Higgs inflation with the Holst and the Nieh-Yan term

TL;DR

This paper explores how the Holst and Nieh-Yan terms, added to the gravitational action in loop quantum gravity, influence Higgs inflation, revealing that the Holst term can support successful inflation with predictions similar to standard models.

Contribution

It derives inflationary predictions considering non-minimal couplings of Holst and Nieh-Yan terms, highlighting their potential to alter inflationary observables.

Findings

Holst term alone can support successful Higgs inflation.

Predictions span the range of upcoming experimental sensitivities.

Nieh-Yan term alone cannot produce successful inflation.

Abstract

The action of loop quantum gravity includes the Holst term and/or the Nieh-Yan term in addition to the Ricci scalar. These terms are expected to couple non-minimally to the Higgs. Thus the Holst and Nieh-Yan terms contribute to the classical equations of motion, and they can have a significant impact on inflation. We derive inflationary predictions in the parameter space of the non-minimal couplings, including non-minimally coupled terms up to dimension 4. Successful inflation is possible even with zero or negative coupling of the Ricci scalar. Notably, inflation supported by the non-minimally coupled Holst term alone gives almost the same observables as the original metric formulation plateau Higgs inflation. A non-minimally coupled Nieh-Yan term alone cannot give successful inflation. When all three terms are considered, the predictions for the spectral index and tensor-to-scalar ratio span almost the whole range probed by upcoming experiments. This is not true for the running of the spectral index, and many cases are highly tuned.