Correlated mixtures of adiabatic and isocurvature cosmological perturbations

TL;DR

The paper studies totally correlated mixtures of adiabatic and isocurvature cosmological perturbations and introduces four elementary hybrid modes, each with two primitive parameters, to assess their impact on CMB and LSS. It combines analytic long-wavelength theory with numerical Boltzmann computations for a scale-invariant primordial spectrum, revealing that correlation can either enhance or suppress the first acoustic peak relative to the Sachs-Wolfe plateau and can shift peak positions depending on the affected species. The results show that correlated hybrids exhibit rich phenomenology through the interplay of Sachs-Wolfe, ISW, and Doppler terms, and that constraining such modes requires combining adiabatic and isocurvature spectra rather than treating them as independent. While current data are not yet decisive, the framework provides a path for future Planck-era constraints on correlated adiabatic/isocurvature components via multi-spectrum analyses.

Abstract

We examine the consequences of the existence of correlated mixtures of adiabatic and isocurvature perturbations on the CMB and large scale structure. In particular, we consider the four types of ``elementary'' totally correlated hybrid initial conditions, where only one of the four matter species (photons, baryons, neutrinos, CDM) deviates from adiabaticity. We then study the height and position of the acoustic peaks with respect to the large angular scale plateau as a function of the isocurvature to adiabatic ratio.

Figures (16)

• Figure 1: CMB anisotropies in the pure adiabatic model ($\lambda = 0$). The solid line represents the total (scalar) contribution. The Sachs-Wolfe, Doppler and Integrated Sachs-Wolfe contributions are respectively represented in long-dashed, short-dashed, and dotted lines. At large angular scales (low $\ell$), the total amplitude is essentially due to the Sachs-Wolfe contribution.
• Figure 2: CMB anisotropies in the pure isocurvature CDM model ($\lambda = \pm\infty$). The solid line represent the total scalar contribution. The Sachs-Wolfe (SW), Doppler and Integrated Sachs-Wolfe contributions are respectively represented in long-dashed, short-dashed, and dotted lines. Note that the power at large scales (low $\ell$) is higher than at the degree-scale.
• Figure 3: CMB anisotropies in CDM-type correlated hybrid models for various values of the parameter $\lambda$. The highest curve is studied in more details in Fig. \ref{['fig_dop']}, the dotted curve represents the (standard) adiabatic case, and the lowest represents the pure isocurvature case shown in Fig. \ref{['fig_iso']}. Note that the height of the acoustic peaks with respect to the Sachs-Wolfe plateau varies with $\lambda$, according to eq. (\ref{['root_lambda']}).
• Figure 4: CMB anisotropies in CDM-type correlated hybrid models for various values of the parameter $\lambda$. The two highest curves are studied in more details in Figs. \ref{['fig_isw']} and \ref{['fig_dop']}.
• Figure 5: CMB anisotropies in CDM-type correlated hybrid models for large (positive) values of the parameter $\lambda$. The solid curve represents the pure isocurvature case of Fig. \ref{['fig_iso']}. Note that the height of the acoustic peaks with respect to the Sachs-Wolfe plateau varies slowly in this range of values for $\lambda$.