# Getting Super-Excited with Modified Dispersion Relations

## TL;DR

This paper explores how modified dispersion relations can produce highly excited or calm excited states in quantum fluctuations, affecting the power spectrum during inflation, with implications for the Effective Field Theory of Inflation.

## Contribution

It identifies conditions under which modified dispersion relations lead to super-excited states and critiques the gluing method for calculating power spectra.

## Key findings

- Modified dispersion relations can produce super-excited states with large corrections to the power spectrum.
- Certain parameter regions yield no modification, leading to calm excited states.
- The gluing method has shortcomings in evaluating Bogolyubov coefficients.

## Abstract

We demonstrate that in some regions of parameter space, modified dispersion relations can lead to highly populated excited states, which we dub as "super-excited" states. In order to prepare such super-excited states, we invoke dispersion relations that have negative slope in an interim sub-horizon phase at high momenta. This behaviour of quantum fluctuations can lead to large corrections relative to the Bunch-Davies power spectrum, which mimics highly excited initial conditions. We identify the Bogolyubov coefficients that can yield these power spectra. In the course of this computation, we also point out the shortcomings of the gluing method for evaluating the power spectrum and the Bogolyubov coefficients. As we discuss, there are other regions of parameter space, where the power spectrum does not get modified. Therefore, modified dispersion relations can also lead to so-called "calm excited states" as well. We conclude by commenting on the possibility of obtaining these modified dispersion relations within the Effective Field Theory of Inflation.