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A lack of correlations in the microwave background temperature between skydirections separated by angles larger than 60 degrees has recently beenconfirmed by data from the Planck satellite. This feature arises as a randomoccurrence within the standard LCDM cosmological model less than 0.3 per centof the time, but so far no other compelling theory to explain this observationhas been proposed. Here we investigate the theoretical cross-correlationfunction between microwave background temperature and the gravitational lensingpotential of the microwave background, which in contrast to the temperaturecorrelation function depends strongly on gravitational potential fluctuationsinterior to our Hubble volume. For standard LCDM cosmology, we generate randomsky realizations of the microwave temperature and gravitational lensing,subject to the constraint that the temperature correlation function matchesobservations, and compare with random skies lacking this constraint. Thedistribution of large-angle temperature-lensing correlation functions in thesetwo cases is different, and the two cases can be clearly distinguished inaround 40 per cent of model realizations. We present an a priori procedure forusing similar large-angle correlations between other types of data, todetermine whether the lack of large-angle correlations is a statistical flukeor points to a shortcoming of the standard cosmological model.

Probing Large-Angle Correlations with the Microwave Background Temperature and Lensing Cross Correlation