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of the primordial gas from starlight produced by the first stars (the so-called Population III stars). The affect that reionization has on the matter in the Universe at early times is captured by using the optical depth 

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where n$_{e}$ is the number density of free electrons and σ$_{T}$ is the Thomson scattering cross-section. With this definition, the probability that a photon that is observed now that was emitted between the time of recombination and reionization, at a time t , has traveled freely is e − τ ( t $^{)}$, with the value being practically constant for emission times between recombination and 

