ABSTRACT
In this chapter, each of the three cosmic backgrounds is modelled as a random Fourier series with respect to an orthonormal basis of a certain Hilbert space whose elements are square-integrable cross-sections of fibre bundles over the two-dimensional sphere. The Copernican principle implies that such a constructed random field must be isotropic. The coefficients of the series become random variables which turn to be pairwise uncorrelated if and only if the basis vectors have a special property: under the action of the symmetry group, each vector generates an irreducible representation of that group. In such a way, various kinds of ‘spherical harmonics’ are constructed in a unified way with the help of the Frobenius reciprocity in numerous explicit examples. Afterwards, the cosmic background is expanded with respect to that basis. A non-exhaustive bunch of directions in current research where the knowledge obtained from this book, may be useful, is described.
