Abstract
The (ordinary) Sachs-Wolfe effect relates primordial matter perturbations to the temperature variations T/T in the cosmic microwave background radiation; T/T can be observed in all directions around us. A standard but idealized model of this effect leads to an infinite set of moment-like equations: the integral of P(k)j2(ky) with respect to k (0<k<) is equal to a given constant, C, for = 0,1,2, ... . Here, P is the power spectrum of the primordial density variations, j is a spherical Bessel function and y is a positive constant. It is shown how to solve these equations exactly for P(k). The same solution can be recovered, in principle, if the first m equations are discarded. Comparisons with classical moment problems (where j2(ky) is replaced by k) are made.
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