### 20 december, Holger Then: Maass waveforms and an application to cosmology

**Abstract.**
A brief outline on the numerical computation of Maass waveforms in
hyperbolic three-space is given. The results are then applied to
cosmology. In a linear perturbed Robertson-Walker universe the
Einstein equations of general relativity can be separated, if one
knows the eigenvalues and eigenfunctions of the Laplacian. Assuming
the universe to be a finite, but non-compact hyperbolic manifold, the
metric perturbations can be expanded in terms of Maass waveforms. This
allows to compute the temperature fluctuations in the cosmic microwave
background (CMB). The assumption of a finite hyperbolic universe
seems rather strange, but comparing the results with astronomical
observations yields evidence for the assumption to be true. The
assumption of a non-compact universe is made for technical reasons
that allow to introduce Maass waveforms. Since this assumption has no
inluence on the CMB, it could also be dropped.