Getting super-excited with modified dispersion relations

We demonstrate that in some regions of parameter space, modified dispersion re- lations 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 neg- ative 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 shortcom- ings 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”. We conclude by commenting on the possibility of obtaining these modified dispersion relations within the Effective Field Theory of Inflation.