  We find a description of hybrid inflation in (3+1)-dimensions using brane
dynamics of Hanany-Witten type. P-term inflation/acceleration of the universe
with the hybrid potential has a slow-roll de Sitter stage and a waterfall stage
which leads towards an N=2 supersymmetric ground state. We identify the
slow-roll stage of inflation with a non-supersymmetric `Coulomb phase' with
Fayet-Iliopoulos term. This stage ends when the mass squared of one of the
scalars in the hypermultiplet becomes negative. At that moment the brane system
starts undergoing a phase transition via tachyon condensation to a fully
Higgsed supersymmetric vacuum which is the absolute ground state of P-term
inflation. A string theory/cosmology dictionary is provided, which leads to
constraints on parameters of the brane construction from cosmological
experiments. We display a splitting of mass levels reminiscent of the Zeeman
effect due to spontaneous supersymmetry breaking.

High Energy Physics - Theory;High Energy Physics - Phenomenology