Constraining Isocurvature Perturbations with CMB Polarization

TL;DR

The role of cosmic microwave background polarization data in constraining the presence of primordial isocurvature modes is examined and a comparably sensitive polarization measurement on the same angular scales will permit a determination of the curvature without the prior assumption of adiabaticity.

Abstract

The role of cosmic microwave background (CMB) polarisation data in constraining the presence of primordial isocurvature modes is examined. While the MAP satellite mission will be unable to simultaneously constrain isocurvature modes and cosmological parameters, the PLANCK mission will be able to set strong limits on the presence of isocurvature modes if it makes a precise measurement of the CMB polarisation sky. We find that if we allow for the possible presence of isocurvature modes, the recently obtained BOOMERANG measurement of the curvature of the universe fails. However, a comparably sensitive polarisation measurement on the same angular scales will permit a determination of the curvature of the universe without the prior assumption of adiabaticity.

Figures (4)

• Figure 1: CMB multipole spectra for the various modes, their cross-correlations, variations in the cosmological parameters. From top to bottom the rows show $l(l+1)C_l/2\pi$ for the temperature, polarization, and temperature-polarization cross correlation, respectively, in $\mu K.$ The $C_l$ spectra for the various modes and their cross correlations are shown in the first two columns. The rightmost column shows the derivatives of the spectra with respect to the different cosmological parameters. The modes are indicated as follows: adiabatic (AD), neutrino isocurvature velocity (NIV), baryon isocurvature (BI), and neutrino isocurvature density (NID). A fiducial model with the parameter choices $\Omega_b=0.06,~\Omega_\Lambda=0.69, ~\Omega_{cdm}=0.25,~h=0.65,~\tau_{reion} =0.1$ and $n_s=1$ has been assumed. Because the CDM isocurvature mode produces a spectrum nearly identical to that of the BI mode, it is not considered separately.
• Figure 2: Breaking the degeneracies with polarization. The top panel indicates the delicate cancellation in the temperature power spectrum between the various components of the most uncertain principal direction. The lower panels show how this cancellation is broken in the polarization and temperature-polarization cross-correlation spectra.
• Figure 3: When only temperature information from PLANCK is taken into account, the uncertainties in the four most poorly measured principal directions are 239%, 60%, 36%, and 23%. These numbers are the inverse square root of the corresponding eigenvalues of the Fisher matrix. When the polarization information anticipated from PLANCK is taken into account as well, these uncertainties are reduced to 11.1%, 10.3%, 6.6%, and 4.6%, respectively. The plots (from top to bottom, respectively) indicate the contributions of the polarisation information at each $l$ to diagonal elements of the Fisher matrix in these directions. The cross correlation contribution is by definition the difference between the total and that obtained from polarisation and temperature information taken separately.
• Figure 4: Polarisation signal of the various modes on large angular scales ($l \hbox{$\sim$} \hbox{$<$} 100$). Measurements on these scales are largely responsible for the degeneracy breaking which polarisation measurements allow.