This statistics is invariant with respect to the type of perturbations and can be considered only as a test on Gaussianity. Second, Minkowski functionals for the CMB polarization field. These functionals are determined by the covariance matrix of second derivatives of Stokes parameters. This matrix is different for scalar and tensor mode. Therefore, Minkowski functionals for CMB polarization field can be considered as a probe of scalar perturbations and gravitational waves.
All results are analytical.