Reconstruction Method in <i>F(G)</i> Gravity: Stability Study and Inflationary Survey

Abstract

The present paper is devoted to reconstruction and cosmological study in modified F(G) theory of gravity. Our reconstruction scheme is based on Friedmann metric induced equations in modified F(G) theory by supposing a power law form for the scale factor of Friedmann metric. Firstly, we deal with the stability study, the obtained model. This survey reveals that for appropriated choice of the reconstructed model parameter, this model is stable under two cosmological evolutions namely the de Sitter and the power law evolutions symbolized by the appropriated scale factor. Secondly, we investigate the inflationary survey by fitting the model with the inflation observables. These observables are determined and their comparison with Planck’s results leads to a special inflationary F(G) model. We prove that this model especially obtained for radiation domination evolution develops an instability, so can fall to ordinary matter domination era or dark energy domination era. This is the key of graceful exit from inflation.