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

We specifically study one aspect of foreground primordial matter density perturbations: the relative gravitational time delay between a pair of light paths converging toward an observer and originating from two points on the last scattering surface separated by the physical scale of an acoustic oscillation. It is found that time delay biases the size of acoustic oscillations systematically toward smaller angles, or larger harmonic numbers l; that is, the mean geometry as revealed by light from the cosmic microwave background becomes that of an open universe if Ω = 1. Since the effect is second-order, its standard deviation δl/l ~ (δΦ)2, where (δΦ)2 ~ 10−9 is the normalization of the primordial matter spectrum P(k), the consequence is too numerically feeble to warrant a reinterpretation of WMAP data. If, however, this normalization were increased to δΦ ≳ 0.01, which is still well within the perturbation limit, the shift in the positions of the acoustic peaks would be substantial enough to implicate inflationary ΛCDM cosmology. Thus, Ω is not the only parameter (and, by deduction, inflation cannot be the only mechanism) of relevance to the understanding of observed large-scale geometry. The physics that explains why δΦ is so small also plays a crucial role, but since this is a separate issue, independent of inflation, might it be less artificial to look for an alternative solution to the flatness problem altogether?