L. Campbell, Q. Parker, W. Saunders, and F. Watson, The 6dF Galaxy survey: Baryon Acoustic Oscillations and the local Hubble constant, Mon. Not. R. Astron. Soc. 416, 3017 (2011).
  48. B. Audren, J. Lesgourgues, K. Benabed, and S. Prunet, Conservative constraints on early cosmology: An illustration of the Monte Python cosmological parameter inference code, J. Cosmol. Astropart. Phys. 02 (2013) 001.
  49. T. Brinckmann and J. Lesgourgues, MontePython 3: Boosted MCMC sampler and other features, Phys. Dark Universe 24, 100260 (2019).
  50. We made some initial runs in which the spectral index niso was varied freely as well. Due to the absence of significant evidence for isocurvature these runs did not converge. Therefore we only present bounds on the simpler yet well motivated scenario niso=1.

  51. S. Dodelson, Modern Cosmology (Academic Press, Amsterdam, 2003).
  52. D. H. Lyth and A. R. Liddle, The Primordial Density Perturbation (Cambridge University Press, Cambridge, England, 2009).
  53. H. Kodama and M. Sasaki, Evolution of isocurvature perturbations. 2. Radiation dust universe, Int. J. Mod. Phys. A 02, 491 (1987).
  54. D. H. Lyth and A. Riotto, Particle physics models of inflation and the cosmological density perturbation, Phys. Rep. 314, 1 (1999).
  55. R. K. Sachs and A. M. Wolfe, Perturbations of a cosmological model and angular variations of the microwave background, Astrophys. J. 147, 73 (1967).

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