On Metastability in Supersymmetric Models

We make a critical reappraisal of `unbounded-from-below' (UFB) constraints in the MSSM and R-parity violating models. We explain why the `traditional' UFB bounds are neither necessary nor sufficient and propose, instead, a sufficient condition which ensures that there are no local minima along the flat directions. This conservative (but meaningful) condition divides the parameter space into regions which are allowed, regardless of cosmology, and regions in which cosmology is expected to play a major role. We study both conditions at low tan-beta and obtain analytic approximations to the UFB bounds for all low tan-beta (<15). Finally we show that R-parity violation just below current experimental limits avoids UFB problems by lifting the dangerous flat directions.