Time Delay by Primordial Density Fluctuations: Its Biasing Effect on the Observed Mean Curvature of the Universe

In this paper we specifically studied one aspect of foreground primordialmatter density perturbations: the relative gravitational time delay between apair of light paths converging towards an observer and originating from twopoints on the last scattering surface separated by the physical scale of anacoustic oscillation. It is found that time delay biases the size of acousticoscillations {\it systematically} towards smaller angles, or larger harmonicnumbers $\ell$, i.e. the mean geometry as revealed by CMB light becomes that ofan open Universe if $\Omega=1$. Since the effect is second order, its standarddeviation $\delta\ell/\ell \sim (\delta\Phi)^2$ where $(\delta\Phi)^2 \sim10^{-9}$ is the normalization of the primordial matter spectrum $P(k)$, theconsequence is too numerically feeble to warrant a re-interpretion of WMAPdata. If, however, this normalization were increased to $\delta\Phi \gtrsim0.01$ which is still well within the perturbation limit, the shift in thepositions of the acoustic peaks would have been substantial enough to implicateinflationary $\Lambda$CDM cosmology. Thus $\Omega$ is not the only parameter(and by deduction inflation cannot be the only mechanism) of relevance to theunderstanding of {\it observed} large scale geometry. The physics that explainswhy $\delta\Phi$ is so small also plays a crucial role, but since this is aseparate issue independent of inflation, might it be less artificial to lookfor an alternative solution to the flatness problem altogether?