  Higgs G-inflation is a Higgs inflation model with a generalized Galileon term
added to the standard model Higgs field, which realizes inflation compatible
with observations. Recently, it was claimed that the generalized Galileon term
induces instabilities during the oscillation phase, and that the simplest Higgs
G-inflation model inevitably suffers from this problem. In this paper, we
extend the original Higgs G-inflation Lagrangian to a more general form, namely
introducing a higher-order kinetic term and generalizing the form of the
Galileon term, so that the Higgs field can oscillate after inflation without
encountering instabilities. Moreover, it accommodates a large region of the n_s
- r plane, most of which is consistent with current observations, leading us to
expect the detection of B-mode polarization in the cosmic microwave background
in the near future.
