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.
Highlights
As a causal manner, inflation scenario can be explain density perturbations originating in areas outside the horizon in the very early universe[1, 2]
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
The measurable radiation from the Big Bang is cosmic microwave background radiation(CMBR), that provides a snapshot of the early universe and our main notion of the early universe has improved significantly over the survey of it
Summary
Inflation scenario can be explain density perturbations originating in areas outside the horizon in the very early universe[1, 2]. The trans-Planckian physics effects in inflation was introduced in [8] Dispersion relations and their concepts in various form have been greatly studied in [9,10,11]. The main point of this paper is that the order of corrections to the power spectrum changes if we consider non-linear initial vacuum mode. To achieve this goal, we use the excited version of α-vacuum and we generalize Danielsson work in the context of α-vacuum[6].
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