[Paper Review] The Creation of Particles in an Expanding Universe

Leonard Parker|ArXiv.org|Jul 7, 2025

Computational Physics and Python Applications45 citations

TL;DR

The thesis analyzes particle creation by a classical gravitational field interacting with quantized spin-0 and spin-1/2 fields in an expanding universe, deriving an adiabatic framework to bound present-day creation rates and showing massless higher-spin fields undergo no production in isotropic expansion.

ABSTRACT

This document is the Ph.D. thesis of Leonard Parker, submitted to Harvard University in 1966. Over the decades, several generations of physicists have been introduced to the concept of particle creation by gravitational fields, a phenomenon that has become a cornerstone in exploring the interplay between gravitation and quantum theory. Yet, the foundational breakthrough that led to the prediction and understanding of this phenomenon remains unfamiliar to many. In the interest of historical accuracy and in recognition of a seminal contribution to physics, the thesis has been retyped and made it freely available as an open-access (arXiv) document. The reissued thesis is accompanied by a Foreword that places the work in its proper historical context. As the team responsible for this new edition, we (Antonio Ferreiro, José Navarro-Salas, and Silvia Pla) hope that future generations will continue to draw inspiration from this pioneering text.

Motivation & Objective

• Motivate the study of particle creation by classical gravity within quantum field theory and general relativity.
• Derive a framework to bound the present-day creation rate per unit volume for spin-0 and spin-1/2 particles.
• Investigate particle creation for massless fields of various spins and identify conformal invariance implications.
• Explore the dependence of creation on the expansion history without invoking perturbative methods.

Proposed method

• Formulate the quantized Klein-Gordon and Dirac equations in a 3-dimensionally Euclidean expanding universe.
• Use an adiabatic approximation to express field evolution during expansion and define time-independent, unique creation/annihilation operators.
• Relate particle number to changes in the number operator between widely separated measurements to obtain upper bounds.
• Handle divergences from naive mode summations by adopting the adiabatic-operator framework.
• Derive that particle creation occurs in pairs and conserve matter-antimatter balance.
• Extend analysis to massless fields via conformal invariance arguments to determine when creation is forbidden.

Experimental results

Research questions

• RQ1 How does a classical expanding spacetime lead to particle creation in quantized fields of spin 0 and 1/2?
• RQ2 Can we bound the present-day particle creation rate per unit volume for mesons and fermions in the actual expanding universe?
• RQ3 What role does conformal invariance play in the production (or suppression) of massless fields of various spins?
• RQ4 How does the choice of expansion history affect observable particle numbers and avoid perturbative inconsistencies?

Key findings

• For spin-0 and spin-1/2 fields, the present-day upper bounds on creation rates per unit volume are finite and depend on Hubble’s constant, current matter density, and particle mass.
• Upper bounds include: π-mesons ≤ 10^-105 g cm^-3 s^-1, electrons ≤ 10^-69 g cm^-3 s^-1, protons ≤ 10^-64 g cm^-3 s^-1, implying less than one proton per litre per 10^30 years.
• Particle creation occurs in pairs (even for neutral particles) with equal matter and antimatter production.
• Massless particles of non-zero spin are not produced in isotropically expanding universes due to conformal invariance, while minimally coupled massless scalars can be produced under certain conditions.
• The formalism yields a consistent set of time-independent creation/annihilation operators within an adiabatic time interval, resolving divergences in naive mode summations.