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WMAP, neutrino degeneracy and non-Gaussianity constraints on isocurvature perturbations in the curvaton model of inflation

Christopher Gordon, Karim A. Malik

TL;DR

This work investigates neutrino degeneracy, $\xi$, within the curvaton model of inflation, showing that nonzero $\xi$ generates neutrino, baryon, and CDM isocurvature perturbations whose amplitude is constrained by WMAP, large-scale structure, and BBN data. The authors derive analytic expressions for the curvaton-induced isocurvature perturbations, connect them to the Sachs-Wolfe effect on large scales, and relate the non-Gaussianity parameter $f_{\rm nl}$ to the curvaton transfer parameter $r$. Using CAMB/COSMOMC with extensive cosmological datasets and a BBN prior on $\xi$, they find that BBN constraints dominate and that neutrino isocurvature is typically subdominant (a few percent or less of the adiabatic mode), with significant model-specific degeneracies between $\xi$ and $r. The results imply that, unless lepton-number is created after curvaton decay, Planck-level data could enhance sensitivity to these isocurvature signatures, and very large negative $f_{\rm nl}$ would challenge the curvaton-decay scenario.

Abstract

In the curvaton model of inflation, where a second scalar field, the "curvaton", is responsible for the observed inhomogeneity, a non-zero neutrino degeneracy may lead to a characteristic pattern of isocurvature perturbations in the neutrino, cold dark matter and baryon components. We find the current data can only place upper limits on the level of isocurvature perturbations. These can be translated into upper limits on the neutrino degeneracy parameter. In the case that lepton number is created before curvaton decay, we find that the limit on the neutrino degeneracy parameter is comparable with that obtained from Big-bang nucleosynthesis. For the case that lepton number is created by curvaton decay we find that the absolute value of the non-Gaussianity parameter, |f_nl|, must be less than 10 (95% confidence interval).

WMAP, neutrino degeneracy and non-Gaussianity constraints on isocurvature perturbations in the curvaton model of inflation

TL;DR

This work investigates neutrino degeneracy, , within the curvaton model of inflation, showing that nonzero generates neutrino, baryon, and CDM isocurvature perturbations whose amplitude is constrained by WMAP, large-scale structure, and BBN data. The authors derive analytic expressions for the curvaton-induced isocurvature perturbations, connect them to the Sachs-Wolfe effect on large scales, and relate the non-Gaussianity parameter to the curvaton transfer parameter . Using CAMB/COSMOMC with extensive cosmological datasets and a BBN prior on , they find that BBN constraints dominate and that neutrino isocurvature is typically subdominant (a few percent or less of the adiabatic mode), with significant model-specific degeneracies between and f_{\rm nl}$ would challenge the curvaton-decay scenario.

Abstract

In the curvaton model of inflation, where a second scalar field, the "curvaton", is responsible for the observed inhomogeneity, a non-zero neutrino degeneracy may lead to a characteristic pattern of isocurvature perturbations in the neutrino, cold dark matter and baryon components. We find the current data can only place upper limits on the level of isocurvature perturbations. These can be translated into upper limits on the neutrino degeneracy parameter. In the case that lepton number is created before curvaton decay, we find that the limit on the neutrino degeneracy parameter is comparable with that obtained from Big-bang nucleosynthesis. For the case that lepton number is created by curvaton decay we find that the absolute value of the non-Gaussianity parameter, |f_nl|, must be less than 10 (95% confidence interval).

Paper Structure

This paper contains 5 sections, 39 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Curvaton generated neutrino isocurvature perturbations
  3. Neutrino Degeneracy Modifications of the Sachs-Wolfe effect
  4. Data Analysis
  5. Conclusions

Figures (3)

  • Figure 1: An illustration of the effect of the lepton degeneracy ($\xi$) on the spectrum of fluctuations. The cosmological parameters (including the amplitude) for all the spectra are taken from the maximum likelihood when $\xi=0$. The solid line is a plot of the pure adiabatic spectrum. The short dashed line is for the case when the lepton number is created before curvaton decay and $\xi=0.3$. The long dashed line is for the case when the lepton number is created by curvaton decay with $\xi=0.3$ and the fraction of the density made up by the curvaton at curvaton decay ($r$) is set to 0.5. The dotted line is the spectrum for when the lepton number is created after curvaton decay (so that there are no isocurvature modes) and $\xi=1$. The binned WMAP TT data is also plotted.
  • Figure 2: Comparison of marginalized probability distributions, using CMB, 2dF and HST data, for lepton degeneracy ($\xi$) when lepton number is created by curvaton decay (short-dashes), for lepton number created after curvaton decay (dotted) and for lepton number created before curvaton decay (long dashes). The BBN constraint on $\xi$ is also plotted (solid line).
  • Figure 3: One and two sigma contours for the 2D marginalized probability distribution, using CMB, 2dF and HST data, of the lepton degeneracy ($\xi$) and the curvaton density proportion at time of curvaton decay ($r$) for the case when lepton number is created by curvaton decay.