Cosmological consequences of a principle of finite amplitudes

TL;DR

This paper investigates the cosmological implications of a principle requiring finite semi-classical transition amplitudes, leading to constraints on early universe models and favoring certain proposals like the no-boundary scenario.

Contribution

It introduces a quantum-inspired criterion for finite transition amplitudes that rules out eternal inflation and cyclic universes, impacting early universe cosmology models.

Findings

Eternal inflation and cyclic universes are ruled out.

Quadratic gravity favors initial conditions for inflation.

Infinite curvature corrections eliminate big bang spacetimes.

Abstract

Over 30 years ago, Barrow & Tipler proposed the principle according to which the action integrated over the entire 4-manifold describing the universe should be finite. Here we explore the cosmological consequences of a related criterion, namely that semi-classical transition amplitudes from the early universe up to current field values should be well defined. On a classical level, our criterion is weaker than the Barrow-Tipler principle, but it has the advantage of being sensitive to quantum effects. We find significant consequences for early universe models, in particular: eternal inflation and strictly cyclic universes are ruled out. Within general relativity, the first phase of evolution cannot be inflationary, and it can be ekpyrotic only if the scalar field potential is trustworthy over an infinite field range. Quadratic gravity eliminates all non-accelerating backgrounds near a putative big bang (thus imposing favourable initial conditions for inflation), while the expected infinite series of higher-curvature quantum corrections eliminates Lorentzian big bang spacetimes altogether. The scenarios that work best with the principle of finite amplitudes are the no-boundary proposal, which gives finite amplitudes in all dynamical theories that we have studied, and string-inspired loitering phases. We also comment on the relationship of our proposal to the swampland conjectures.