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

TL;DR

This paper investigates early universe cosmology using a renormalized quantum scalar field, predicting accelerated expansion and dark energy behavior consistent with observational data, and addressing the fine-tuning problem.

Contribution

It introduces the use of an asymptotically free Halpern-Huang scalar field in Einstein's equations to model early universe dynamics with novel predictions.

Findings

Hubble parameter follows a power law: H ~ t^{-p}

Universe expands with accelerated rate: a ~ exp(t^{1-p})

Dark energy decays as t^{-2p}, avoiding fine-tuning

Abstract

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.