Do Baryons Trace Dark Matter in the Early Universe?

Baryon-density perturbations of large amplitude may exist if they are compensated by dark-matter perturbations such that the total density is unchanged. Primordial abundances and galaxy clusters allow these compensated isocurvature perturbations (CIPs) to have amplitudes as large as $\sim 10\%$. CIPs will modulate the power spectrum of cosmic microwave background (CMB) fluctuations—those due to the usual adiabatic perturbations—as a function of position on the sky. This leads to correlations between different spherical-harmonic coefficients of the temperature and/or polarization maps, and induces polarization $B$ modes. Here, the magnitude of these effects is calculated and techniques to measure them are introduced. While a CIP of this amplitude can be probed on large scales with existing data, forthcoming CMB experiments should improve the sensitivity to CIPs by at least an order of magnitude.

Figure 1

The $B$-mode power spectrum (in $\mu {\mathrm{K}}^2$) for the CIP-induced contribution from decoupling (solid black curve), contrasted with contributions from patchy scattering (short-dashed green curve), and patchy screening (dotted red curve) at reionization. We use a scale-invariant spectrum of CIPs with the amplitude $A\simeq 0.017$ that saturates the galaxy-cluster bound.

Figure 2

Shown are the errors in $C_L^{\Delta }$ from the $TT$, $TE$, $EE$, $TB$, and $EB$ estimators for the CIP perturbation $\Delta$ at the surface of last scatter for (a) WMAP and (b) a CMB polarization satellite, with the specifications spelled out in the EPIC mission concept study. Also shown (signal) is the power spectrum $C_L^{\Delta }$ for a scale-invariant spectrum of CIPs with the maximum amplitude allowed by galaxy clusters.

Figure 3

(a) Shown are the total expected errors in $C_L^{\Delta }$ from the combined $TT$, $TE$, $EE$, $TB$, and $EB$ estimators for the CIP perturbation $\Delta$ at the surface of last scatter for several current and forthcoming CMB experiments. Also shown (signal) is the power spectrum $C_L^{\Delta }$ for a scale-invariant spectrum of CIPs with the maximum amplitude allowed by galaxy clusters. (b) The signal-to-noise as a function of the rms fluctuation in the galaxy cluster baryon–to–dark-matter ratio along different lines of sight at $z\simeq 1091$. The vertical line shows the upper limit to the rms amplitude from galaxy clusters (excluded region is shaded).