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

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 $\sim \exp (-6N)$, where $N$ is the number of e-foldings.