 Reionization optical depth in an open matter universe

ID: reionization-optical-depth-in-an-open-matter-universe

For full hydrogen ionization after instantaneous reionization,

n_{e 0} = 3 Ω_{b} H_{0}^{2} / (8 π G m_{p})

and

H (z) = H_{0} (1 + z) 1 + Ω_{m} z

. Integrating Thomson scattering gives

κ = \frac{Ω _{b} C _{H}}{Ω _{m}^{2}} {u^{3} - 1 - 3 (1 - Ω_{m}) (u - 1)}, u = 1 + Ω_{m} z_{re}, C_{H} = \frac{σ _{T} c H _{0}}{4 π G m _{p}} .

For

Ω_{m} = 1

κ = Ω_{b} C_{H} [(1 + z_{re})^{3/2} - 1]

. At fixed baryon density and redshift, lowering the matter density reduces the expansion rate and increases the optical depth.

// Target: cosmology.bigb

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