  We carry out a theoretical investigation of overpressurized superfluid phases
of He-4 by means of quantum Monte Carlo (QMC) simulations. As a function of
density, we study structural and superfluid properties, and estimate the energy
of the roton excitation by inverting imaginary-time density correlation
functions computed by QMC, using Maximum Entropy. We estimate the pressure at
which the roton energy vanishes to be about 100 bars, which we identify with
the spinodal density, i.e., the upper limit for the existence of a metastable
superfluid phase.
