Raising anti de Sitter vacua to de Sitter vacua in heterotic M theory

We explore the possibility of obtaining de Sitter vacua in strongly coupled heterotic models by adding various corrections to the supergravity potential energy. We show that, in a generic compactification scenario, Fayet-Iliopoulos terms can generate a de Sitter vacuum. The cosmological constant in this vacuum can be fine tuned to be consistent with observation. We also study moduli potentials in nonsupersymmetric compactifications of E₈×E₈ theory with anti five-branes and E₈×E¯₈ theory. We argue that they can be used to create a de Sitter vacuum only if some of the Kahler structure moduli are stabilized at values much less than the Calabi-Yau scale.