Efficient diagrammatic computation method for higher order correlation functions of local type primordial curvature perturbations
Abstract
We present a new efficient method for computing the non-linearity parameters of the higher order correlation functions of local type curvature perturbations in inflation models having a Script N-component scalar field, focusing on the non-Gaussianity generated during the evolution on super-horizon scales. In contrast to the naive expectation that the number of operations necessary to compute the n-point functions is proportional to Script Nn, it grows only linearly in Script N in our formalism. Hence, our formalism is particularly powerful for the inflation models composed of a multi-component scalar field, including the models in which the slow-roll conditions are violated after the horizon crossing time. Explicit formulas obtained by applying our method are provided for n = 2, 3, 4 and 5, which correspond to power-, bi-, tri- and quad-spectra, respectively. We also discuss how many parameters we need to parameterize the amplitude and the shape of the higher order correlation functions of local type.
- Publication:
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Journal of Cosmology and Astroparticle Physics
- Pub Date:
- February 2009
- DOI:
- 10.1088/1475-7516/2009/02/012
- arXiv:
- arXiv:0810.3053
- Bibcode:
- 2009JCAP...02..012Y
- Keywords:
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- Astrophysics;
- General Relativity and Quantum Cosmology;
- High Energy Physics - Theory
- E-Print:
- 17 pages, 11 figures, 2 tables, minor revisions