Effect of the Generalized Uncertainty Principle on the Primordial Power Spectrum: Lattice Schrödinger Picture

Abstract

In the lattice Schrodinger picture, we investigate the effect of the generalized uncertainty principle (GUP) on the power spectrum of primordial inflaton perturbations in inflationary cosmology. Among the nonlinear dispersion relations obtainable from the GUP, we study the particular case of a Corley-Jacobson type dispersion relation with positive quartic correction which arises from quantum gravitational fluctuations of the background metric. We consider the evolution of the massless minimally and massive non-minimally coupled scalar fields in de Sitter space. Through the matching conditions of wave functionals at some critical conformal time, we find that all the oscillatory and steady correction terms to the standard power spectrum for slow-roll inflation can be expressed in terms of the powers of one dimensionless critical quantity 1/z(subscript c), which is proportional to the ratio between the Hubble constant h during inflation and the cutoff energy scale M. The proportionality constant is the square root of the dimensionless parameter in the nonlinear dispersion relation. For some large values of this parameter, it becomes possible to detect the trans-Planckian effect in future CMB experiments.