  We study the finite temperature and density effects on beta decay rates to
compute their contributions to nucleosynthesis. QED type corrections to beta
decay from the hot and dense background are estimated in terms of the
statistical corrections to the self-mass of an electron. For this purpose, we
re-examine the hot and dense background contributions to the electron mass and
compute its effect to the beta decay rate, helium yield, energy density of the
universe as well as the change in neutrino temperature from the first order
contribution to the self-mass of electrons during these processes. We
explicitly show that the thermal contribution to the helium abundance at T = m
of a cooling universe 0.045 % is higher than the corresponding contribution to
helium abundance of a heating universe 0.031% due to the existence of hot
fermions before the beginning of nucleosynthesis and their absence after the
nucleosynthesis, in the early universe. Thermal contribution to helium
abundance was a simple quadratic function of temperature, before and after the
nucleosynthesis. However, this quadratic behavior was not the same before the
decoupling temperature due to weak interactions; so the nucleosynthesis did not
even start before the universe had cooled down to the neutrino decoupling
temperatures and QED became a dominant theory. It is also explicitly shown that
the chemical potential in the core of supermassive and superdense stars affect
beta decay and their helium abundance but the background contributions depend
on the ratio between temperature and chemical potential and not the chemical
potential or temperature only. It has been noticed that temperature plays a
role of regulating parameter in an extremely dense systems.
