# Hybrid loop quantum cosmology and predictions for the cosmic microwave background

## TL;DR

This paper explores how hybrid loop quantum cosmology affects primordial perturbations and predicts observable signatures in the cosmic microwave background, including tensor modes and quantum geometry effects, comparing these with Planck data.

## Contribution

It extends previous scalar perturbation studies by including tensor modes and analyzing their power spectra within the hybrid loop quantum cosmology framework.

## Key findings

- Predicted power spectra for scalar and tensor perturbations.
- Analyzed tensor-to-scalar ratio and spectral index consistency.
- Compared quantum geometry effects with observational data.

## Abstract

We investigate the consequences of the hybrid quantization approach for primordial perturbations in loop quantum cosmology, obtaining predictions for the cosmic microwave background and comparing them with data collected by the Planck mission. In this work, we complete previous studies about the scalar perturbations and incorporate tensor modes. We compute their power spectrum for a variety of vacuum states. We then analyze the tensor-to-scalar ratio and the consistency relation between this quantity and the spectral index of the tensor power spectrum. We also compute the temperature-temperature, electric-electric, temperature-electric, and magnetic-magnetic correlation functions. Finally, we discuss the effects of the quantum geometry in these correlation functions and confront them with observations.