Unified solutions of extended Gauss-Bonnet gravity

We study some scale factor power-law solutions of the field equations of the extended Gauss Bonnet gravity in the spatial FRW (Friedmann-Robertson-Walker) universe. We consider the lagrangian density given by F(R, G) = f (G) + R + alpha R-2 which exhibits a modification comparing with the modified Gauss Bonnet gravity. After constructing the Friedmann equations and finding the power-law solution we obtain the real valued of our model describing a mechanism that shows transitions among three stages of the universe (inflation, deceleration, acceleration) in an unified way. In particular, in this unified solution we obtained an inflation model without using any scalar field description when alpha > 0, and also we verified our early time inflationary scenario using observational parameters, i.e. n(s), r. Further, we research for the power-law solution of our model when the universe is in the phantom phase. Here, it is observed that the acceleration of the universe in phantom region is composed of two phases which congruent with the recent observations.