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

The propagation of light through a Universe of (a) isothermal mass spheresamidst (b) a homogeneous matter component, is considered. We demonstrate by ananalytical proof that as long as a small light bundle passes {\it through}sufficient number of (a) at various impact parameters - a criterion of greatimportance - its average convergence will exactly compensate the divergencewithin (b). The net effect on the light is statistically the same as if all thematter in (a) is `fully homogenized'. When applying the above ideas towardsunderstanding the angular size of the primary acoustic peaks of the microwavebackground, however, caution is needed. The reason is that most (by mass) of(a) are in galaxies - their full mass profiles are not sampled by passing light- at least the inner 20 kpc regions of these systems are missed by the majorityof rays, while the rest of the rays would map back to unresolvable butmagnified, randomly located spots to compensate for the loss in angular size.Therefore, a scanning pair of WMAP beams finds most frequently that the largesttemperature difference occurs when each beam is placed at diametricallyopposite points of the Dyer-Roeder collapsed sections. This is the {\it mode}magnification, which corresponds to the acoustic {\it peaks}, and is less thanthe mean (or the homogeneous pre-clumping angular size). Since space was seento be Euclidean without taking the said adjustment into account, the truedensity of the Universe should be supercritical. Our analysis gives $\Omega_m=$ 0.278 $\pm$ 0.040 and $\Omega_{\Lambda} =$ 0.782 $\pm$ 0.040.Comment: ApJ 623, L1 (2005