Simulating cosmic microwave background maps in multiconnected spaces

This paper describes the computation of cosmic microwave background (CMB) anisotropies in a universe with multiconnected spatial sections and focuses on the implementation of the topology in standard CMB computer codes. The key ingredient is the computation of the eigenmodes of the Laplacian with boundary conditions compatible with multiconnected space topology. The correlators of the coefficients of the decomposition of the temperature fluctuation in spherical harmonics are computed and examples are given for spatially flat spaces and one family of spherical spaces, namely, the lens spaces. Under the hypothesis of Gaussian initial conditions, these correlators encode all the topological information of the CMB and suffice to simulate CMB maps.