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

By Michael Maziashvili

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.Comment: 14 pages, clarifying remark adde

Topics: General Relativity and Quantum Cosmology, High Energy Physics - Theory
Year: 2012
DOI identifier: 10.1103/PhysRevD.85.125026
OAI identifier: oai:arXiv.org:1104.4187
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