Deviation from Slow-Roll Regime in the EGB Inflationary Models with $r\sim N_e^{-1}$

Understand

We consider Einstein-Gauss-Bonnet (EGB) inflationary models using the effective potential approach.

• We present evolution equations in the slow-roll regime using the effective potential and the tensor-to-scalar ratio.
• The choice of the effective potential is related to an expression of the spectral index in terms of e-folding number $N_e$.
• The satisfaction of the slow-roll regime is mostly related to the form of the tensor-to-scalar ratio $r$.