Deviation from Slow-Roll Regime in the EGB Inflationary Models with <i>r</i> ∼ <inline-formula><math display="inline"><semantics><mrow><msubsup><mi mathvariant="bold-italic">N</mi><mi mathvariant="bold-italic">e</mi><mrow><mo mathvariant="bold">−</mo><mn mathvariant="bold">1</mn></mrow></msubsup></mrow></semantics></math></inline-formula>

Abstract

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 Ne. The satisfaction of the slow-roll regime is mostly related to the form of the tensor-to-scalar ratio r. The case of r∼1/Ne2 leads to a generalization of α-attractors inflationary parameters to Einstein–Gauss–Bonnet gravity with exponential effective potential. Moreover, the cosmological attractors include models with r∼1/Ne. And we check the satisfaction of the slow-roll regime during inflation for models with r∼1/Ne.

Keywords

• Einstein–Gauss–Bonnet gravity
• slow-roll regime
• inflation