Electromagnetic dispersion in the Brans-Dicke cosmology

Abstract

In this letter, the dispersion of an electromagnetic wave in an ionized cosmic medium is calculated for the spatially flat form of the Brans-Dieke cosmology. Consider a cosmological model which is, like all the Robertson-Walker universes, conformally fiat. Let t be a t ime co-ordinate for which the line element is proportional to that of special relativity. Then, on the light-cone dr ~ cdt, r being the radial coordinate and e the speed of light in empty space. For spatially fiat cosmologies, the cosmic t ime t is related to t by dt/dt ~ R, R being both the scale factor and the conformal factor (1). Let n denote the refractive index for an electromagnetic wave propagating through the cosmic medium; subscripts 1 and 0 will denote values of quantit ies at the times of emission and reception, respectively. For the simplest plasma model, n 2 : 1 f ~ / p in which ]~ is the plasma hequency and the wave frequency / is tha t measured by a co-moving ovserver; with R0= 1, ] = ]o/2. T h e local group speed is cn, so radiation is delayed, locally, relative to empty-space propagation, by a t ime (n -~ 1) per uni t time. The total time delay, relative to free-space propagation, is T on the t scale or on the t scale, where