Scalar Quadratic Maximum-likelihood Estimators for the CMB Cross-power Spectrum

Estimating the cross-correlation power spectra of cosmic microwave background (CMB), in particular, T B and EB spectra, is important for testing parity symmetry cosmology diagnosing insidious instruments systematics. The Quadratic Maximum Likelihood (QML) estimator provides optimal estimates but it computationally very expensive. hybrid pseudo-Cl fast performs poorly on large scales. As a natural extension previous work (Chen et al. 2021), this article, we present new unbiased based Smith-Zaldarriaga (SZ) approach E-B separation scalar QML to reconstruct spectrum, called QML-SZ estimator. Our relies ability construct maps, which allows us use obtain spectrum. By reducing pixel number algorithm complexity, computational cost nearly one order magnitude smaller running time two orders faster test situations.