Conformal Invariance, Dynamical Dark Energy and the CMB
  General Relativity receives quantum corrections relevant at cosmological
distance scales from the conformal scalar degrees of freedom required by the
trace anomaly of the quantum stress tensor in curved space. In the theory
including the trace anomaly terms, the cosmological "constant" becomes
dynamical and hence potentially dependent upon both space and time. The
fluctuations of these anomaly scalars may also influence the spectrum and
statistics of the Cosmic Microwave Background. Under the hypothesis that scale
invariance should be promoted to full conformal invariance, an hypothesis
supported by the exact equivalence of the conformal group of three dimensions
with the de Sitter group SO(4,1), the form of the CMB bispectrum can be fixed,
and the trispectrum constrained. The non-Gaussianities predicted by conformal
invariance differ from those suggested by simple models of inflation.
