  We study Higgs inflation in the context of generalized G-inflation, i.e. the
most general single-field inflation model with second-order field equations.
The four variants of Higgs inflation proposed so far in the literature can be
accommodated at one time in our framework. We also propose yet another class of
Higgs inflation, the running Einstein inflation model, that can naturally arise
from the generalized G-inflation framework. As a result, five Higgs inflation
models in all should be discussed on an equal footing. Concise formulas for
primordial fluctuations in these generalized Higgs inflation models are
provided, which will be helpful to determine which model is favored from the
future experiments and observations such as the Large Hadron Collider and the
Planck satellite.
