  We investigate the issue of how accurately we can constrain the lepton number
asymmetry xi_nu = mu_nu/T_nu in the Universe by using future observations of 21
cm line fluctuations and cosmic microwave background (CMB). We find that
combinations of the 21 cm line and the CMB observations can constrain the
lepton asymmetry better than big-bang nucleosynthesis (BBN). Additionally, we
also discuss constraints on xi_nu in the presence of some extra radiation, and
show that the 21 cm line observations can substantially improve the constraints
obtained by CMB alone, and allow us to distinguish the effects of the lepton
asymmetry from the ones of extra radiation.
