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(Lack of) Cosmological evidence for dark radiation after Planck

Licia Verde, Stephen M. Feeney, Daniel J. Mortlock, Hiranya V. Peiris

TL;DR

The paper tackles whether Planck-era cosmological data necessitate extensions to neutrino physics beyond ΛCDM, by examining $N_{ m eff}$ and $M_ u$ with Bayesian model comparison. It combines Bayes factors, the Savage–Dickey Density Ratio, and the Profile Likelihood Ratio to compare nested models against ΛCDM, using Planck temperature data (Planck), WP polarization, CMB lensing, and external datasets (BAO, $H_0$, SN). The main finding is that there is no Bayesian evidence favoring increased $N_{ m eff}$ or non-zero $M_ u$; ΛCDM with $N_{ m eff}=3.046$ remains favored across most data combinations, with only mild exceptions when specific tensions (notably in $H_0$) are included. The prior-independent PLR results corroborate the evidence, and the work highlights that while neutrinos are known to be massive, their cosmological imprint is too small to detect with current data; future polarization measurements are anticipated to tighten these constraints further.

Abstract

We use Bayesian model comparison to determine whether extensions to Standard-Model neutrino physics -- primarily additional effective numbers of neutrinos and/or massive neutrinos -- are merited by the latest cosmological data. Given the significant advances in cosmic microwave background (CMB) observations represented by the Planck data, we examine whether Planck temperature and CMB lensing data, in combination with lower redshift data, have strengthened (or weakened) the previous findings. We conclude that the state-of-the-art cosmological data do not show evidence for deviations from the standard cosmological model (which has three massless neutrino families). This does not mean that the model is necessarily correct -- in fact we know it is incomplete as neutrinos are not massless -- but it does imply that deviations from the standard model (e.g., non-zero neutrino mass) are too small compared to the current experimental uncertainties to be inferred from cosmological data alone.

(Lack of) Cosmological evidence for dark radiation after Planck

TL;DR

The paper tackles whether Planck-era cosmological data necessitate extensions to neutrino physics beyond ΛCDM, by examining and with Bayesian model comparison. It combines Bayes factors, the Savage–Dickey Density Ratio, and the Profile Likelihood Ratio to compare nested models against ΛCDM, using Planck temperature data (Planck), WP polarization, CMB lensing, and external datasets (BAO, , SN). The main finding is that there is no Bayesian evidence favoring increased or non-zero ; ΛCDM with remains favored across most data combinations, with only mild exceptions when specific tensions (notably in ) are included. The prior-independent PLR results corroborate the evidence, and the work highlights that while neutrinos are known to be massive, their cosmological imprint is too small to detect with current data; future polarization measurements are anticipated to tighten these constraints further.

Abstract

We use Bayesian model comparison to determine whether extensions to Standard-Model neutrino physics -- primarily additional effective numbers of neutrinos and/or massive neutrinos -- are merited by the latest cosmological data. Given the significant advances in cosmic microwave background (CMB) observations represented by the Planck data, we examine whether Planck temperature and CMB lensing data, in combination with lower redshift data, have strengthened (or weakened) the previous findings. We conclude that the state-of-the-art cosmological data do not show evidence for deviations from the standard cosmological model (which has three massless neutrino families). This does not mean that the model is necessarily correct -- in fact we know it is incomplete as neutrinos are not massless -- but it does imply that deviations from the standard model (e.g., non-zero neutrino mass) are too small compared to the current experimental uncertainties to be inferred from cosmological data alone.

Paper Structure

This paper contains 11 sections, 11 equations, 2 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Methods and datasets
  3. Bayes factor
  4. Savage-Dickey Density Ratio
  5. Profile likelihood ratio
  6. Data
  7. Results
  8. Evidence
  9. Profile likelihood ratios and comparison with Evidence
  10. Exploring degeneracies with other interesting parameters: the case of $n_s$
  11. Conclusions and future avenues

Figures (2)

  • Figure 1: Summary of the Evidence ratios for the models discussed in the text for selected dataset combinations. The Evidence for the simplest model ($\Lambda$CDM) is substantial to strong, except when the "discrepant" $H_0$ measurement is added. In this case there is still no evidence to favor the more-complex $\Lambda$CDM+$N_{\rm eff}$ model.
  • Figure 2: Profile likelihood ratio for the Planck "Gold" set alone and combined with BAO, $H_0$ and lensing data. The error bars for the Gold and Gold+lensing sets are computed using the corresponding $\Lambda$CDM chain as described in the main text; errors must be estimated for the other two plots as $\Lambda$CDM chains are not available. The dot-dashed vertical lines show the standard $N_{\rm eff}$ value of 3.046.