  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: $a\sim\exp t^{1-p}$. This gives "dark energy", with an
equivalent cosmological constant that decays in time like $t^{-2p}$, which
avoids the "fine-tuning" problem. The power law predicts a simple relation for
the galactic redshift. Comparison with data leads to the speculation that the
universe experienced a crossover transition, which was completed about 7
billion years ago.
