Reconstruction of the observable universe from the integrated Sachs-Wolfe effect

TL;DR

This paper explores reconstructing gravitational perturbations of the universe from the ISW effect in the CMB using a tomographic approach, demonstrating mathematical stability and numerical feasibility.

Contribution

It introduces a novel tomographic reconstruction method for gravitational perturbations from the ISW effect, with mathematical analysis and numerical validation.

Findings

Stable inversion of the X-ray transform in cosmology demonstrated

Numerical methods show feasibility of reconstructing gravitational perturbations

Potential for improved understanding of universe's structure from CMB data

Abstract

The integrated Sachs-Wolfe (ISW) effect is a property of the Cosmic Microwave Background (CMB), in which photons from the CMB are gravitationally redshifted, causing the anisotropies in the CMB. An intriguing question is whether one can infer the gravitational perturbations from the ISW effect observed near the Earth. In this work, we address the question using a tomographic reconstruction approach, similar to X-ray CT reconstruction in medical imaging. We develop the mathematical analysis for the stable inversion of the X-ray transform in the cosmological setting. In addition, we provide a numerical study of reconstruction methods, thereby demonstrating the feasibility and potential of the tomography method.