  We present constraints on cosmological and star formation parameters based on
combining observations of the Wilkinson Microwave Anisotropy Probe (WMAP) and
high-redshift quasars from the Sloan Digital Sky Survey (SDSS). We use a
semi-analytic model for reionization (Chiu and Ostriker 2000) that takes into
account a number of important physical processes both within collapsing halos
and in the intergalactic medium. Assuming that the efficiency of producing UV
photons per baryon is constant, we derive a constraint of the form sigma_8
Omega_0^0.5~0.33 in a flat, Lambda-dominated universe with h=0.72, n=0.99, and
Omega_b h^2=0.024. However, the calculated optical depth to electron scattering
of tau_es~0.06 is well below the value found by WMAP of 0.17+/-(0.04~0.07)
(Spergel et al 2003). Since the WMAP constraints on tau_es are somewhat
degenerate with the value of the spectral index n, we then permit the
primordial spectral index n to float and fix Omega_0 h^2=0.14, while
normalizing the power spectrum using WMAP. In addition, we allow the
UV-efficiency to have time-dependence. Combining the WMAP constraints with the
quasar transmission data, our analysis then favors a model with
tau_es=0.11^{+0.02}_{-0.03}, n=0.96^{+0.02}_{-0.03}$, implying
sigma_8=0.83^{+0.03}_{-0.05} (95% confidence), and an effective UV-efficiency
that was at least ~10x greater at z >> 6. These results indicate that the
quasar and WMAP observations are consistent. If future observations confirm an
optical depth to electron scattering tau_es~0.1, then it would appear that no
more "exotic" sources of UV-photons, such as mini-quasars or AGNs, are
necessary; but our analysis indicates that a determination of tau_es>~0.17
would require a more radical solution.
