  Current data of high-redshift absorption-line systems imply that hydrogen
reionization occurred before redshifts of about 5. Previous works on
reionization by the first stars or quasars have shown that such scenarios are
described by a large number of cosmological and astrophysical parameters. Here,
we adopt a semi-analytic model of stellar reionization in order to quantify how
the optical depth to reionization depends on such parameters, and combine this
with constraints from the cosmic microwave background (CMB). We find this
approach to be particularly useful in alleviating the well-known degeneracy in
CMB parameter extraction between the optical depth to reionization and the
amplitude of the primordial power spectrum, due to the complementary
information from the reionization model. We also examine translating
independent limits on astrophysical parameters into those on cosmological
parameters, or conversely, how improved determinations of cosmological
parameters will constrain astrophysical unknowns.
