Conformal Invariance and Cosmic Background Radiation

Abstract

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. [S0031-9007(97)03472-8] PACS numbers: 98.70.Vc, 98.80.Hw With the discovery of the anisotropy in the cosmic microwave background radiation (CMBR) [1], cosmology has accelerated its transition from a field based largely on speculation to one in which observational data can be brought to bear on our understanding of the Universe. The CMBR anisotropy is the most sensitive available probe of the primordial density fluctuations from which the large scale structure of the Universe arose. Since the pioneering work of Harrison and Zel’dovich [2] it has been reasonable to suppose that these primordial fluctuations were generated with a scale invariant spectrum during an early epoch in the history of the Universe at the threshold of its classical evolution. Inflationary models are a particular