  In the primordial Big Bang nucleosynthesis (BBN), only the lightest nuclides
(D, $^3$He, $^4$He, and $^7$Li) were synthesized in appreciable quantities, and
these relics provide us a unique window on the early universe. Currently, BBN
simulations give acceptable agreement between theoretical and observed
abundances of D and $^4$He, but it is still difficult to reconcile the
predicted $^7$Li abundance with the observation for the Galactic halo stars.
The BBN model overestimates the primordial $^7$Li abundance by about a factor
of three, so called the cosmological lithium problem, a long-lasting pending
issue in BBN. Great efforts have been paid in the past decades, however, the
conventional nuclear physics seems unable to resolve such problem. It is
well-known that the classical Maxwell-Boltzmann (MB) velocity distribution has
been usually assumed for nuclei in the Big-Bang plasma. In this work, we have
thoroughly investigated the impact of non-extensive Tsallis statistics
(deviating from the MB) on thermonuclear reaction rates involved in standard
models of BBN. It shows that the predicted primordial abundances of D, $^4$He,
and $^7$Li agree very well with those observed ones by introducing a
non-extensive parameter $q$. It is discovered that the velocities of nuclei in
a hot Big-Bang plasma indeed violate the classical Maxwell-Boltzmann (MB)
distribution in a very small deviation of about 6.3--8.2%. Thus, we have for
the first time found a new solution to the cosmological lithium problem without
introducing any mysterious theories. Furthermore, the implications of
non-extensive statistics in other exotic high-temperature and density
astrophysical environments should be explored, which might offer new insight
into the nucleosynthesis of heavy elements.
