Observational constraints on the curvaton model of inflation

TL;DR

The paper assesses observational constraints on curvaton models that yield correlated adiabatic and isocurvature perturbations. It derives a simple analytic large-scale CMB relation for mixed perturbations and performs a numerical analysis with WMAP, ACBAR, 2dF, HST, and nucleosynthesis data using CosmoMC. The key finding is that isocurvature contributions are not favored relative to purely adiabatic models, though a significant correlated baryon isocurvature component cannot be ruled out, and several curvaton-decay scenarios are strongly constrained or ruled out. The work connects decay history to non-Gaussianity, finding that some scenarios could yield Planck-detectable $f_{NL}$, thus enabling discrimination among competing curvaton realizations.

Abstract

Simple curvaton models can generate a mixture of of correlated primordial adiabatic and isocurvature perturbations. The baryon and cold dark matter isocurvature modes differ only by an observationally null mode in which the two perturbations almost exactly compensate, and therefore have proportional effects at linear order. We discuss the CMB anisotropy in general mixed models, and give a simple approximate analytic result for the large scale CMB anisotropy. Working numerically we use the latest WMAP observations and a variety of other data to constrain the curvaton model. We find that models with an isocurvature contribution are not favored relative to simple purely adiabatic models. However a significant primordial totally correlated baryon isocurvature perturbation is not ruled out. Certain classes of curvaton model are thereby ruled out, other classes predict enough non-Gaussianity to be detectable by the Planck satellite. In the appendices we review the relevant equations in the covariant formulation and give series solutions for the radiation dominated era.

Figures (4)

• Figure 1: Posterior marginalized probability distributions (solid lines) of the cosmological parameters including correlated matter isocurvature modes, using the data described in the text. $B$ is the ratio of the (effective) baryon isocurvature to adiabatic perturbation amplitude in the primordial era, $\hbox{$\Omega_{b}$} h^2$ and $\hbox{$\Omega_{c}$} h^2$ are the physical matter densities in baryons and CDM, $H_0 ~\text{km}~\text{s}^{-1} \text{Mpc}^{-1}$ is the Hubble parameter today, $z_{\text{re}}$ is the effective reionization redshift, and $n_s$ is the spectral index. We assume a flat universe with cosmological constant. Dotted lines show the mean likelihoods of the samples, and agree well with the marginalized curves, indicating the full distribution is fairly Gaussian and unskewed Lewis02.
• Figure 2: Posterior distribution of $B = \hbox{$\cal S$}^{\text{eff}}_{{b}}/\zeta$ in the primordial era, and the spectral index $n_s$. The plot is generated from a smoothed number density of Monte Carlo samples generated using the data described in the text. The contours enclose $68\%$ and $95\%$ of the probability, and the shading is by the mean likelihood of the samples.
• Figure 3: Plots of the un-normalized posterior probability distribution for $r \approx \rho_{\rm curvaton}/ \rho_{\rm total}$ when the curvaton decays. The distributions are for the numbered scenarios described in the text: (4) CDM created by curvaton decay and baryon number after curvaton decay (green long dashes), (5) baryon number created by curvaton decay and CDM after curvaton decay (cyan dash-dot line), (7) both CDM and baryon number created by curvaton decay (black solid line), (8) CDM created before curvaton decay and baryon number by curvaton decay (blue dotted line), (9) baryon number created before curvaton decay and CDM by curvaton decay (red short dashed line).
• Figure 4: Plots of the un-normalized posterior probability distribution for the amount of non-Gaussianity, $f_{nl}$. The line styles are the same as in Fig. \ref{['r']}.