Cosmic microwave background: Polarization and temperature anisotropies from symmetric structures - art. no. 123004

Perturbations in the cosmic microwave background (CMB) are generated by pri mordial inhomogeneities. I consider the case of CMB anisotropies from one s ingle ordered perturbation source, or seed, existing well before decoupling between matter and radiation. Such structures could have been left by high energy symmetries breaking in the early universe. I focus on the cases of spherical and cylindrical symmetry of the seed. I give general analytic exp ressions for the polarization and temperature Linear perturbations, factori ng out of the Fourier integral the dependence on the photon propagation dir ection and on the geometric coordinates describing the seed. I show how the CMB perturbations manifestly reflect the: symmetries of their seeds. In pa rticular, polarization is uniquely linked to the shape of the source becaus e of its tensorial nature. CMB anisotropies are obtained with a line of sig ht integration. They are a function of the position and orientation of the seed along the photons path. This treatment highlights the undulatory prope rties of the CMB. I show with. numerical examples how the polarization and temperature perturbations propagate beyond the size of their seeds, reachin g the CMB sound horizon at the time considered. Just like the waves from a pebble thrown in a pond, CMB anisotropy from a seed intersecting the last s cattering surface appears as a series of temperature and polarization waves surrounding the seed, extending on the scale of the CMB sound horizon at d ecoupling, roughly 1 deg in the sky. Each wave is characterized by its own value of the: CMB perturbation, with the same mean amplitude of the signal coming from the seed interior; as expected for a linear structure with size L less than or equal to H-1 and density contrast delta at decoupling, the temperature anisotropy is delta T/T similar or equal to delta(L/H-1)(2), ro ughly ten times stronger than the polarization. These waves could allow one to distinguish relies from high energy processes of the early universe fro m pointlike astrophysical sources, because of their angular extension and a mplitude. Also, the marked analogy between polarization and temperature sig nals offers cross correlation possibilities for the future detection instru ments. It would be interesting to detect these signals in the next 10 are m in CMB map provided by the Planck Surveyor satellite experiment. [S0556-282 1(99)07410-X].