A proposal is made for a cosmological D3/D7 model with a constant magnetic
flux along the D7 world-volume. It describes an N=2 gauge model with
Fayet-Iliopoulos terms and the potential of the hybrid P-term inflation. The
motion of the D3-brane towards D7 in a phase with spontaneously broken
supersymmetry provides a period of slow-roll inflation in the de Sitter valley,
the role of the inflaton being played by the distance between D3 and D7-branes.
After tachyon condensation a supersymmetric ground state is formed: a D3/D7
bound state corresponding to an Abelian non-linear (non-commutative) instanton.
In this model the existence of a non-vanishing cosmological constant is
associated with the resolution of the instanton singularity. We discuss a
possible embedding of this model into a compactified M-theory setup.Comment: 30 pages, 4 figures, LaTeX; v2, minor typos corrected, one reference
adde
