Are the WMAP Angular Magnification Measurements Consistent with an Inhomogeneous Critical Density Universe?

The propagation of light through a universe of isothermal mass spheres amidst a homogeneous matter component is considered. We demonstrate by an analytical proof that as long as a small light bundle passes through a sufficient number of isothermal mass spheres at various impact parameters—a criterion of great importance—its average convergence will exactly compensate the divergence within a homogeneous matter component. The net effect on the light is statistically the same as if all the matter in isothermal mass spheres were "fully homogenized." When applying the above ideas toward understanding the angular size of the primary acoustic peaks of the microwave background, however, caution is needed. The reason is that (by mass) most isothermal mass spheres are in galaxies—their full mass profiles are not sampled by passing light—and at least the inner 20 kpc regions of these systems are missed by the majority of rays, while the rest of the rays would map back to unresolvable but magnified, randomly located spots to compensate for the loss in angular size. Therefore, a scanning pair of WMAP beams finds most frequently that the largest temperature difference occurs when each beam is placed at diametrically opposite points of the Dyer-Roeder collapsed sections. This is the mode magnification, which corresponds to the acoustic peaks, and is less than the mean (or the homogeneous preclumping angular size). Since space was seen to be Euclidean without taking the said adjustment into account, the true density of the universe should be supercritical. Our analysis gives Ωm = 0.278 ± 0.040 and ΩΛ = 0.782 ± 0.040.