  We investigate the Dvali-Gabadadze-Porrati (DGP) model corrected by higher
curvature brane terms. We show that these corrections have a dramatic impact on
the spectrum of the model at the linearized level. Owing to the presence of
higher derivatives in the field equations very massive ghost excitations with
mass of order of Planck mass are generated in the ordinary branch of the model.
These excitations describe an instability of Minkowski vacuum with time-scale
of order of the Hubble time. At large distances these tachyonic excitations are
expected to decouple from brane-localized matter. Our modified DGP model
represents therefore a very promising framework for solving of the cosmological
constant problem, in which Planck-scale physics is responsible for the
elementary excitations driving the accelerated expansion of the universe, but
the time-scale of the instability is settled by gravitational physics at large
scales.
