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In this paper the focus is on inflationary dynamics in the context ofEinstein Gauss-Bonnet gravitational theories. We investigate the implicationsof the slow-roll condition on the slow-roll indices and we investigate how theinflationary dynamical evolution is affected by the presence of theGauss-Bonnet coupling to the scalar field. For exemplification of our analysiswe investigate how the dynamics of inflationary cubic, quartic order and alsoexponential scalar potentials are affected by the non-trivial Gauss-Bonnetcoupling to the scalar field. As we demonstrate it is possible to obtain aviable phenomenology compatible with the observational data, although thecanonical scalar field theory with cubic and quartic order potentials does notyield phenomenologically acceptable results. In addition, with regard to theexponential potential example, the Einstein Gauss-Bonnet extension of thesingle canonical scalar field model has an inherent mechanism that can triggerthe graceful exit from inflation. Furthermore we introduce a bottom-upreconstruction technique, in the context of which by fixing thetensor-to-scalar ratio and the Hubble rate as a function of the $e$-foldingsnumber, one is capable of reproducing the Einstein Gauss-Bonnet theory whichgenerates the aforementioned quantities. We illustrate how the method works byusing some relatively simple examples.

Viable Inflation in Scalar-Gauss-Bonnet Gravity and Reconstruction from Observational Indices