Agegraphic reconstruction of modified F(R) and F({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_eff, 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.