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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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 http://www.sdss.org/dr12/. The Planck data can be accessed via http://pla.esac.esa.int/pla/.

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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, http://www.sdss3.org/). 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 (http://www.esa.int/Planck), 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.

Author information


  1. Institute of Theoretical Physics, University of Amsterdam, Amsterdam, The Netherlands

    • Daniel Baumann
    •  & Benjamin Wallisch
  2. Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth, UK

    • Florian Beutler
  3. Lawrence Berkeley National Laboratory, Berkeley, CA, USA

    • Florian Beutler
    •  & Christophe Yèche
  4. Department of Physics, University of California, San Diego, La Jolla, CA, USA

    • Raphael Flauger
    •  & Daniel Green
  5. Physics Department, Brookhaven National Laboratory, Upton, NY, USA

    • Anže Slosar
  6. Instituto de Física, Universidad Nacional Autónoma de México, Mexico City, Mexico

    • Mariana Vargas-Magaña
  7. DAMTP, University of Cambridge, Cambridge, UK

    • Benjamin Wallisch
  8. IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette, France

    • Christophe Yèche


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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.

Competing interests

The authors declare no competing interests.

Corresponding author

Correspondence to Daniel Green.

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