# Improving Small-Scale CMB Lensing Reconstruction

## TL;DR

This paper introduces a new, more optimal method for small-scale CMB lensing reconstruction called Gradient-Inversion, which outperforms traditional quadratic estimators in simulations, promising enhanced cosmological insights.

## Contribution

The paper develops and validates a novel Gradient-Inversion method for small-scale CMB lensing reconstruction, improving accuracy over quadratic estimators in idealized simulations.

## Key findings

- Reduces errors on lensing auto-power spectrum by a factor of ~4 at L=5000-9000.
- Achieves a factor of ~2.6 improvement in cross-correlation errors.
- Demonstrates potential for more precise small-scale CMB lensing measurements.

## Abstract

Over the past decade, the gravitational lensing of the Cosmic Microwave Background (CMB) has become a powerful tool for probing the matter distribution in the Universe. The standard technique used to reconstruct the CMB lensing signal employs the quadratic estimator (QE) method, which has recently been shown to be suboptimal for lensing measurements on very small scales in temperature and polarization data. We implement a simple, more optimal method for the small-scale regime, which involves taking the direct inverse of the background gradient. We derive new techniques to make continuous maps of lensing using this "Gradient-Inversion" (GI) method and validate our method with simulated data, finding good agreement with predictions. For idealized simulations of lensing cross- and autospectra that neglect foregrounds, we demonstrate that our method performs significantly better than previous quadratic estimator methods in temperature; at $L=5000-9000$, it reduces errors on the lensing auto-power spectrum by a factor of $\sim 4$ for both idealized CMB-S4 and Simons Observatory-like experiments and by a factor of $\sim 2.6$ for cross-correlations of CMB-S4-like lensing reconstruction and the true lensing field. We caution that the level of the neglected small-scale foreground power, while low in polarization, is very high in temperature; though we briefly outline foreground mitigation methods, further work on this topic is required. Nevertheless, our results show the future potential for improved small-scale CMB lensing measurements, which could provide stronger constraints on cosmological parameters and astrophysics at high redshifts.