Back-door fine-tuning in supersymmetric low scale inflation

Low scale inflation has many virtues and it has been claimed that its natural realisation in the supersymmetric Standard Model can be achieved rather easily. In this Letter we demonstrate that the dynamics of the hidden sector responsible for supersymmetry breaking and the structure of the soft terms affects significantly, and in fact often spoils, the would-be inflationary dynamics. We also point out that the issue of the cosmological constant cancellation in the post-inflationary vacuum strongly affects supersymmetric inflation. It is important to note the crucial difference between the freezing of the modulus and actually stabilising it-the first approach misses parts of the scalar potential which turn out to be relevant for inflation. We argue that it is more likely that low scale supersymmetric inflation occurs at a critical point at the origin of the field space than at an inflection point away from the origin, as the necessary fine-tuning in the second case is typically larger.