Inflation and the fine-tuning problem

Abstract

I describe a recently derived stochastic approach to inflaton dynamics which can address some serious problems associated with conventional inflationary theory. Using this theory I derive an exact solution to the stochastic dynamics for the case of a $\ensuremath{\lambda}{\ensuremath{\varphi}}^{4}$ potential and use it to study the generated primordial density fluctuations. It is found that on both subhorizon and superhorizon scales the theory predicts Gaussian fluctuations to a very high accuracy along with a near-scale-invariant spectrum. Of most interest is that the amplitude constraint is found to be satisfied for $\ensuremath{\lambda}\ensuremath{\sim}{10}^{\ensuremath{-}5}$ rather than for $\ensuremath{\lambda}\ensuremath{\sim}{10}^{\ensuremath{-}14}$ of the conventional theory. This represents a dramatic easing of the fine-tuning constraints, a feature likely to generalize to a wide range of potentials.