The isocurvature fraction after WMAP 3-year data

TL;DR

The paper investigates whether cosmological perturbations are strictly adiabatic or contain an isocurvature component by using a minimal extension to the adiabatic model: a single, totally correlated isocurvature mode with a shared spectral index $n_s$. It employs Bayesian parameter estimation and model selection, using the Savage-Dickey density ratio to compare the base model $M_0$ against extended models $I_x$ that include an isocurvature fraction $f_x$. The analysis finds posterior bounds $f_{ci} o [-0.10,0.06]$, $f_{ne} o [-0.20,0.12]$, and $f_{nv} o [-0.18,0.22]$, with the data disfavoring large isocurvature content and showing that subdominant isocurvature ($\sim$10–20%) is not ruled out. Overall, purely adiabatic initial conditions are strongly favored, though the conclusions depend on prior choices; stronger data would be needed to decisively detect subdominant isocurvature components. The work underscores the role of Occam's razor in cosmological model selection and provides a framework for evaluating more complex isocurvature scenarios.

Abstract

I revisit the question of the adiabaticity of initial conditions for cosmological perturbations in view of the 3-year WMAP data. I focus on the simplest alternative to pure adiabatic conditions, namely a superposition of the adiabatic mode and one of the 3 possible isocurvature modes, with the same spectral index as the adiabatic component. I discuss findings in terms of posterior bounds on the isocurvature fraction and Bayesian model selection. The Bayes factor (models likelihood ratio) and the effective Bayesian complexity are computed for several prior ranges for the isocurvature content. I find that the CDM isocurvature fraction is now constrained to be less than about 10%, while the fraction in either the neutrino entropy or velocity mode is below about 20%. Model comparison strongly disfavours mixed models that allow for isocurvature fractions larger than unity, while current data do not allow to distinguish between a purely adiabatic model and models with a moderate (ie, below about 10%) isocurvature contribution. The conclusion is that purely adiabatic conditions are strongly favoured from a model selection perspective. This is expected to apply in even stronger terms to more complicated superpositions of isocurvature contributions.

Figures (2)

• Figure 1: Normalized posterior probability density for the isocurvature fraction parameter $f_x$. CMB and large scale structure data are compatible with purely adiabatic initial conditions, with a slight tendency towards negatively correlated isocurvature components.
• Figure 2: Result of model selection between a purely adiabatic model and an extended model featuring a totally (anti--)correlated isocurvature component, as a function of the prior available range for the isocurvature fraction, $\Delta f$. Top panel: the Bayes factor strongly disfavours models with $\Delta f \gg 1$ because of the Occam's razor effect, while models predicting an isocurvature fraction below about $10\%$ in any of the three modes cannot presently be ruled out ($\ln B < 1$). The dotted line gives the Gaussian approximation to the Bayes factor, Eq. \ref{['eq:Gauss']}, for the CDM isocurvature mode. Bottom panel: the Bayesian complexity gives the effective number of parameters the data can support. For $\Delta f \,\hbox{$<$}\hbox{$\sim$}\, 1$ the isocurvature component in the neutrino entropy and velocity modes is not supported by the data. The errors have been computed as the variance of 10 random sub--chains, and the neutrino entropy and velocity modes have been shifted horizontally to the left and to the right, respectively, for clarity.