Abstract
We study the effect of large baryonic isocurvature perturbations on the abundance of deuterium (D) produced in big bang nucleosynthesis (BBN). Large baryonic isocurvature perturbations existing at the BBN epoch (T∼ 0.1 MeV) change the D abundance by a second order effect, which, together with the recent precise measurement of D abundance, leads to a constraint on the amplitude of the power spectrum of the baryonic isocurvature perturbations. We derive the upper limit on the amplitude 
SB≲ 0.016 (2σ) for scales k−1 ≳ 0.0025 pc. This is the most stringent constraint for 0.1 Mpc-1 ≲ k ≲ 4 × 108 Mpc-1. We apply the BBN constraint to the relaxation leptogenesis scenario, where large baryonic isocurvature perturbations are produced in the last Nlast e-fold of inflation, and we obtain a constraint on Nlast.