Inflationary observables in loop quantum cosmology

TL;DR

This paper computes cosmological observables in loop quantum cosmology with inverse-volume corrections, analyzing inflationary solutions, perturbations, and their implications for early universe phenomenology.

Contribution

It provides a comprehensive calculation of inflationary observables in loop quantum cosmology, including scalar and tensor perturbations with quantum corrections, and discusses parametrization effects.

Findings

Computation of scalar and tensor indices with quantum corrections.

Conservation of comoving curvature perturbation at large scales.

Potentially sizable quantum effects on tensor-to-scalar ratio.

Abstract

The full set of cosmological observables coming from linear scalar and tensor perturbations of loop quantum cosmology is computed in the presence of inverse-volume corrections. Background inflationary solutions are found at linear order in the quantum corrections; depending on the values of quantization parameters, they obey an exact or perturbed power-law expansion in conformal time. The comoving curvature perturbation is shown to be conserved at large scales, just as in the classical case. Its associated Mukhanov equation is obtained and solved. Combined with the results for tensor modes, this yields the scalar and tensor indices, their running, and the tensor-to-scalar ratio, which are all first order in the quantum correction. The latter could be sizable in phenomenological scenarios. Contrary to a pure minisuperspace parametrization, the lattice refinement parametrization is in agreement with both anomaly cancellation and our results on background solutions and linear perturbations. The issue of the choice of parametrization is also discussed in relation with a possible superluminal propagation of perturbative modes, and conclusions for quantum spacetime structure are drawn.