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