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In this paper, we investigate various types of Fubini instantons in the Dilatonic Einstein–Gauss–Bonnet theory of gravitation which describes the decay of the vacuum state at a hilltop potential through tunneling without barrier. It is shown that the vacuum states are modified by the non-minimally coupled higher-curvature term. Accordingly, we present the new solutions which describe the tunneling from new vacuum states in anti-de Sitter and de Sitter backgrounds. The decay probabilities of the vacuum states are also influenced. We thus show that the semiclassical exponents can be decreased for specific parameter ranges, thereby increasing tunneling probability

Fubini instantons in Dilatonic Einstein–Gauss–Bonnet theory of gravitation