Full-sky lensing reconstruction of gradient and curl modes from CMB maps

TL;DR

This paper introduces a full-sky lensing reconstruction method that separately estimates gradient and curl modes from CMB maps, enabling detection of vector and tensor perturbations and improving systematics checks.

Contribution

It extends the optimal quadratic estimator to include curl modes, allowing separate reconstruction and analysis of vector and tensor sources in CMB lensing.

Findings

Gradient and curl modes can be reconstructed separately due to parity symmetry.

Estimated signal-to-noise ratios for primordial gravitational waves and cosmic strings.

Comparison with flat-sky estimator shows advantages of the new formalism.

Abstract

We present a method of lensing reconstruction on the full sky, by extending the optimal quadratic estimator proposed by Okamoto & Hu (2003) to the case including the curl mode of deflection angle. The curl mode is induced by the vector and tensor metric perturbations, and the reconstruction of the curl mode would be a powerful tool to not only check systematics in the estimated gradient mode but also probe any vector and tensor sources. We find that the gradient and curl modes can be reconstructed separately, thanks to the distinctive feature in the parity symmetry between the gradient and curl modes. We compare our estimator with the flat-sky estimator proposed by Cooray et al (2005). Based on the new formalism, the expected signal-to-noise ratio of the curl mode produced by the primordial gravitational-waves and a specific model of cosmic strings are estimated, and prospects for future observations are discussed.