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 non-supersymmetric compactifications of $E_8\times E_8$ theory with anti five-branes and $E_8\times {\bar{E}}_8$ 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.