Research output: Contribution to journal › Article

Original language | English |
---|---|

Pages (from-to) | 1393-1404 |

Journal | Inverse problems |

Volume | 15 |

Issue number | 6 |

DOIs | |

State | Published - 1 Dec 1999 |

The (ordinary) Sachs-Wolfe effect relates primordial matter
perturbations to the temperature variations δT/T in the cosmic
microwave background radiation; δT/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)jl2(ky) with respect to k (0 <k <
∞) is equal to a given constant, Cl, for l = 0, 1,
2,.... Here, P is the power spectrum of the primordial density
variations, jl 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 jl2(ky) is replaced by kl) are
made.

ID: 31459817