Sub-degree CMB anisotropies from inflationary bubbles

Abstract

It is well known that processes of first order phase transitions may have occurred in the inflationary era. If one or more occurred well before the end of inflation, the nucleated bubbles are stretched to large scales and the primordial power spectrum contains a scale dependent non-Gaussian component provided by the remnants of the bubbles. We predict the anisotropies in the cosmic microwave background (CMB) induced by inflationary bubbles. We build a general analytic model for describing a bubbly perturbation; we evolve each Fourier mode using the linear theory of perturbations from reheating until decoupling; we get the CMB anisotropies by considering the bubbly perturbation intersecting the last scattering surface. The CMB image of an inflationary bubble is a series of concentric isothermal rings of different color (sign of $δT/T$) on the scale of the sound horizon at decoupling ($\le 1^{o}$ in the sky); the resulting anisotropy is therefore strongly non-Gaussian. The mean amplitude of $δT/T$ for a bubble of size $L$ follows the known estimates for linear perturbations, $δT/T\simeqδρ/ρ\cdot (L/H^{-1})^{2}$. In particular, bubbles with size corresponding to the seeds of the observed large scale voids (tens of comoving Mpc) induce an interesting pattern of CMB anisotropies on the sub-degree angular scale, to be further investigated and compared with the forthcoming high resolution CMB maps provided by the MAP and the Planck experiments.