Shrinking and the True Power Spectrum at Decoupling

In this paper we examine the change in the estimated spatial power spectra at decoupling due to the effects of our clumpy universe which modify observational distances. We find that scales at decoupling can be significantly underestmated in our approximation of neglecting the shear of the ray bundle. We compare our results with other work on lensing and speculate on the implications for structure formation. In particular we examine a proposal to use the position of the first Doppler peak to determine $\Omega$, and find that shrinking will modify the esimated curvature, so that it must be included to obtain an accurate estimate of $\Omega$. Finally we consider future applications and improvements of our results.