Thompson Scattering in an Expanding Universe

TL;DR

This paper derives how the Thomson scattering cross section changes over time in an expanding universe, showing it varies inversely with the square of the cosmic scale factor, using perturbation methods in a cosmological context.

Contribution

It introduces a derivation of the time-dependent Thomson cross section in an expanding universe using the Einstein-Infeld-Hoffmann method and perturbation theory.

Findings

Thomson cross section varies as 1/R(t)^2 over time.

Derived equations of motion for electrons in an expanding universe.

Perturbative evaluation in an Einstein-de Sitter cosmology.

Abstract

The Thompson cross section for scattering of electromagnetic waves by a free electron in an expanding universe is derived here. The equations of motion of the electron are obtained using the Einstein-Infeld-Hoffmann (EIH) surface integral method. These integrals are evaluated approximately by perturbing off an Einstein-deSitter cosmological field. It is found that the Thompson cross section varies with time as the inverse square of the cosmic scale factor R(t).