We study in a quantitative manner the lepton asymmetry L ( net leptons number per photon ) in the Universe and its impact on Universe expansion . This is quantified via the standard tool , the effective number of Dirac neutrinos N _ { \nu } ^ { \mathrm { eff } } . Specifically , we present the dependence of N _ { \nu } ^ { \mathrm { eff } } on the ambient temperature and the neutrino chemical potential and show the resultant neutrino yields in the cosmic background . We then obtain the dependence of |L| and the baryon-number to lepton-number ratio , B / |L| , on N _ { \nu } ^ { \mathrm { eff } } . Our results suggest that a value |L| = 0.46 \pm 0.06 and B \simeq ( 1.33 \pm 0.18 ) \times 10 ^ { -9 } |L| may be considered .