Abstract
The surface of last scattering of the photons in the cosmic microwave
background is not a spherical shell. Apart from its finite width, each photon
experiences a different gravitational potential along its journey to us,
leading to different travel times in different directions. Since all photons
were released at the same cosmic time, the photons with longer travel times
started farther away from us than those with shorter times. Thus, the surface
of last scattering is corrugated, a deformed spherical shell. We present an
estimator quadratic in the temperature and polarization fields that could
provide a map of the time delays as a function of position on the sky. The
signal to noise of this map could exceed unity for the dipole, thereby
providing a rare insight into the universe on the largest observable scales.
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