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arXiv · 1211.2157

Consistency condition for inflation from (broken) conformal symmetry

Koenraad Schalm·Gary Shiu·Ted van der Aalst
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Abstract

We investigate the symmetry constraints on the bispectrum, i.e. the three-point correlation function of primordial density fluctuations, in slow-roll inflation. It follows from the defining property of slow-roll inflation that primordial correlation functions inherit most of their structure from weakly broken de Sitter symmetries. Using holographic techniques borrowed from the AdS/CFT correspondence, the symmetry constraints on the bispectrum can be mapped to a set of stress-tensor Ward identities in a weakly broken 2+1-dimensional Euclidean CFT. We construct the consistency condition from these Ward identities using conformal perturbation theory. This requires a second order Ward identity and the use of the evolution equation. Our result also illustrates a subtle difference between conformal perturbation theory and the slow roll expansion.

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Koenraad Schalm, Gary Shiu, Ted van der Aalst. 2013-03-27. Consistency condition for inflation from (broken) conformal symmetry. https://doi.org/10.1088/1475-7516%2F2013%2F03%2F005

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