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 ξ. This expression is used to derive an effective potential, which agrees with earlier results obtained in Landau gauge, and the independence of ξ explicitly indicates the gauge-invariance of the calculation. 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 H2 in the absence of additional chiral matter. The contribution due to a chiral multiplet running in the loop is however non-vanishing in the presence of Yukawa couplings to the Higgs field. When applied to a flat direction of the MSSM with VEV w, a logarithmically running correction of order h2H2w2 arises, where h is a 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.