This chapter focuses on the central motivation for much of what can be labeled ‘quantum gravity’ in the earliest phases of research, namely that it provides a potentially abundant resource for curing problems in quantum field theory. While it was rare to have fully worked out examples along these lines, it provided a much needed impetus to the study of quantum gravity at a time when there were few other reasons to bother with it. The primary problem was the ubiquitous divergences, which proved extremely stubborn and worrying to field theorists. Not all of the approaches were looked at involved gravitation directly, however, and focused more on ways of generating a discrete structure (with a minimal length or maximum energy) that would provide a physical cutoff, thus grounding a finite theory. These filtered through into gravitational research only later than our timeframe, in a variety of ways, including the small scales necessarily reached in gravitational collapse.
GRAPH-THEORY INDUCED GRAVITY AND STRONGLY-DEGENERATE FERMIONS IN A SELF-CONSISTENT EINSTEIN UNIVERSE
