Lensing effect on the relative orientation between the Cosmic Microwave Background ellipticities and the distant galaxies

The low redshift structures of the Universe act as lenses in a similar way on the Cosmic Microwave Background 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 non-uniform 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 alignement between CMB and the galactic ellipticities relative to the uniform distribution. The relatively high signal-to-noise ratio we found should makes 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.