Trans-Planckian Physics from a Nonlinear Dispersion Relation
Abstract
Description
We study a particular nonlinear dispersion relation $ω_p(k_p)$ -- a series expansion in the physical wavenumber $k_p$ -- for modeling first-order corrections in the equation of motion of a test scalar field in a de Sitter spacetime from trans-Planckian physics in cosmology. Using both a numerical approach and a semianalytical one, we show that the WKB approximation previously adopted in the literature should be used with caution, since it holds only when the comoving wavenumber $k\gg aH$. We determine the amplitude and behavior of the corrections on the power spectrum for this test field. Furthermore, we consider also a more realistic model of inflation, the power-law model, using only a numerical approach to determine the corrections on the power spectrum.
11 pages, 10 figures. Some changes made, comments and references added, a figure added, typos corrected, conclusions unchanged, version accepted for pubblication in Phys. Rev. D
11 pages, 10 figures. Some changes made, comments and references added, a figure added, typos corrected, conclusions unchanged, version accepted for pubblication in Phys. Rev. D