Higher order nonlinear parameters with Planck constraints

Abstract

We investigate how higher order non-linear parameters affect lower order ones through loop effects. We calculate the loop corrections up to two-loops and explicitly show that the tree contribution is stable against loop terms in most cases. We argue that, nevertheless, observational constraints on non-linear parameters such as f NL and τ NL can also give a limit even for higher order ones due to the loop contribution. We discuss these issues for both single-source and multi-source cases.

Forecasts on the Dark Energy and Primordial Non-Gaussianity Observations With the Tianlai Cylinder Array

“…The exact numbers of the predicted 1 − σ errors for Tianlai pathfinders and for the full-scale Tianlai are listed in table 2. On large scales, the matter bispectrum is well described by the tree-level expression, and the loop corrections remain very small (Tasinato et al 2013;Gong & Takahashi 2014). Higher order terms such as the trispectrum could contribute significantly to the bispectrum of high density peaks (Sefusatti 2009;Jeong & Komatsu 2009), but as the HI gas is much less biased than observable galaxies -for the Tianlai experiment, the HI bias is not far from 1 -we expect such contribution to be less significant, though the exact amount can not be obtained without going through the lengthy calculations.…”