Affleck-Dine baryogenesis and inflation in supergravity with strongly stabilized moduli

Constructing models of inflation and/or baryogenesis in the context of = 1 supergravity is known to be difficult as the finite energy density during inflation typically generates large (order the Hubble scale) mass terms. This is the well-known η problem in inflation. The same effect gives masses along low energy flat directions of the scalar potential thus potentially preventing Affleck-Dine baryogenesis to occur. It has been shown that adding a chiral multiplet S coupled to the inflaton (with a shift symmetry) can serve to stabilize the inflationary potential and allows one to derive simple inflationary potentials without an η problem. Here, we show that by coupling the same stabilizing field S to the flat direction, may naturally lead to a negative mass-squared contribution to the flat direction thus generating the necessarily large vacuum expectation value needed to realize Affleck-Dine baryogenesis. We trace the evolution of the inflaton, stabilizer, and flat direction field, as well as a Polonyi-like modulus responsible for soft supersymmetry breaking.