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

Michael Maziashvili*

  • Center for Elementary Particle Physics, ITP, Ilia State University, 3—5 Cholokashvili Avenue, Tbilisi 0162, Georgia

  • *maziashvili@gmail.com

Phys. Rev. D 85, 125026 – Published 19 June, 2012

DOI: https://doi.org/10.1103/PhysRevD.85.125026

Abstract

The effect of string- and quantum-gravity-inspired minimum-length deformed quantization on a free, massless scalar field is studied on the de Sitter background at the level of second quantization. An 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 nonlinear 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 exp(6N), where N is the number of e-foldings.

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