Contributions to the nonlinear integrated Sachs-Wolfe effect: Birkinshaw-Gull effect and gravitational self-energy density

TL;DR

This paper analytically investigates the nonlinear integrated Sachs-Wolfe effect in a dark energy universe, identifying key contributions like the Birkinshaw-Gull effect and gravitational self-energy changes, providing theoretical insights into this subtle relativistic phenomenon.

Contribution

It introduces a purely analytical approach to distinguish two main contributions to the nonlinear iSW-effect, enhancing understanding of its theoretical underpinnings.

Findings

Shape and amplitude similar to previous work

Identified two distinct contributions: self-energy change and moving gravitational lenses

Provides insights into the relativistic nature of the nonlinear iSW-effect

Abstract

In this paper, we recompute contributions to the spectrum of the nonlinear integrated Sachs-Wolfe (iSW)/Rees-Sciama effect in a dark energy cosmology. Focusing on the moderate nonlinear regime, all dynamical fields involved are derived from the density contrast in Eulerian perturbation theory. Shape and amplitude of the resulting angular power spectrum are similar to that derived in previous work. With our purely analytical approach we identify two distinct contributions to the signal of the nonlinear iSW-effect: the change of the gravitational self-energy density of the large scale structure with (conformal) time and gravitational lenses moving with the large scale matter stream. In the latter we recover the Birkinshaw-Gull effect. As the nonlinear iSW-effect itself is inherently hard to detect, observational discrimination between its individual contributions is almost excluded. Our analysis, however, yields valuable insights into the theory of the nonlinear iSW-effect as a post-Newtonian relativistic effect on propagating photons.