Radiative Lifting of Flat Directions of the MSSM in de Sitter Background

The one-loop effective potential for a charged scalar field in de Sitter background is studied. We derive an approximate form for the gauge boson propagator with a general covariant gauge-fixing parameter \xi. This expression is used to derive an explicitly gauge-invariant effective potential, which agrees with earlier results obtained in Landau gauge. Adding the scalar- and fermion-loop contributions, that arise in a supersymmetric Higgs model, we find that the effective potential is vanishing to first order in the Hubble rate H^2. The contribution due to a chiral multiplet running in the loop is however non-vanishing. When applied to a flat direction of the MSSM with VEV w, a logarithmically running correction of order $h^2 H^2 w^2$ arises, where h is Yukawa coupling. This is of particular importance for D-term inflation or models endowed with a Heisenberg symmetry, where Hubble scale mass terms for flat directions from supergravity corrections are absent.