  The primordial lithium abundance inferred from observations of metal-poor
stars is ~3 times smaller than the theoretical value in standard big bang
nucleosynthesis (BBN) model. We assume a simple model including a sterile
neutrino nu_H with mass of O(10) MeV which decays long after BBN. We then
investigate cosmological effects of a sterile neutrino decay. We formulate the
injection spectrum of nonthermal photons induced by electrons and positrons
generated at the nu_H decay, as a function of the nu_H mass and the photon
temperature. We then consistently solve (1) the cosmic thermal history, (2)
nonthermal nucleosynthesis induced by the nonthermal photons, (3) the
baryon-to-photon ratio eta, and (4) the effective neutrino number N_eff.
Amounts of energy injection at the nu_H decay are constrained from limits on
primordial D and 7Li abundances, the N_eff value, and the cosmic microwave
background energy spectrum. We find that 7Be is photodisintegrated and the Li
problem is partially solved for the lifetime 10^4-10^5 s and the mass >~ 14
MeV. 7Be destruction by more than a factor of 3 is not possible because of an
associated D over-destruction. In the parameter region, the eta value is
decreased slightly, while the N_eff value is increased by a factor of <~ 1. In
this study, errors in photodisintegration cross sections of 7Be(g, a)3He and
7Li(g, a)3H that have propagated through literatures are corrected. It is then
found that the new photodisintegration rates are 2.3 to 2.5 times smaller than
the old rates, so that efficiencies of 7Be and 7Li photodisintegration are
significantly smaller.
