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 model analytically 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 marks 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 it reaches the CMB sound horizon in 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 (less than or equal to 1 degrees on the sky). Polarization and temperature rings are strictly correlated; photons coming from the centre 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 delta at decoupling, delta T/T is roughly delta(L/H-1)(2); the polarization is about 10 per cent 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 cold dark matter (CDM) Gaussian and bubbly non-Gaussian fluctuations, we simulate and analyse 10 degrees x 10 degrees sky patches with angular resolution of about 3.5 arcmin. The CMB power associated with the bubbles is entirely on subdegree angular scales (200 less than or equal to l less than or equal to 1000), which will be explored by the forthcoming high-resolution CMB experiments with per cent 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.