  This paper studies the quantum corrections to the Higgs inflation model in
the context of the Einstein-Cartan (E-C) gravity in the large-$ N $ limit with
$N$ being the number of real scalar components in Higgs. Recently, it is
realized that the Higgs inflation in the E-C formalism smoothly connects those
in the metric and the Palatini formalisms in the presence of a non-minimal
coupling between the Higgs fields and the Nieh-Yan term. This motivates us to
investigate the quantum corrections to the E-C Higgs inflation and to clarify
how the Ricci curvature squared $ R^2 $ induced by the quantum corrections
succeeds in Ultraviolet (UV)-extending the Higgs inflation in metric formalism
while it fails in the Palatini case. We show that a generalized $ R^2 $-term
required for the renormalization in the E-C formalism induces a new scalar
degree of freedom (DoF), the scalaron, which gradually decouples with the
system due to its increasing mass as approaching the Palatini limit. The
presence of the scalaron extends the UV cutoff at vacuum of the original model
except for the parameter space close to the Palatini limit. This UV-extension
is expected to solve the strong coupling problem that may exist during
(p)reheating in the absence of the scalaron.
