http://arxiv.org/abs/1712.00089
We show that there is an infinite family of slow-roll parameters histories which can produce the same spectrum of comoving curvature perturbations. After expressing the slow-roll parameters in terms of the scale factor this degeneracy can be shown to be related to the freedom in the choice of the initial conditions for the second order differential equation relating the coefficients of the curvature perturbation equations to the scale factor. This freedom implies that in general there is no one-to-one correspondence between the spectrum and higher order correlation functions, unless some special conditions are satisfied by the slow-roll parameters.
We give some numerical example of expansion histories with the same spectrum but different bispectra. We also compute what kind of perturbations of the de-Sitter scale factor can produce the same spectrum but different slow-roll parameters and higher correlation functions.
A. Cadavid and A. Romano
Mon, 4 Dec 17
42/72
Comments: 6 pages, 8 figures
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