A note on inflation and transplanckian physics

TL;DR

The paper investigates whether transplanckian physics can alter inflationary predictions for CMBR fluctuations. It uses a simple toy model with vacuum-choice ambiguities and analyzes mode evolution in the Heisenberg picture, emphasizing a zeroth-order adiabatic vacuum and finite-time initial conditions tied to the scale $\Lambda$. The main result is a leading correction of order $H/\Lambda$ to the standard spectrum, with a modulated form $P_\phi=(\frac{H}{2\pi})^2\left(1 - \frac{H}{\Lambda}\sin\left(\frac{2\Lambda}{H}\right)\right)$, suggesting possible observational implications if Planck-scale physics leaves imprints on cosmological perturbations. This work highlights the sensitivity of inflationary predictions to vacuum choice and provides a conservative framework for estimating transplanckian effects, potentially bridging Planck-scale physics and cosmological data.

Abstract

In this paper we consider the influence of transplanckian physics on the CMBR anisotropies produced by inflation. We consider a simple toy model that allows for analytic calculations and argue on general grounds, based on ambiguities in the choice of vacuum, that effects are expected with a magnitude of the order of $H/Λ$, where $H$ is the Hubble constant during inflation and $Λ$ the scale for new physics, e.g. the Planck scale.