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

TL;DR

This paper explores the reconstruction of modified $F(R)$ and $F(rak{G})$ gravities within the agegraphic dark energy model, providing conditions for effective equations of state and demonstrating reconstruction feasibility in flat universe models.

Contribution

It introduces a method for reconstructing $F(R)$ and $F(rak{G})$ gravity models using the agegraphic dark energy framework without matter fields.

Findings

Reconstruction is feasible for both phantom and non-phantom eras.

Conditions for effective equation of state parameter are derived.

Consistent reconstruction conditions are established for $F(R)$ and $F(rak{G})$] ,

Abstract

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 $w_{\mathrm{eff}}$, 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.