Scalar Field Cosmology I: Asymptotic Freedom and the Initial-Value Problem

Understand

The purpose of this work is to use a renormalized quantum scalar field to investigate very early cosmology, in the Planck era immediately following the big bang.

• Renormalization effects make the field potential dependent on length scale, and are important during the big bang era.
• We use the asymptotically free Halpern-Huang scalar field, which is derived from renormalization-group analysis, and solve Einstein's equation with Robertson-Walker metric as an initial-value problem.
• The main prediction is that the Hubble parameter follows a power law: $H\equiv\dot{a}/a\sim t^{-p}$, and the universe expands at an accelerated rate: $a\sim\exp t^{1-p}$.