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

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.

14 pages, clarifying remark added

References in corpus (4)

• Minimum Length Cutoff in Inflation and Uniqueness of the Action
• Free particle wavefunction in light of the minimum-length deformed quantum mechanics and some of its phenomenological implications
• Corrections to the black body radiation due to minimum-length deformed quantum mechanics
• Inflation with a stringy minimal length, reworked

Cited by in corpus (5)

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• Emergent Universe Model from Modified Heisenberg Algebra
• A squeezed review on coherent states and nonclassicality for non-Hermitian systems with minimal length
• Minimum length, extra dimensions, modified gravity and black hole remnants
• Quantum probes for universal gravity corrections