High Energy Theory Seminar: Conformal Invariance, Dark Energy and CMB Non-Gaussianity
A universe dominated by dark energy naturally gives rise to correlation functions possessing full conformal invariance. This is a consequence of the conformal group of flat 3-dimensional spatial sections being isomorphic to the de Sitter symmetry group SO(4,1), and hence independent of specifi c model assumptions. Assuming this full symmetry holds leads to a de finite prediction for the shape of the non-Gaussian CMB bispectrum, quite different from single field slow roll inflation.
The de Sitter cosmological horizon induces a different possible embedding of the conformal group of the 2-sphere in the de Sitter group, which leads to a different prediction for the angular correlations of CMB non-Gaussianity on the sky. Conformal symmetry also leads to a prediction of a relation between the spectral indices of scalar and tensor modes.
A quantum origin for the CMB fluctuations in the scalar gravitational sector from the conformal anomaly that could give rise both to these non-Gaussianities without a slow roll inflaton fi eld and dynamical dark energy is proposed, Detection of non-Gaussian correlations in the CMB with one of the bispectral shape functions predicted by conformal invariance thus can be used both to establish the physical origins of primordial density fluctuations, and provide important clues to the nature of cosmological dark energy.
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