# ForecastCompIsocurv

We forecast constraints on the variance of the amplitude of compensated isocurvature perturbations based on the second order effect on the CMB power spectrum. Details can be found here: http://arxiv.org/pdf/1511.04441v2.pdf

Brief overview:

We parametrize the effect of a sky-varying CIP as $\Omega_b =\bar \Omega_b [1+\Delta (\hat n)] \quad$ $\Omega_c = \bar \Omega_c - \bar \Omega_b \Delta(\hat n)$

We expand the amplitude of the compensated isocurvature perturbations in spherical harmonics as $\Delta(\hat n) = \sum_{LM} Y_L^M(\hat n) \Delta_{LM}$, and the CIP angular power spectrum is given by $\langle{\Delta_{LM}\Delta_{L'M'}^{*}}\rangle = \delta_{LL'} \delta_{MM'} C_L^\Delta$

Our constraints are on the variance of the CIP amplitude, $\Delta^2_{\rm rms}\equiv \langle{\Delta^2}\rangle$, which can be expressed in terms of the CIP power spectrum as $\Delta^2_{\rm rms} = \sum_{L=1}^{L_{\rm max}} \dfrac{(2L+1)}{4\pi} C_L^\Delta$

The observable signature is the second order effect on the CMB power spectrum $C_\ell^{\rm obs} \approx C_\ell|_{\Delta = 0} + \frac{1}{2} \frac{d^2 C_\ell}{d \Delta^2} \Delta^2_{\rm rms}$

Results:

Using Planck, our best constraint is: $\Delta_{\rm rms}^2\leq 5.0\times 10^{-3}$

With S4, we can reach up to an order of magnitude improvement:

- S4 forecast as a function of sensitivity and beam size: File:S4CIPsNoise.pdf

- S4 forecast as a function of the sky coverage: File:S4CIPsfsky.pdf