Constraints on modified Gauss-Bonnet gravity during big bang
  nucleosynthesis
  The modified gravity is considered to be one of possible explanations of the
accelerated expansions of the present and the early universe. We study effects
of the modified gravity on big bang nucleosynthesis (BBN). If effects of the
modified gravity are significant during the BBN epoch, they should be observed
as changes of primordial light element abundances. We assume a $f(G)$ term with
the Gauss-Bonnet term $G$, during the BBN epoch. A power-law relation of $df/dG
\propto t^p$ where $t$ is the cosmic time was assumed for the function $f(G)$
as an example case. We solve time evolutions of physical variables during BBN
in the $f(G)$ gravity model numerically, and analyzed calculated results. It is
found that a proper solution for the cosmic expansion rate can be lost in some
parameter region. In addition, we show that calculated results of primordial
light element abundances can be significantly different from observational
data. Especially, observational limits on primordial D abundance leads to the
strongest constraint on the $f(G)$ gravity. We then derive constraints on
parameters of the $f(G)$ gravity taking into account the existence of the
solution of expansion rate and final light element abundances.
