We obtain restrictions on the universal baryon fraction , f _ { B } \equiv \Omega _ { B } / \Omega _ { 0 } , by assuming that the observed microlensing events towards the Large Magellanic Cloud are due to baryonic MACHOs in the halo of the Galaxy and by extracting a bound to the total mass of the Milky Way from the motion of tracer galaxies in the Local Group .
We find a lower bound f _ { B } > 0.29 ^ { +0.18 } _ { -0.15 } .
Consistency with the predictions of primordial nucleosynthesis leads to the further constraint on the total mass density , { { { { \Omega _ { 0 } \mathrel { \mathchoice { \lower 3.6 pt \vbox { \halign { \cr } $ \displaystyle% \hfill < $ \cr$ \displaystyle \hfill \sim$ } } } { \lower 3.6 pt \vbox { \halign { \cr } $% \textstyle \hfill < $ \cr$ \textstyle \hfill \sim$ } } } { \lower 3.6 pt \vbox { \halign { \cr } $% \scriptstyle \hfill < $ \cr$ \scriptstyle \hfill \sim$ } } } { \lower 3.6 pt \vbox { \halign { % \cr } $ \scriptscriptstyle \hfill < $ \cr$ \scriptscriptstyle \hfill \sim$ } } } } 0.2 .