First constraint on the neutrino-induced phase shift in the spectrum of baryon acoustic oscillations


The existence of the cosmic neutrino background is a robust prediction of the hot big bang model. These neutrinos were a dominant component of the energy density in the early Universe and therefore played an important role in the evolution of cosmological perturbations. The energy density of the cosmic neutrino background has been measured using the abundances of light elements and the anisotropies of the cosmic microwave background. A complementary and more robust probe is provided by a distinct shift in the temporal phase of sound waves in the primordial plasma that is produced by fluctuations in the neutrino density. Here, we report on the first constraint on this neutrino-induced phase shift in the spectrum of baryon acoustic oscillations of the BOSS DR12 data. Constraining the acoustic scale using Planck data while marginalizing over the effects of neutrinos in the cosmic microwave background, we find a non-zero phase shift at greater than 95% confidence. Besides providing a new test of the cosmic neutrino background, our work is the first application of the baryon acoustic oscillation signal to early Universe physics.

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Fig. 1: Phase shift induced by free-streaming neutrinos and other light relics.
Fig. 2: Observational constraints on the amplitude of the phase shift β.
Fig. 3: Current and future constraints on the amplitude of the phase shift β.

Data availability

The data that support the figures in this paper and other findings of this study are available from the corresponding author upon reasonable request. The BOSS DR12 data are available at The Planck data can be accessed via


  1. 1.

    Weinberg, S. Universal neutrino degeneracy. Phys. Rev. 128, 1457–1473 (1962).

    ADS  Article  Google Scholar 

  2. 2.

    Ringwald, A. Prospects for the direct detection of the cosmic neutrino background. Nucl. Phys. A 827, 501C–506C (2009).

    ADS  Article  Google Scholar 

  3. 3.

    Betts, S. et al. Development of a relic neutrino detection experiment at PTOLEMY: Princeton Tritium Observatory for Light, Early-Universe, Massive-Neutrino Yield. Preprint at (2013).

  4. 4.

    Bashinsky, S. & Seljak, U. Neutrino perturbations in CMB anisotropy and matter clustering. Phys. Rev. D 69, 083002 (2004).

    ADS  Article  Google Scholar 

  5. 5.

    Baumann, D., Green, D., Meyers, J. & Wallisch, B. Phases of new physics in the CMB. J. Cosmol. Astropart. Phys. 01, 007 (2016).

    ADS  Article  Google Scholar 

  6. 6.

    Follin, B., Knox, L., Millea, M. & Pan, Z. First detection of the acoustic oscillation phase shift expected from the cosmic neutrino background. Phys. Rev. Lett. 115, 091301 (2015).

    ADS  Article  Google Scholar 

  7. 7.

    Baumann, D., Green, D. & Zaldarriaga, M. Phases of new physics in the BAO spectrum. J. Cosmol. Astropart. Phys. 11, 007 (2017).

    ADS  MathSciNet  Article  Google Scholar 

  8. 8.

    Baumann, D., Green, D. & Wallisch, B. Searching for light relics with large-scale structure. J. Cosmol. Astropart. Phys. 08, 029 (2018).

    ADS  Article  Google Scholar 

  9. 9.

    Mangano, G. et al. Relic neutrino decoupling including flavor oscillations. Nucl. Phys. B 729, 221–234 (2005).

    ADS  Article  Google Scholar 

  10. 10.

    Planck Collaboration Planck 2015 results. XIII. Cosmological parameters. Astron. Astrophys. 594, A13 (2016).

  11. 11.

    Bashinsky, S. & Bertschinger, E. Dynamics of cosmological perturbations in position space. Phys. Rev. D 65, 123008 (2002).

    ADS  Article  Google Scholar 

  12. 12.

    Eisenstein, D., Seo, H.-J. & White, M. On the robustness of the acoustic scale in the low-redshift clustering of matter. Astrophys. J. 664, 660–674 (2007).

    ADS  Article  Google Scholar 

  13. 13.

    Brust, C., Kaplan, D. E. & Walters, M. New light species and the CMB. J. High Energy Phys. 12, 058 (2013).

    ADS  Article  Google Scholar 

  14. 14.

    Chacko, Z., Cui, Y., Hong, S. & Okui, T. Hidden dark matter sector, dark radiation and the CMB. Phys. Rev. D 92, 055033 (2015).

    ADS  Article  Google Scholar 

  15. 15.

    Baumann, D., Green, D. & Wallisch, B. New target for cosmic axion searches. Phys. Rev. Lett. 117, 171301 (2016).

    ADS  Article  Google Scholar 

  16. 16.

    Beutler, F. et al. The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: baryon acoustic oscillations in Fourier space. Mon. Not. R. Astron. Soc. 464, 3409–3430 (2017).

  17. 17.

    Eisenstein, D., Seo, H.-J., Sirko, E. & Spergel, D. Improving cosmological distance measurements by reconstruction of the baryon acoustic peak. Astrophys. J. 664, 675–679 (2007).

    ADS  Article  Google Scholar 

  18. 18.

    Padmanabhan, N. et al. A two-percent distance to z = 0.35 by reconstructing baryon acoustic oscillations – I. Methods and application to the Sloan Digital Sky Survey. Mon. Not. R. Astron. Soc. 427, 2132–2145 (2012).

  19. 19.

    Reid, B. et al. SDSS-III baryon oscillation spectroscopic survey data release 12: galaxy target selection and large scale structure catalogs. Mon. Not. R. Astron. Soc. 455, 1553–1573 (2016).

  20. 20.

    Alam, S. et al. The eleventh and twelfth data releases of the Sloan Digital Sky Survey: final data from SDSS-III. Astrophys. J. Suppl. 219, 12 (2015).

    ADS  Article  Google Scholar 

  21. 21.

    Alam, S. et al. 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, 2617–2652 (2017).

  22. 22.

    Ross, A. et al. The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: observational systematics and baryon acoustic oscillations in the correlation function. Mon. Not. R. Astron. Soc. 464, 1168–1191 (2017).

  23. 23.

    Vargas-Magaña, M. et al. The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: theoretical systematics and baryon acoustic oscillations in the galaxy correlation function. Mon. Not. R. Astron. Soc. 477, 1153–1188 (2018).

  24. 24.

    Planck Collaboration Planck 2018 results. VI. Cosmological parameters. Preprint at (2018).

  25. 25.

    Planck Collaboration Planck intermediate results. LI. Features in the cosmic microwave background temperature power spectrum and shifts in cosmological parameters. Astron. Astrophys. 607, A95 (2017).

  26. 26.

    Font-Ribera, A. et al. DESI and other dark energy experiments in the era of neutrino mass measurements. J. Cosmol. Astropart. Phys. 05, 023 (2014).

    ADS  MathSciNet  Article  Google Scholar 

  27. 27.

    Lewis, A., Challinor, A. & Lasenby, A. Efficient computation of CMB anisotropies in closed FRW models. Astrophys. J. 538, 473–476 (2000).

    ADS  Article  Google Scholar 

  28. 28.

    Blas, D., Lesgourgues, J. & Tram, T. The cosmic linear anisotropy solving system (CLASS) II: Approximation schemes. J. Cosmol. Astropart. Phys. 07, 034 (2011).

    ADS  Article  Google Scholar 

  29. 29.

    Lewis, A. & Bridle, S. Cosmological parameters from CMB and other data: a Monte-Carlo approach. Phys. Rev. D 66, 103511 (2002).

    ADS  Article  Google Scholar 

  30. 30.

    Pérez, F. & Granger, B. IPython: a system for interactive scientific computing. Comput. Sci. Eng. 9, 21–29 (2007).

    Article  Google Scholar 

  31. 31.

    Audren, B., Lesgourgues, J., Benabed, K. & Prunet, S. Conservative constraints on early cosmology: an illustration of the Monte Python cosmological parameter inference code. J. Cosmol. Astropart. Phys. 02, 001 (2013).

    ADS  Article  Google Scholar 

  32. 32.

    The Astropy Collaboration Astropy: a community Python package for astronomy. Astron. Astrophys. 558, A33 (2013).

  33. 33.

    Foreman-Mackey, D., Hogg, D., Lang, D. & Goodman, J. emcee: the MCMC hammer. Publ. Astron. Soc. Pac. 125, 306–312 (2013).

    ADS  Article  Google Scholar 

  34. 34.

    Hunter, J. Matplotlib: a 2D graphics environment. Comput. Sci. Eng. 9, 90–95 (2007).

    Article  Google Scholar 

  35. 35.

    Hand, N. et al. nbodykit: an open-source, massively parallel toolkit for large-scale structure. Astron. J. 156, 160 (2018).

    ADS  Article  Google Scholar 

  36. 36.

    van der Walt, S., Colbert, S. & Varoquaux, G. The NumPy array: a structure for efficient numerical computation. Comput. Sci. Eng. 13, 22–30 (2011).

    Article  Google Scholar 

  37. 37.

    Mehta, K. et al. Galaxy bias and its effects on the baryon acoustic oscillations measurements. Astrophys. J. 734, 94 (2011).

    ADS  Article  Google Scholar 

  38. 38.

    Xu, X., Cuesta, A., Padmanabhan, N., Eisenstein, D. & McBride, C. Measuring D A and H at z = 0.35 from the SDSS DR7 LRGs using baryon acoustic oscillations. Mon. Not. R. Astron. Soc. 431, 2834–2860 (2013).

  39. 39.

    Ding, Z. et al. Theoretical systematics of future baryon acoustic oscillation surveys. Mon. Not. R. Astron. Soc. 479, 1021–1054 (2018).

  40. 40.

    Sherwin, B. & White, M. The impact of wrong assumptions in BAO reconstruction. Preprint at (2018).

  41. 41.

    Gelman, A. & Rubin, D. Inference from iterative simulation using multiple sequences. Statist. Sci. 7, 457–472 (1992).

    ADS  Article  Google Scholar 

  42. 42.

    Kitaura, F.-S. et al. The clustering of galaxies in the SDSS-III baryon oscillation spectroscopic survey: mock galaxy catalogs for the BOSS final data release. Mon. Not. R. Astron. Soc. 456, 4156–4173 (2016).

  43. 43.

    Klypin, A., Yepes, G., Gottlober, S., Prada, F. & Hess, S. MultiDark simulations: the story of dark matter halo concentrations and density profiles. Mon. Not. R. Astron. Soc. 457, 4340–4359 (2016).

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D.B. thanks the Leung Center for Cosmology and Particle Astrophysics at the National Taiwan University and the Institute for Advanced Study for hospitality while this work was being completed, and is supported by a Vidi grant of the Netherlands Organisation for Scientific Research (NWO), funded by the Dutch Ministry of Education, Culture and Science (OCW). F.B. is a Royal Society University Research Fellow. R.F. is supported in part by the Alfred P. Sloan Foundation, the Department of Energy, under grant no. DE-SC0009919, a grant from the Simons Foundation/SFARI 560536, and by NASA under grant no. 17-ATP17-0193. D.G. thanks the University of California, Berkeley for hospitality while this work was being completed. A.S. thanks the Cosmoparticle Hub at University College London for hospitality during periods where parts of this manuscript were prepared. M.V.-M. is partially supported by Programa de Apoyo a Proyectos de Investigación e Innovación Tecnológica (PAPITT) no. IA102516 and no. IA101518, Proyecto Conacyt Fronteras no. 281 and Proyecto LANCAD-UNAM-DGTIC-319. B.W. is grateful to the CERN theory group for its hospitality and acknowledges support by a Cambridge European Scholarship from the Cambridge Trust, a Research Studentship Award of the Cambridge Philosophical Society, an STFC Studentship and a Visiting PhD Fellowship of the Delta-ITP consortium, a program of NWO.

This work is based on observations obtained by the Sloan Digital Sky Survey III (SDSS-III, Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation and the US Department of Energy Office of Science. This research also partly uses observations obtained with the Planck satellite (, an ESA science mission with instruments and contributions directly funded by ESA Member States, NASA and Canada. Some parts of this work were undertaken on the COSMOS Shared Memory System at DAMTP (University of Cambridge), operated on behalf of the STFC DiRAC HPC Facility. This equipment is funded by BIS National E-Infrastructure Capital grant ST/J005673/1 and STFC grants ST/H008586/1 and ST/K00333X/1. This research also used resources of the HPC cluster ATOCATL at IA-UNAM, Mexico and of the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the US Department of Energy under contract no. DE-AC02-05CH11231.

The authors acknowledge the use of CAMB27, CLASS28, CosmoMC/GetDist29, IPython30, Montepython31, and the Python packages Astropy32, emcee33, Matplotlib34, nbodykit35 and NumPy/SciPy36.

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F.B. and M.V.-M. led the Fourier- and configuration-space analyses, respectively. R.F. performed cross-checks of these analyses and led work on the CMB prior. D.B., D.G. and B.W. contributed theoretical work developing the modified BAO analysis. B.W. led the forecasts and validation of the modified analysis. A.S. and C.Y. contributed to the early Fourier-space analysis. A.S. initiated and coordinated the collaboration. D.B. and D.G. led the writing of the manuscript. All authors were active participants in regular discussions and contributed to the design of the analyses, the interpretation of the results and the review of the manuscript.

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Correspondence to Daniel Green.

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Baumann, D., Beutler, F., Flauger, R. et al. First constraint on the neutrino-induced phase shift in the spectrum of baryon acoustic oscillations. Nat. Phys. 15, 465–469 (2019).

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