Does gravitational time delay perturbation affect CMB acoustic scale anisotropy ?

In this paper we specifically studied one aspect of foreground primordial matter density perturbations: the relative gravitational time delay between a pair of light paths converging towards 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 in principle time delay biases the size of acoustic oscillations systematically towards smaller angles, or larger harmonic numbers l, i.e. the mean geometry as revealed by CMB light becomes that of an open Universe if Ω = 1. Since the effect is second order, its standard deviation δl/l ∼ (δΦ) where (δΦ) ∼ 10 is the normalization of the primordial matter spectrum P (k), the consequence is too numerically feeble to warrant a re-interpretion of WMAP data. If 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 have been 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 large scale geometry. The physics that explains why δΦ is so small also plays a crucial role in solving the flatness problem.