A Note on Infinities in Eternal Inflation

TL;DR

This paper critiques the assumption of point-like universe nucleation in eternal inflation, arguing that considering a finite nucleation region resolves the infinite universe paradox and aligns better with quantum cosmology.

Contribution

It challenges the traditional point-like nucleation model in eternal inflation, proposing that finite nucleation regions prevent the formation of infinite universes at finite times.

Findings

Point-like nucleation leads to infinite universes at finite proper-time.

Finite nucleation regions result in universes that become infinite only after infinite proper-time.

The critique aligns eternal inflation models with quantum cosmology principles.

Abstract

In some well-known scenarios of open-universe eternal inflation, developed by Vilenkin and co-workers, a large number of universes nucleate and thermalize within the eternally inflating mega-universe. According to the proposal, each universe nucleates at a point, and therefore the boundary of the nucleated universe is a space-like surface nearly coincident with the future light cone emanating from the point of nucleation, all points of which have the same proper-time. This leads the authors to conclude that at the proper-time t = t_{nuc} at which any such nucleation occurs, an infinite open universe comes into existence. We point out that this is due entirely to the supposition of the nucleation occurring at a single point, which in light of quantum cosmology seems difficult to support. Even an infinitesimal space-like length at the moment of nucleation gives a rather different result -- the boundary of the nucleating universe evolves in proper-time and becomes infinite only in an infinite time. The alleged infinity is never attained at any finite time.