Trans-Planckian Physics from a Nonlinear Dispersion Relation

Abstract

We study a particular nonlinear dispersion relation ${\omega }_p(k_p)$ -- 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

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• Phenomenological implications of modified loop cosmologies: an overview
• High-order Primordial Perturbations with Quantum Gravitational Effects
• Inflationary spectra with inverse-volume corrections in loop quantum cosmology and their observational constraints from Planck 2015 data
• Scalar and tensor perturbations in loop quantum cosmology: High-order corrections
• Constructing analytical solutions of linear perturbations of inflation with modified dispersion relations
• Getting Super-Excited with Modified Dispersion Relations
• A resolution of the Trans-Planckian problem in the R_h=ct universe
• Modified dispersion relations, inflation and scale invariance
• Stable initial conditions and analytical investigations of cosmological perturbations in a modified loop quantum cosmology