Effects of inflationary bubbles on the polarization and temperature anisotropies of the cosmic microwave background

We predict the imprint of linear bubbly perturbations on the polarization and temperature anisotropies of the cosmic microwave background (CMB). We analytically model a bubbly density perturbation at the beginning of the radiation dominated era and we apply the linear theory of cosmological perturbations to compute its time evolution. At decoupling, it uniquely signs the CMB polarization and temperature anisotropy sky. As predicted by recent general work regarding spatially limited cosmological seeds, during evolution the perturbation propagates beyond the size of the bubble and reaches the CMB sound horizon at the time considered. Therefore, its signal appears as a series of concentric rings, each characterized by its own amplitude and sign, on the scale of the sound horizon at decoupling (≤ 1o on the sky). Polarization and temperature rings are strictly correlated; photons coming from the center of the bubble are not polarized, because of the spherical symmetry of the present problem. As expected for linear perturbations with size L and density contrast δ at decoupling, δT/T is roughly δ(L/H); the polarization is about 10% of the temperature anisotropy. We predict the impact of a distribution of bubbles on the CMB polarization and temperature power spectra. Considering models containing both CDM Gaussian and bubbly non-Gaussian fluctuations, we simulate and analyze 10o × 10o sky patches with angular resolution of about 3.5 ′ . The CMB power associated with the bubbles is entirely on sub-degree angular scales (200 ≤ l ≤ 1000), that will be explored by the forthcoming high resolution CMB experiments with the percent precision. Depending on the parameters of the bubbly distribution we find extra-power with respect to the ordinary CDM Gaussian fluctuations; we infer simple analytical scalings of the power induced by bubbly perturbations and we constrain our parameters with the existing data.