Getting super-excited with modified dispersion relations

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". We conclude by commenting on the possibility of obtaining these modified dispersion relations within the Effective Field Theory of Inflation.

Extended effective field theory of inflation

“…In order to have a stable vacuum in the deep UV, where the dispersion relation is dominated by the k 6 , we consider β 0 > 0 7 . If Hubble crossing takes place when ω 2 ∼ k 2 , transitions between regions with a different dispersion relation can lead to excited initial states [7]. In this case, if α 0 < 0, one can have relatively large corrections, much bigger than one, compared to the standard inflationary predictions for the two point function.…”

“…On the other hand, if α 0 < 0, there could be large modulation factors on the power spectrum. In [7], we focused on the range of parameters for α 0 and β 0 such that…”

“…In [7], we had also assumed that the mode never becomes lighter than the Hubble parameter up until the last horizon crossing. That would mean that the equation ω 2 = 2H 2 has only one solution.…”

“…This can be achieved by setting α 0 ∼ 0.2 and β 0 = α 2 0 /4. Latter was studied in [7] as a dispersion relation that realises super-excited states with large occupation numbers. The mode equation has one turning point for such values of parameters, corresponding to a single horizon crossing.…”

Non-unitary evolution in the general extended EFT of inflation & excited initial states

“…The scheme was originally motivated by the studies in condensed matter physics that suggested departure from Lorentzian dispersion relation beyond some momentum cutoff [14,15]. It was shown in [16] that two formalisms of excited initial state and MDR could be related to each other and how a range of possibilities that arise within the excited state setup, appears in the formalism of MDR by changing the functional behavior and/or the coefficients of the dispersion relation. Although in the study of the new physics on inflationary observables, the MDRs were introduced in the setup of the cosmological perturbation theory through some ad hoc condensed matter procedure, with the advent of the Effective Field Theory of Inflation (EFToI) [17] and HořavaIt-Lifshitz gravity [18,19], such MDRs found a clear origin within the field of high energy physics.…”