# A Quantum Complete Prelude to Inflation

## TL;DR

This paper demonstrates that inflationary spacetimes can be extended quantum mechanically in a way that prevents quantum fields from crossing geodesic borders, ensuring a form of quantum completeness and stability near singularities.

## Contribution

It introduces the concept of quantum complete extensions of inflationary spacetimes, showing that quantum fields are confined by evolution semigroups, which prevents migration across geodesic borders.

## Key findings

- Quantum fields are prohibited from migrating across geodesic borders.
- Anisotropic Bianchi type-I cosmologies serve as quantum complete preludes to inflation.
- Quantum fields become free and enjoy contractive evolution near borders.

## Abstract

It is shown that the inflationary paradigm admits quantum complete extensions of space-time. The extended inflationary spacetimes still have geodesic borders, but quantum fields are prohibited from migrating across these borders by their evolution semigroups. The geodesic singularities lurking across the borders lack a physical description because the evolution semigroups give vanishing probabilistic support to quantum fields for populating regions bordering on these singularities. As an example, anisotropic Bianchi type-I cosmologies are shown to be quantum complete preludes to inflation. They admit Kasner-like geometries close to their geodesic borders. Quantum fields enjoy a contractive evolution in these asymptotic regions and ultimately become free. As a consequence, quantum probes cannot migrate across the geodesic border of Bianchi type-I cosmologies.