Particle creation and particle number in an expanding universe

TL;DR

This paper explains the development of a method to define particle number in an expanding universe, revealing particle creation from vacuum and its implications for cosmology, including the inflationary perturbations.

Contribution

The paper introduces the adiabatic regularization method for defining particle number in curved spacetime and demonstrates the absence of particle creation in conformally invariant fields in flat FLRW universes.

Findings

Particles are created from vacuum in expanding universes.

Conformal invariance prevents particle creation for certain fields.

The method links particle creation to inflationary perturbations.

Abstract

I describe the logical basis of the method that I developed in 1962 and 1963 to define a quantum operator corresponding to the observable particle number of a quantized free scalar field in a spatially-flat isotropically expanding (and/or contracting) universe. This work also showed for the first time that particles were created from the vacuum by the curved space-time of an expanding spatially-flat FLRW universe. The same process is responsible for creating the nearly scale-invariant spectrum of quantized perturbations of the inflaton scalar field during the inflationary stage of the expansion of the universe. I explain how the method that I used to obtain the observable particle number operator involved adiabatic invariance of the particle number (hence, the name adiabatic regularization) and the quantum theory of measurement of particle number in an expanding universe. I also show how I was led in a surprising way, to the discovery in 1964 that there would be no particle creation by these spatially-flat FLRW universes for free fields of any integer or half-integer spin satisfying field equations that are invariant under conformal transformations of the metric. The methods I used to define adiabatic regularization for particle number, were based on generally-covariant concepts like adiabatic invariance and measurement that were fundamental and determined results that were unique to each given adiabatic order.