Parametrization of the primordial power spectrum in loop quantum cosmology
Phys. Rev. D 113, 126026 – Published 25 June, 2026
DOI: https://doi.org/10.1103/hx8j-v94t
Abstract
We investigate the imprints on the angular power spectra of cosmological perturbations of a preinflationary bounce phase, as described by the hybrid and dressed metric approaches to loop quantum cosmology. For this purpose, we derive a new parametrization of the primordial power spectrum at the end of the inflationary regime. Apart from slow-roll coefficients and cosmological parameters that are present in the standard cosmological scenario without quantum modifications, this parametrization additionally depends only on preinflationary physics. More specifically, we find a dependence on the number of e-folds during the bounce epoch and on a characteristic suppression scale which, given the e-folds accumulated during cosmic evolution, is determined by the energy density at the bounce. Recall that this density depends on the Immirzi parameter and the area gap known from loop quantum gravity. This leads to a robust and accurate parametrization of the primordial power spectrum. Since in preinflationary scenarios there is no preferred vacuum state, we adopt the nonoscillatory adiabatic Hamiltonian diagonalization proposal, which selects a vacuum that is optimally adapted to the background dynamics and yields a nonoscillatory primordial power spectrum. With this choice, we show that the tensor-to-scalar ratio in both quantization approaches coincides with its expression in the standard model when the observed scales are not much smaller than the power-suppressed region. Computing also the angular power spectrum, we find that, for a total cosmic expansion of about 140 e-folds, both the hybrid and the dressed metric approaches exhibit excellent agreement with Planck data at high multipoles, while apparently improving the fit with respect to for low multipole numbers.