Constraints on isocurvature models from the WMAP first-year data

TL;DR

This paper tests whether correlated isocurvature perturbations can coexist with adiabatic fluctuations in a flat $\Lambda$CDM universe by performing a comprehensive MCMC analysis over 4 primordial modes (AD, CI, NID, NIV) including their cross-correlations, using the WMAP first-year data extended with small-scale CMB measurements and the 2dFGRS power spectrum. It finds that with a single isocurvature mode, the allowed non-adiabatic contribution is modest ($f_{\mathrm{ISO}}\sim 0.1$–$0.15$), but permitting two or all three modes substantially relaxes the constraint ($f_{\mathrm{ISO}}$ up to $\sim 0.6$ in some cases), due to constructive/destructive interference and degeneracies among parameters. The results show pronounced degeneracies, with large isocurvature fractions achievable without a statistically significant improvement in fit, and they depend sensitively on priors and the mode-parameterization used. Overall, current data do not require isocurvature components, but they do admit substantial correlated isocurvature admixtures within a degenerate parameter space, highlighting the need for careful prior choices in cosmological inference from CMB and LSS observations.

Abstract

We investigate the constraints imposed by the first-year WMAP CMB data extended to higher multipole by data from ACBAR, BOOMERANG, CBI and the VSA and by the LSS data from the 2dF galaxy redshift survey on the possible amplitude of primordial isocurvature modes. A flat universe with CDM and Lambda is assumed, and the baryon, CDM (CI), and neutrino density (NID) and velocity (NIV) isocurvature modes are considered. Constraints on the allowed isocurvature contributions are established from the data for various combinations of the adiabatic mode and one, two, and three isocurvature modes, with intermode cross-correlations allowed. Since baryon and CDM isocurvature are observationally virtually indistinguishable, these modes are not considered separately. We find that when just a single isocurvature mode is added, the present data allows an isocurvature fraction as large as 13+-6, 7+-4, and 13+-7 percent for adiabatic plus the CI, NID, and NIV modes, respectively. When two isocurvature modes plus the adiabatic mode and cross-correlations are allowed, these percentages rise to 47+-16, 34+-12, and 44+-12 for the combinations CI+NID, CI+NIV, and NID+NIV, respectively. Finally, when all three isocurvature modes and cross-correlations are allowed, the admissible isocurvature fraction rises to 57+-9 per cent. The sensitivity of the results to the choice of prior probability distribution is examined.

Figures (24)

• Figure 1: Shape of prior distribution for the observables $z_{\langle \hbox{\scriptsizeI,I} \rangle}$ and $z_{\langle \hbox{\scriptsizeI,J} \rangle}.$ Our prior distribution of matrices subject to the constraint that $tr(zz^T)=1$ and that $z_{\langle \hbox{\scriptsizeI,J} \rangle}$ have only positive eigenvalues, in the absence of data, would give these posterior distributions for the fractional auto-correlations $z_{\langle \hbox{\scriptsizeI,I} \rangle}$ (dashed) and cross-correlations $z_{\langle \hbox{\scriptsizeI,J} \rangle}$ (dot-dashed) for $N=4$. The solid curve shows the distribution for $z_{\langle \hbox{\scriptsizeI,I} \rangle}$ that would result if the positive definiteness requirement were suppressed.
• Figure 2: Pure adiabatic model. Posterior distributions for the cosmological parameters using CMB data (dot-dashed) and CMB+LSS data (dashed).
• Figure 3: Adiabatic plus CI. We indicate the marginalized posterior distributions of the various parameters for the adiabatic (AD) and CDM isocurvature (CI) mixed models with correlations allowed (solid) using CMB+LSS, with the result for the pure adiabatic model (dashed) included for comparison. $\langle \hbox{\scriptsizeI,J} \rangle$ denotes $z_{\langle \hbox{\scriptsizeI,J} \rangle}$.
• Figure 4: Adiabatic plus NID. Distributions as described in Fig. \ref{['hist_ci']}, for correlated adiabatic and neutrino density isocurvature models.
• Figure 5: Adiabatic plus NIV. Distributions as described in Fig. \ref{['hist_ci']}, for correlated adiabatic and neutrino velocity isocurvature models.