  In this paper we show that the Germani-Kehagias model of Higgs inflation (or
New Higgs Inflation), where the Higgs boson is kinetically non-minimally
coupled to the Einstein tensor is in perfect compatibility with the latest
Planck and BICEP2 data. Moreover, we show that the tension between the Planck
and BICEP2 data can be relieved within the New Higgs inflation scenario by a
negative running of the spectral index. Regarding the unitarity of the model,
we argue that it is unitary throughout the evolution of the Universe. Weak
couplings in the Higgs-Higgs and Higgs-graviton sectors are provided by a large
background dependent cut-off scale during inflation. In the same regime, the W
and Z gauge bosons acquire a very large mass, thus decouple. On the other hand,
if they are also non-minimally coupled to the Higgs boson, their effective
masses can be enormously reduced. In this case, the W and Z bosons are no
longer decoupled. After inflation, the New Higgs model is well approximated by
a quartic Galileon with a renormalizable potential. We argue that this can
unitarily create the right conditions for inflation to eventually start.

High Energy Physics - Phenomenology;Cosmology and Nongalactic Astrophysics;General Relativity and Quantum Cosmology;High Energy Physics - Theory