Big Bang Nucleosynthesis constraints on Barrow entropy
  We use Big Bang Nucleosynthesis (BBN) data in order to impose constraints on
the exponent of Barrow entropy. The latter is an extended entropy relation
arising from the incorporation of quantum-gravitational effects on the
black-hole structure, parameterized effectively by the new parameter $\Delta$.
When considered in a cosmological framework and under the light of the
gravity-thermodynamics conjecture, Barrow entropy leads to modified
cosmological scenarios whose Friedmann equations contain extra terms. We
perform a detailed analysis of the BBN era and we calculate the deviation of
the freeze-out temperature comparing to the result of standard cosmology. We
use the observationally determined bound on $ |\frac{\delta {T}_f}{{T}_f}|$ in
order to extract the upper bound on $\Delta$. As we find, the Barrow exponent
should be inside the bound $\Delta\lesssim 1.4\times 10^{-4}$ in order not to
spoil the BBN epoch, which shows that the deformation from standard
Bekenstein-Hawking expression should be small as expected.
