Hiroyuki Funakoshi, Kei Yamamoto
We study the primordial bispectrum of curvature perturbation in the uniform-density slicing generated by the interaction between the inflaton and isotropic background gauge fields. We derive the action up to cubic order in perturbation and take into account all the relevant effects in the leading order of slow-roll expansion. We first treat the quadratic vertices perturbatively and confirm the results of past studies, while identifying their regime of validity. We then extend the analysis to include the effect of the quadratic vertices at all orders by introducing exact linear mode functions, allowing us to make a reliable prediction long after horizon crossing where the features of both power spectrum and bispectrum are drastically different. It is shown that the spectra become constant and scale invariant in the limit of large e-folding, which implies the model can be consistent with the observational constraints regardless of the magnitude of the background gauge fields. It is found that depending on the period of inflation that falls into the observable window, the value of $f_{NL}$ in the squeezed limit may well be within the reach of Planck.
View original:
http://arxiv.org/abs/1212.2615
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