Primordial power spectrum from the dressed metric approach in loop cosmologies

TL;DR

This study compares the primordial power spectra predictions of three loop quantum cosmology models, analyzing how different regularizations and treatments affect the spectrum's amplitude across regimes.

Contribution

It provides a detailed comparison of standard and modified loop quantum cosmology models, highlighting the impact of regularizations and ambiguities on primordial spectra predictions.

Findings

Power spectrum is scale-invariant in the ultra-violet regime across all models.

Significant amplitude differences (up to 50%) occur in the infra-red and intermediate regimes.

Infra-red power spectrum magnitude in mLQC-I is of the order of the Planck scale.

Abstract

We investigate the consequences of different regularizations and ambiguities in loop cosmological models on the predictions in the scalar and tensor primordial spectrum of the cosmic microwave background using the dressed metric approach. Three models, standard loop quantum cosmology (LQC), and two modified loop quantum cosmologies (mLQC-I and mLQC-II) arising from different regularizations of the Lorentzian term in the classical Hamiltonian constraint are explored for chaotic inflation in spatially-flat Friedmann-Lema\^itre-Robertson-Walker (FLRW) universe. In each model, two different treatments of the conjugate momentum of the scale factor are considered. The first one corresponds to the conventional treatment in dressed metric approach, and the second one is inspired from the hybrid approach which uses the effective Hamiltonian constraint. For these two choices, we find the power spectrum to be scale-invariant in the ultra-violet regime for all three models, but there is at least a $10\%$ relative difference in amplitude in the infra-red and intermediate regimes. All three models result in significant differences in the latter regimes. In mLQC-I, the magnitude of the power spectrum in the infra-red regime is of the order of Planck scale irrespective of the ambiguity in conjugate momentum of the scale factor. The relative difference in the amplitude of the power spectrum between LQC and mLQC-II can be as large as $50\%$ throughout the infra-red and intermediate regimes. Differences in amplitude due to regularizations and ambiguities turn out to be small in the ultra-violet regime.