  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.
