Soft supersymmetry breaking with tiny cosmological constant in flux compactified N=1 Supergravity

Using the flux compactification scenario in a generic supergravity model we construct a set of conditions which are necessary to generate de-Sitter or anti de-Sitter vacua for appropriate choices of the parameters in superpotential. It is shown that a mass spectrum consistent with softly broken TeV scale supersymmetry in a minimal supersymmetric standard model at the observable sector can be obtained along with a tiny cosmological constant when the Kahler and superpotential of the hidden sector satisfy a set of general constraints. Constructing a specific model with Kahler and superpotentials which satisfy the above constraints, it is demonstrated that all the hidden sector fields have vacuum expectation values close to Planck scale and the resulting low energy potential does not have any flat direction.