We revisit the constraints on the small scale density perturbations ( 10 ^ { 4 } \mathrm { Mpc } ^ { -1 } \lesssim k \lesssim 10 ^ { 5 } \mathrm { Mpc } ^ { -1 } ) from the modification of the freeze-out value of the neutron-proton ratio at big-bang nucleosynthesis era .
Around the freeze-out temperature T \sim 0.5 \mathrm { MeV } , the universe can be divided into several local patches which have different temperatures since any perturbation which enters the horizon after the neutrino decoupling has not diffused yet .
Taking account of this situation , we calculate the freeze-out value in detail .
We find that the small scale perturbations decrease the n-p ratio in contrast to previous works .
With use of the latest observed ^ { 4 } He abundance , we obtain the constraint on the power spectrum of the curvature perturbations as \Delta ^ { 2 } _ { \mathcal { R } } \lesssim 0.018 on 10 ^ { 4 } \mathrm { Mpc } ^ { -1 } \lesssim k \lesssim 10 ^ { 5 } \mathrm { Mpc } ^ { -1 } .