CMB: polarization and temperature waves from spatially limited cosmological structures

The most known inflationary model leaves traces in the form of Gaussian scale-invariant perturbations. It univoquely marks the CMB angular power spectrum. However, high energy physics may be more complicated and may leave other (and richer) traces, in the form of non-Gaussian scale-dependent perturbations. In this work we change our mind to the second issue. Instead of the CMB angular power spectrum only, we predict the temperature and polarization anisotropies from single well shaped spatially limited structures. These are generally characterized by some symmetries, and here we concentrate on the spherical ones. The treatment developed allows to express the anisotropy pattern as a function of (i) the geometrical coordinates of the particular structure under investigation, including its position relative to the last scattering surface, and (ii) the photon propagation direction $n̂.$ Due to the wave-like behavior of the relevant equations, the general phenomenology that turns out is that for a localized initial inhomogeneity, the corresponding CMB perturbation propagates beyond the initial size, generating waves traveling outward with the sound velocity $cs,$ and reaching the size of the sound horizon at the time we are examinating it. This behavior is a common feature of both the pure temperature and polarization anisotropies. The natural test of these computations will be the comparison with the observational data from the forthcoming high resolution CMB maps from the Planck mission.