D3-D7 inflationary model and M theory

A proposal is made for a cosmological D3-D7 model with a constant magnetic flux along the D7 world volume. It describes an $\mathcal{N}=2\mathrm{}$ 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.