The Dispersion-Redshift Relation of Fast Radio Bursts and the Intergalactic Baryon Fraction It Implies

The dispersion measure of a fast radio burst counts the free electrons along its line of sight, and its average growth with redshift — the Macquart relation — weighs the ionised intergalactic medium directly. This paper evaluates the relation from a stated cosmology: with all cosmic baryons ionised and placed in the intergalactic medium, the predicted intergalactic dispersion is 532 pc per cubic centimetre at redshift 0.5, 1.09e+03 at redshift 1, 2.12e+03 at redshift 2 and 3.03e+03 at redshift 3. Inverting an adopted observed mean of 800 pc per cubic centimetre at redshift 1 gives an intergalactic baryon fraction of 0.737, leaving 0.263 of baryons in galaxies, their halos and collapsed structures. The local slope of the relation at redshift 1 is 1.09e+03 pc per cubic centimetre per unit redshift, which sets the redshift precision a dispersion measurement can deliver. The computation is a numerical integral over the expansion history, with the ionisation factor stated explicitly.