Critical dynamics in the early universe

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Abstract
Methods and concepts for the study of phase transitions mediated by a time-dependent order-parameter field in curved spacetimes are discussed. A practical example is the derivation of an effective (quasi-)potential for the description of 'slow-roll' inflation in the early universe. The author first summarizes early results on viewing the symmetry behavior of constant background fields in curved but static spacetimes as finite size effect, and the use of derivative expansions for constructing effective actions for slowly-varying background fields. He then introduces the notion of a dynamical finite size effect to explain how an exponential expansion of the scale factor imparts a finite size to the system and how the symmetry behavior in de Sitter space can be understood qualitatively in this light. He reasons why exponential inflation can be described equivalently by a scale transformation, thus rendering this special class of dynamics as effectively static. Finally he shows how, in this view, one can treat the class of 'slow-roll' inflation as a dynamic perturbation off the effectively static class of exponential inflation and understand it as a dynamical critical phenomenon in cosmology.
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