PRESERVING FLAT DIRECTIONS DURING INFLATION

Supersymmetry is generally broken by the non-vanishing vacuum energy d ensity present during inflation. In supergravity models, such a source of supersymmetry breaking typically makes a contribution to scalar ma sses of order m(-2) similar to H-2, where H-2 similar to V/M(p)(2) is the Hubble parameter during inflation. We show that in supergravity mo dels which possess a Heisenberg symmetry, supersymmetry breaking makes no contribution to scalar masses, leaving supersymmetric flat directi ons flat at tree-level, One-loop corrections in general lift the flat directions, but naturally give small negative squared masses similar t o -g(2)H(2)/(4 pi)(2) for, all flat directions that do not involve the stop. No-scale supergravity of the SU(N, 1) type and the untwisted se ctors from orbifold compactifications are special cases of this genera l set of models. We point out the importance of the preservation of fl at directions for baryogenesis.