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143. The structure of correlation functions in single-field inflation
This is a guest post by Sarah Shandera from the University of Columbia. Dmitry.
Dmitry has asked me to write a post about my recent paper, arXiv:0812.0818, about correlation functions in single field inflation. The motivation behind this work is the potential of very near-future data (from the Planck satellite and large scale structure surveys) to more significantly test the Gaussianity of primordial fluctuations. In standard single-field slow-roll models, the flatness (and smoothness) of the potential guarantees that the primordial fluctuations are Gaussian to a part in 
. Current observational bounds only require the primordial fluctuations to be Gaussian to a part in 
or 
– still pretty Gaussian, but leaving a surprising amount of room for some interesting physics. Measurements of non-Gaussianity would be a very useful tool for understanding the fundamental picture of inflation, because they probe interactions of the inflaton, and because observations can distinguish between wide classes of models. There are many different statistics that can be used to test Gaussianity. Clearly the 
-point functions are one class of possibilities, but there are also measures like Minkowski functionals or galaxy cluster number counts that depend on an integrated contribution from a series of correlation functions. Often, this series can be simply truncated to depend on a few lower-order moments (for example, when the non-Gaussianity comes from the non-linear gravitational evolution), and this truncation looks suggestively like a perturbative series for the fundamental interactions.
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