Minimum-length deformed quantization of a free field on de Sitter background and corrections to the inflaton perturbations

TL;DR

This paper investigates how a minimum-length deformation inspired by string and quantum gravity theories affects a free scalar field in de Sitter space, revealing non-Gaussian features and corrections to the inflaton perturbation spectrum.

Contribution

It provides an analytic solution for the deformed field operator and estimates the resulting non-Gaussianity and power spectrum corrections in a de Sitter background.

Findings

The field operator exhibits non-linear dependence on creation and annihilation operators.

The power spectrum correction is comparable to previous first quantization studies.

Non-Gaussianity in the four-point function is suppressed by a factor of approximately exp(-6N).

Abstract

The effect of string and quantum gravity inspired minimum-length deformed quantization on a free, massless scalar field is studied on de Sitter background at the level of second quantization. Analytic solution of a field operator is obtained to the first order in deformation parameter. Using this solution we then estimate the two point and four point correlation functions (with respect to the Bunch-Davies vacuum). The field operator shows up a non-linear dependence on creation and annihilation operators, therefore the perturbation spectrum proves to be non-Gaussian. The correction to the power spectrum is of the same order as obtained previously in a similar study that incorporates the minimum-length deformed momentum operator into the first quantization picture and then proceeds in the standard way for second quantization. The non-Gaussianity comes at the level of four point correlation function; its magnitude appears to be suppressed by the factor $\sim\exp(-6N)$, where $N$ is the number of e-foldings.