Loop quantum cosmology and tensor perturbations in the early universe

TL;DR

This paper investigates tensor perturbations in loop quantum cosmology, analyzing their spectrum and quantum corrections, with implications for early universe models and potential observational signatures.

Contribution

It provides a detailed analysis of tensor modes within loop quantum cosmology, including inverse-volume and holonomy corrections, and discusses their observational implications.

Findings

Tensor spectrum is blue tilted in superinflationary regime without holonomy corrections.

Quantum corrections in the quasi-classical regime slightly enhance the red tilt.

Standard perturbative techniques may be unreliable in highly nonperturbative background dynamics.

Abstract

We study the tensor modes of linear metric perturbations within an effective framework of loop quantum cosmology. After a review of inverse-volume and holonomy corrections in the background equations of motion, we solve the linearized tensor modes equations and extract their spectrum. Ignoring holonomy corrections, the tensor spectrum is blue tilted in the near-Planckian superinflationary regime and may be observationally disfavoured. However, in this case background dynamics is highly nonperturbative, hence the use of standard perturbative techniques may not be very reliable. On the other hand, in the quasi-classical regime the tensor index receives a small negative quantum correction, slightly enhancing the standard red tilt in slow-roll inflation. We discuss possible interpretations of this correction, which depends on the choice of semiclassical state.