Non-Linear Trans-Planckian Corrections of Spectra due to the Non-trivial Initial States

Abstract

Recent Planck results motivated us to use non-Bunch-Davies vacuum. In this paper, we use the excited-de Sitter mode as non-linear initial states during inflation to calculate the corrected spectra of the initial fluctuations of the scalar field. First, we consider the field in de Sitter space-time as background field and for the non-Bunch-Davies mode, we use the perturbation theory to the second order approximation. Also, unlike conventional renormalization method, we offer de Sitter space-time as the background instead Minkowski space-time. This approach preserve the symmetry of curved space-time and stimulate us to use excited mode. By taking into account this alternative mode and the effects of trans-Planckian physics, we calculate the power spectrum in standard approach and Danielsson argument. The calculated power spectrum with this method is finite, corrections of it is non-linear, and in de Sitter limit corrections reduce to linear form that obtained from several previous conventional methods.

arXiv comment6 pages, Published in Physics Letters B

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• An Asymptotic Method for Selection of Inflationary Modes
• Particle Creation and Excited-de Sitter Modes
• Higher Order Corrections to Asymptotic-de Sitter Inflation
• Large Angular Scale CMB Anisotropy from an Excited Initial Mode
• Inflation in Non-de Sitter Background with Coherent States
• Accelerating Universe in Terms of Hankel Function Index