Preinflationary perturbations from the closed algebra approach in loop quantum cosmology

In this paper, the scalar and tensor perturbations in the closed algebra approach of loop quantum cosmology are studied. Instead of the distant past in the contracting phase, we choose the moment at which the initial conditions are imposed to be the silent point, which circumvents the problem due to the signature change in the superinflationary phase and results in a well-defined Cauchy problem. For the ultraviolet and infrared modes, different approaches are applied in order to obtain analytical solutions with high accuracy. While previous numerical simulations reveal an exponentially divergent power spectrum in the ultraviolet regime, when the initial conditions are imposed in the remote contracting phase, we find a special set of initial conditions at the silent point, which can reproduce results that arc consistent with current observations.