The effect of long range gravitational perturbations on the first acoustic peak of the cosmic microwave background

In the standard cosmological model, the temperature anisotropy of the cosmic microwave background is interpreted as variation in the gravitational potential at the point of emission, due to the emitter being embedded in a region ${\cal C}$ of over- or under-density spanning the length (or size) scale $\lambda$ on which the anisotropy is measured. If the Universe is inhomogeneous, however, similar density contrasts of size $\lambda$ are also located everywhere surrounding ${\cal C}$. Since they are superposition states of many independent Fourier modes with no preferred direction, such primordial clumps and voids should not be configured according to some prescribed spatial pattern. Rather, they can randomly trade spaces with each other while preserving the Harrison-Zeldovich character of the matter spectrum. The outcome is an {\it extra} perturbation of the potential when averaged over length $\lambda$ at the emitter, and consequently an additional anisotropy on the same scale, which has apparently been overlooked. Unlike the conventional application of the Sachs-Wolfe effect to the WMAP observations, this extra effect is {\it not} scale independent over the $P(k) \sim k$ part of the matter spectrum, but increases towards smaller lengths, as $\sqrt{k}$. The consequence is a substantial revision of the currently advertised values of the key cosmological parameters, {\it unless} one postulates a more rapid decrease in the gravitational force with distance than that given by the inverse-square law.