Agegraphic reconstruction of modified $F(R)$ and $F(\mathcal{G})$ gravities

The cosmological reconstruction of modified $F(R)$ and $F(\mathcal{G})$ gravities with agegraphic dark energy (ADE) model in a spatially flat universe without matter field is investigated by using e-folding “$N$” as a forward way. After calculating a consistent $F(R)$ in ADE’s framework, we obtain conditions for effective equation of state parameter $w_{\mathrm{e}\mathrm{f}\mathrm{f}}$, and see that reconstruction is possible for both phantom and non-phantom era. These calculations also are done for $F(\mathcal{G})$ gravity and the condition for a consistent reconstruction is obtained.