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 ( ) 
that takes into account a number of important physical processes both within collapsing halos ( e.g. , H _ { 2 } cooling ) and in the intergalactic medium ( e.g. , H _ { 2 } cooling , Compton cooling , and photoionization heating ) .
We find that the Gunn-Peterson absorption data provide tight constraints on the power spectrum at small scales in a manner analogous to that derived from the cluster mass function .
Assuming that the efficiency of producing UV photons per baryon is constant , the constraint takes on the form \sigma _ { 8 } \Omega _ { 0 } ^ { 0.5 } \approx 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 } \sim 0.06 
is well below the value found by WMAP of 0.17 \pm ( 0.04 \sim 0.07 ) .
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 fixing the best fit WMAP determination of \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 } 
( all at 95 % confidence ) , and an effective UV-efficiency that was at least \sim 10 \times greater at z \gg 6 .
The implied UV-efficiencies is not unreasonable for stars , spanning the range from 10 ^ { -5.5 } \sim 10 ^ { -4 } .
These results indicate that the quasar and WMAP observations are consistent .
If future observations confirm an optical depth to electron scattering \tau _ { es } \sim 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 } \gtrsim 0.17 would require a more radical solution .