# A tale of two modes: neutrino free-streaming in the early universe

## Abstract

We present updated constraints on the free-streaming nature of cosmological neutrinos from cosmic microwave background (CMB) temperature and polarization power spectra, baryonic acoustic oscillation data, and distance ladder measurements of the Hubble constant. Specifically, we consider a Fermi-like four-fermion interaction between massless neutrinos, characterized by an effective coupling constant G {sub eff}, and resulting in a neutrino opacity τ-dot {sub ν∝} G {sub eff}{sup 2} T {sub ν}{sup 5}. Using a conservative flat prior on the parameter log{sub 10}( G {sub eff} MeV{sup 2}), we find a bimodal posterior distribution with two clearly separated regions of high probability. The first of these modes is consistent with the standard ΛCDM cosmology and corresponds to neutrinos decoupling at redshift z {sub ν,dec} > 1.3×10{sup 5}, that is before the Fourier modes probed by the CMB damping tail enter the causal horizon. The other mode of the posterior, dubbed the 'interacting neutrino mode', corresponds to neutrino decoupling occurring within a narrow redshift window centered around z {sub ν,dec}∼8300. This mode is characterized by a high value of the effective neutrino coupling constant, log{sub 10}( G {sub eff} MeV{sup 2}) = −1.72 ± 0.10 (68% C.L.), together with a lower value of the scalarmore »

- Authors:

- McWilliams Center for Cosmology, Department of Physics, Carnegie Mellon University, 5000 Forbes Ave., Pittsburgh, PA 15213 (United States)
- Department of Physics, Harvard University, 17 Oxford St., Cambridge, MA 02138 (United States)
- Physics Department, University of California, Davis, CA 95616 (United States)

- Publication Date:

- OSTI Identifier:
- 22676093

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2017; Journal Issue: 07; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; AMPLITUDES; BARYONS; COMPARATIVE EVALUATIONS; COSMOLOGY; COUPLING CONSTANTS; DECOUPLING; DISTANCE; DISTRIBUTION; FERMI INTERACTIONS; FLUCTUATIONS; MAXIMUM-LIKELIHOOD FIT; MEV RANGE; NEUTRINOS; OPACITY; OSCILLATIONS; POLARIZATION; RED SHIFT; RELICT RADIATION; SPECTRA; UNIVERSE

### Citation Formats

```
Lancaster, Lachlan, Cyr-Racine, Francis-Yan, Knox, Lloyd, and Pan, Zhen, E-mail: lachlanl@princeton.edu, E-mail: fcyrraci@physics.harvard.edu, E-mail: lknox@ucdavis.edu, E-mail: zhpan@ucdavis.edu.
```*A tale of two modes: neutrino free-streaming in the early universe*. United States: N. p., 2017.
Web. doi:10.1088/1475-7516/2017/07/033.

```
Lancaster, Lachlan, Cyr-Racine, Francis-Yan, Knox, Lloyd, & Pan, Zhen, E-mail: lachlanl@princeton.edu, E-mail: fcyrraci@physics.harvard.edu, E-mail: lknox@ucdavis.edu, E-mail: zhpan@ucdavis.edu.
```*A tale of two modes: neutrino free-streaming in the early universe*. United States. doi:10.1088/1475-7516/2017/07/033.

```
Lancaster, Lachlan, Cyr-Racine, Francis-Yan, Knox, Lloyd, and Pan, Zhen, E-mail: lachlanl@princeton.edu, E-mail: fcyrraci@physics.harvard.edu, E-mail: lknox@ucdavis.edu, E-mail: zhpan@ucdavis.edu. Sat .
"A tale of two modes: neutrino free-streaming in the early universe". United States.
doi:10.1088/1475-7516/2017/07/033.
```

```
@article{osti_22676093,
```

title = {A tale of two modes: neutrino free-streaming in the early universe},

author = {Lancaster, Lachlan and Cyr-Racine, Francis-Yan and Knox, Lloyd and Pan, Zhen, E-mail: lachlanl@princeton.edu, E-mail: fcyrraci@physics.harvard.edu, E-mail: lknox@ucdavis.edu, E-mail: zhpan@ucdavis.edu},

abstractNote = {We present updated constraints on the free-streaming nature of cosmological neutrinos from cosmic microwave background (CMB) temperature and polarization power spectra, baryonic acoustic oscillation data, and distance ladder measurements of the Hubble constant. Specifically, we consider a Fermi-like four-fermion interaction between massless neutrinos, characterized by an effective coupling constant G {sub eff}, and resulting in a neutrino opacity τ-dot {sub ν∝} G {sub eff}{sup 2} T {sub ν}{sup 5}. Using a conservative flat prior on the parameter log{sub 10}( G {sub eff} MeV{sup 2}), we find a bimodal posterior distribution with two clearly separated regions of high probability. The first of these modes is consistent with the standard ΛCDM cosmology and corresponds to neutrinos decoupling at redshift z {sub ν,dec} > 1.3×10{sup 5}, that is before the Fourier modes probed by the CMB damping tail enter the causal horizon. The other mode of the posterior, dubbed the 'interacting neutrino mode', corresponds to neutrino decoupling occurring within a narrow redshift window centered around z {sub ν,dec}∼8300. This mode is characterized by a high value of the effective neutrino coupling constant, log{sub 10}( G {sub eff} MeV{sup 2}) = −1.72 ± 0.10 (68% C.L.), together with a lower value of the scalar spectral index and amplitude of fluctuations, and a higher value of the Hubble parameter. Using both a maximum likelihood analysis and the ratio of the two mode's Bayesian evidence, we find the interacting neutrino mode to be statistically disfavored compared to the standard ΛCDM cosmology, and determine this result to be largely driven by the low- l CMB temperature data. Interestingly, the addition of CMB polarization and direct Hubble constant measurements significantly raises the statistical significance of this secondary mode, indicating that new physics in the neutrino sector could help explain the difference between local measurements of H {sub 0}, and those inferred from CMB data. A robust consequence of our results is that neutrinos must be free streaming long before the epoch of matter-radiation equality in order to fit current cosmological data.},

doi = {10.1088/1475-7516/2017/07/033},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 07,

volume = 2017,

place = {United States},

year = {Sat Jul 01 00:00:00 EDT 2017},

month = {Sat Jul 01 00:00:00 EDT 2017}

}