Conformal invariance and cosmic background radiation

The spectrum and statistics of the cosmic microwave background radiation (CMBR) are investigated under the hypothesis that scale invariance of the primordial density fluctuations should be promoted to full conformal invariance, allowing for deviations from naive scaling. The spectral index of the two-point function of density fluctuations is determined by the trace anomaly to be greater than one, implying less power at large distance scales than a Harrison-Zel'dovich spectrum. Conformal invariance also implies non-Gaussian Statistics of the CMBR and determines the large angular dependence of its three-point correlations.