Shrinking and the True Power Spectrum at Decoupling

TL;DR

This paper investigates how the clumpy universe affects the estimation of the power spectrum at decoupling, revealing that neglecting shear leads to underestimation and impacts curvature and structure formation analyses.

Contribution

It introduces a correction for the effects of shear on the power spectrum at decoupling, highlighting the importance of including shrinking effects in cosmological measurements.

Findings

Decoupling scales are significantly underestimated when shear is neglected.

Shrinking effects influence the estimation of the universe's curvature.

Implications for using the Doppler peak position to determine  are discussed.

Abstract

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.