Gauge-invariant treatment of the integrated Sachs-Wolfe effect on general spherically symmetric spacetimes

TL;DR

This paper derives a gauge-invariant formula for the integrated Sachs-Wolfe effect in general spherically symmetric spacetimes, aiding the comparison of theoretical models with observations, especially in Lemaitre-Tolman-Bondi cosmologies.

Contribution

It introduces a novel gauge-invariant approach to analyze the integrated Sachs-Wolfe effect in spherically symmetric spacetimes, extending previous methods.

Findings

Formula applicable to Lemaitre-Tolman-Bondi models

Facilitates comparison between theory and observations

Enhances understanding of cosmic acceleration without cosmological constant

Abstract

On the basis of the Gerlach-Sengupta theory of gauge-invariant perturbations, a formula of the integrated Sachs-Wolfe effect for a central observer is derived on general spherically symmetric spacetimes. It will be useful for comparative studies of theoretical and observational aspects of the integrated Sachs-Wolfe effect in the Lemaitre-Tolman-Bondi cosmological models which have been noticed by explaining the apparent acceleration without cosmological constant.