Because the baryon-to-photon ratio \eta _ { 10 } is in some doubt , we drop nucleosynthetic constraints on \eta _ { 10 } and fit the three cosmological parameters ( h, \Omega _ { \mathrm { M } } , \eta _ { 10 } ) to four observational constraints : Hubble parameter h _ { \mathrm { o } } = 0.70 \pm 0.15 , age of the universe t _ { \mathrm { o } } = 14 ^ { +7 } _ { -2 } Gyr , cluster gas fraction f _ { \mathrm { o } } \equiv f _ { \mathrm { G } } h ^ { 3 / 2 } = 0.060 \pm 0.006 , and effective shape parameter \Gamma _ { \mathrm { o } } = 0.255 \pm 0.017 .
Errors quoted are 1 \sigma , and we assume Gaussian statistics .
We experiment with a fifth constraint \Omega _ { \mathrm { o } } = 0.2 \pm 0.1 from clusters .
We set the tilt parameter n = 1 and the gas enhancement factor \Upsilon = 0.9 .
We consider CDM models ( open and \Omega _ { \mathrm { M } } = 1 ) and flat \Lambda CDM models .
We omit HCDM models ( to which the \Gamma _ { \mathrm { o } } constraint does not apply ) .
We test goodness of fit and draw confidence regions by the \Delta \chi ^ { 2 } method .
CDM models with \Omega _ { \mathrm { M } } = 1 ( SCDM models ) are accepted only because the large error on h _ { \mathrm { o } } allows h < 0.5 .
Baryonic matter plays a significant role in \Gamma _ { \mathrm { o } } when \Omega _ { \mathrm { M } } \sim 1 .
Open CDM models are accepted only for \Omega _ { \mathrm { M } } \gtrsim 0.4 .
The combination of the four other constraints with \Omega _ { \mathrm { o } } \approx 0.2 is rejected in CDM models with 98 % confidence , suggesting that light may not trace mass . \Lambda CDM models give similar results .
In all of these models , \eta _ { 10 } \gtrsim 6 is favored strongly over \eta _ { 10 } \lesssim 2 .
This suggests that reports of low deuterium abundances on QSO lines of sight may be correct , and that observational determinations of primordial ^ { 4 } He may have systematic errors .
Plausible variations on n and \Upsilon in our models do not change the results much .
If we drop or change the crucial \Gamma _ { \mathrm { o } } constraint , lower values of \Omega _ { M } and \eta _ { 10 } are permitted .
The constraint \Gamma _ { \mathrm { o } } = 0.15 \pm 0.04 , derived recently from the IRAS redshift survey , favors \Omega _ { M } \approx 0.3 and \eta _ { 10 } \approx 5 but does not exclude \eta _ { 10 } \approx 2 .