The Robustness of Inflation to Changes in Super-Planck-Scale Physics
Robert H. Brandenberger, Jerome Martin
TL;DR
The paper investigates whether the inflationary perturbation spectrum is affected by super-Planck-scale physics by replacing the linear dispersion with nonlinear forms from Unruh and Corley–Jacobson, tracking the evolution of modes in a flat FRW background. A master formula for the late-time power spectrum $P_\Phi(n)$ is derived, requiring $F(k)$, initial conditions, and the background evolution; analysis shows that Unruh-type dispersion can preserve scale-invariance for exponential inflation, while Corley–Jacobson dispersion can produce tilts, exponential growth, or oscillations depending on parameters and initial state, indicating non-robustness to UV physics. These findings suggest that predictions of weakly coupled inflationary models are sensitive to sub-Planck-scale physics, whereas strongly coupled models may retain robustness; the work thus highlights a potential link between fundamental high-energy physics and cosmological observations. $n^3 P_\Phi(n)$ exhibits distinct scaling: for linear dispersion, $n^3 P_\Phi(n) \sim n^{4+2\beta}$, whereas Unruh dispersion with $\beta=-2$ yields $n^3 P_\Phi(n) \sim n^0$, and Corley–Jacobson with complex $b_m$ introduces $e^{2 z[\eta_1(n)]}$ and oscillations.
Abstract
We calculate the spectrum of density fluctuations in models of inflation based on a weakly self-coupled scalar matter field minimally coupled to gravity, and specifically investigate the dependence of the predictions on modifications of the physics on length scales smaller than the Planck length. These modifications are encoded in terms of modified dispersion relations. Whereas for some classes of dispersion relations the predictions are unchanged compared to the usual ones which are based on a linear dispersion relation, for other classes important differences are obtained, involving tilted spectra, spectra with exponential factors and with oscillations. We conclude that the predictions of inflationary cosmology in these models are not robust against changes in the super-Planck-scale physics.