Quantum Fields in a Big Crunch/Big Bang Spacetime

TL;DR

This paper investigates quantum field behavior during a Big Crunch/Big Bang transition, demonstrating a unique matching rule that preserves the vacuum state and results in finite particle production when interactions are considered.

Contribution

It introduces a novel matching rule for quantum fields across a cosmological singularity, ensuring a consistent vacuum state and finite particle production in a cyclic universe model.

Findings

No particle production for free fields in the adiabatic vacuum.

Finite particle production when interactions are included.

Establishes a formal link to quantum field theory on de Sitter spacetime.

Abstract

We consider quantum field theory on a spacetime representing the Big Crunch/Big Bang transition postulated in the ekpyrotic or cyclic cosmologies. We show via several independent methods that an essentially unique matching rule holds connecting the incoming state, in which a single extra dimension shrinks to zero, to the outgoing state in which it re-expands at the same rate. For free fields in our construction there is no particle production from the incoming adiabatic vacuum. When interactions are included the total particle production for fixed external momentum is finite at tree level. We discuss a formal correspondence between our construction and quantum field theory on de Sitter spacetime.