# Preinflationary perturbations from the closed algebra approach in loop quantum cosmology

## TL;DR

This paper investigates scalar and tensor perturbations in loop quantum cosmology's closed algebra approach, proposing initial conditions at the silent point to produce observationally consistent power spectra, addressing previous divergence issues.

## Contribution

It introduces a novel initial condition setup at the silent point in the super-inflationary phase, improving the analytical and numerical modeling of perturbations in loop quantum cosmology.

## Key findings

- Initial conditions at the silent point yield power spectra consistent with observations.
- Different approaches for UV and IR modes enable high-accuracy analytical solutions.
- Reproduces observational results despite previous divergence problems.

## Abstract

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 super-inflationary 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 are consistent with current observations.