Higgs inflation with the Holst and the Nieh–Yan term

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 nonminimally 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 nonminimal couplings, including nonminimally 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 nonminimally coupled Holst term alone gives almost the same observables as the original metric formulation plateau Higgs inflation. A nonminimally 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.