Lensing Effect on the Relative Orientation between the Cosmic Microwave Background Ellipticities and the Distant Galaxies

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Abstract
The low-redshift structures of the universe act as lenses in a similar way on the cosmic microwave background (CMB) light and on the distant galaxies (say at redshift about unity). As a consequence, the CMB temperature distortions are expected to be statistically correlated with the galaxy shear, exhibiting a nonuniform distribution of the relative angle between the CMB and the galactic ellipticities. Investigating this effect, we find that its amplitude is as high as a 10% excess of alignment between CMB and the galactic ellipticities relative to the uniform distribution. The relatively high signal-to-noise ratio we found should make possible a detection with the planned CMB data sets, provided that a galaxy survey follow-up can be done on a sufficiently large area. It would provide a complementary bias-independent constraint on the cosmological parameters.
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