  We have studied the proton-capture reaction 3H(p,{\gamma})4He. It plays a
role in the nucleosynthesis of primordial elements in the early Universe
leading to the pre-stellar formation of 4He nuclei. All results of our
researches and more new data from works show that the contribution of the
3H(p,{\gamma})4He capture reaction into the processes of primordial
nucleosynthesis is relatively small. However, it makes sense to consider this
process for making the picture complete of the formation of prestellar 4He and
clearing of mechanisms of this reaction. Furthermore, we have considered the
3He(2H,{\gamma})5Li reaction in the low energy range in the modified potential
cluster model with splitting of orbital states according to Young tableaux and,
in some cases, with forbidden states. These reaction also form part of the
nucleosynthesis chain of the processes occurring in the early stages of
formation of stable stars, and are possible candidates for overcoming the
well-known problem of the A = 5 gap in the synthesis of light elements in the
primordial Universe. Continuing study we have considered the radiative capture
4He(3He, {\gamma})7Be at superlow energies, which has a undeniable interest for
nuclear astrophysics, since it takes part in the proton-proton fusion chain,
and new experimental data on the astrophysical S-factors of this process at
energies down to 90 keV and 23 keV and data on the radiative capture reaction
4He(3H,{\gamma})7Li down to 50 keV appeared recently. Moreover, radiative
capture reactions 4He(3He,{\gamma})7Be and 4He(2H,{\gamma})6Li may have played
a certain role in prestellar nucleosynthesis after the Big Bang, when the
temperature of the Universe decreased to the value of 0.3 T9.
