In ation and Supergravity No-Go Theorem

We introduce the motivation for in ation as an additional phase of the early universe and then discuss some of the ways in which its theoretical grounding is being approached from the point of view of stringy cosmology, and, speci cally, its low-energy regime supergravity. F-term and D-term models are discussed and some limits on the admissible potentials are derived. A supergravity no-go theorem is then discussed. We prove that a very large class of ten-dimensional supergravity models does not have a stable compacti cation into either de Sitter or Minkowski space. We conclude that string-theoretic non-perturbative methods must be used to create such vacua and only then can in ation be properly modelled and we give an example for just such a calculation. Unfortunately, even though the moduli remain xed, no in ation occurs. We conclude with a statement that no working in ationary model with stable moduli has yet been found.