Inflation with a Planck-scale frequency cutoff

TL;DR

The paper investigates whether a Planck-scale cutoff in an expanding universe can alter inflationary predictions by bounding the proper frequency of a scalar field on a de Sitter background. It introduces a dispersive function $F(k,a)$ with a fixed cutoff $\kappa_0$ and analyzes the adiabatic vacuum and horizon-crossing behavior, comparing to the standard $|u_k|^2$ amplitude. For $\sigma = \kappa_0/H \gg 1$ and gradual $F$, the predictions recover the usual inflationary amplitude; deviations occur if the cutoff is near horizon or the transition is too smooth, potentially producing scale-dependent features. The paper emphasizes the need for an explicit mode-creation or dissipation mechanism in cosmology, which is not apparent in the black hole analogy, and discusses implications for possible non-Gaussianities. Overall, it frames how Planck-scale physics might leave observable imprints or be screened, guiding phenomenology for trans-Planckian effects in inflation.

Abstract

The implementation of a Planck-scale high frequency and short wavelength cutoff in quantum theories on expanding backgrounds may have potentially nontrivial implications, such as the breaking of local Lorentz invariance and the existence of a yet unknown mechanism for the creation of vacuum modes. In scenarios where inflation begins close to the cutoff scale, these effects could have observable consequences as trans-Planckian modes are redshifted to cosmological scales. In close analogy with similar studies of Hawking radiation, a simple theory of a minimally coupled scalar field in de Sitter space is studied, with a high frequency cutoff imposed by a nonlinear dispersion relation. Under certain conditions the model predicts deviations from the standard inflationary scenario. We also comment on the difficulties in generalizing fluid models of Hawking radiation to cosmological space-times.