Initial state of matter fields and trans-Planckian physics: Can CMB observations disentangle the two?

TL;DR

This paper demonstrates that modifications in the initial quantum state of matter fields can replicate any inflationary perturbation spectrum, making it impossible for CMB observations alone to distinguish between different trans-Planckian physics models.

Contribution

It provides a method to construct initial quantum states that reproduce any given spectrum, showing CMB data cannot differentiate between initial state effects and trans-Planckian modifications.

Findings

Any perturbation spectrum can be generated by suitable initial states.

Modified spectra from trans-Planckian physics can be represented by squeezed states.

CMB observations are limited to constraining initial states, not trans-Planckian models.

Abstract

The standard, scale-invariant, inflationary perturbation spectrum will be modified if the effects of trans-Planckian physics are incorporated into the dynamics of the matter field in a phenomenological manner, say, by the modification of the dispersion relation. The spectrum also changes if we retain the standard dynamics but modify the initial quantum state of the matter field. We show that, given {\it any} spectrum of perturbations, it is possible to choose a class of initial quantum states which can exactly reproduce this spectrum with the standard dynamics. We provide an explicit construction of the quantum state which will produce the given spectrum. We find that the various modified spectra that have been recently obtained from `trans-Planckian considerations' can be constructed from suitable squeezed states above the Bunch-Davies vacuum in the standard theory. Hence, the CMB observations can, at most, be useful in determining the initial state of the matter field in the standard theory, but it can {\it not} help us to discriminate between the various Planck scale models of matter fields. We study the problem in the Schrodinger picture, clarify various conceptual issues and determine the criterion for negligible back reaction due to modified initial conditions.