Lensing Bias to CMB Polarization Measurements of Compensated Isocurvature Perturbations

TL;DR

This paper investigates how gravitational lensing biases affect the detection of compensated isocurvature perturbations (CIPs) in the CMB, showing that lensing increases noise and impacts measurement sensitivity.

Contribution

It identifies and quantifies lensing-induced biases in CMB polarization measurements of CIPs, providing correction methods and assessing detection prospects.

Findings

Lensing triples the noise power of CIP estimators on large scales.

Lensing-ISW and reionization-lensing correlations contaminate cross power measurements.

Detection threshold for CIPs increases by 50% due to lensing effects.

Abstract

Compensated isocurvature perturbations are opposite spatial fluctuations in the baryon and dark matter (DM) densities. They arise in the curvaton model and some models of baryogenesis. While the gravitational effects of baryon fluctuations are compensated by those of DM, leaving no observable impacts on the cosmic microwave background (CMB) at first order, they modulate the sound horizon at recombination, thereby correlating CMB anisotropies at different multipoles. As a result, CIPs can be reconstructed using quadratic estimators similarly to CMB detection of gravitational lensing. Because of these similarities, however, the CIP estimators are biased with lensing contributions that must be subtracted. These lensing contributions for CMB polarization measurement of CIPs are found to roughly triple the noise power of the total CIP estimator on large scales. In addition, the cross power with temperature and $E$-mode polarization are contaminated by lensing-ISW (integrated Sachs-Wolfe) correlations and reionization-lensing correlations respectively. For a cosmic-variance-limited (CVL) temperature and polarization experiment measuring out to multipoles $l_{\max} = 2500$, the lensing noise raises the detection threshold by a factor of 1.5, leaving a $2.7\sigma$ detection possible for the maximal CIP signal in the curvaton model.