| Summary: | The swampland criteria are generically in tension with single-field slow-roll inflation because the first swampland criterion requires small tensor-to-scalar ratio while the second swampland criterion requires either large tensor-to-scalar ratio or large scalar spectral tilt. The challenge to single-field slow-roll inflation imposed by the swampland criteria can be avoided by modifying the relationship between the tensor-to-scalar ratio and the slow-roll parameter. We show that the Gauss−Bonnet inflation with the coupling function inversely proportional to the potential overcomes the challenge by adding a constant factor in the relationship between the tensor-to-scalar ratio and the slow-roll parameter. For the Gauss−Bonnet inflation, while the swampland criteria are satisfied, the slow-roll conditions are also fulfilled, so the scalar spectral tilt and the tensor-to-scalar ratio are consistent with the observations. We use the potentials for chaotic inflation and the E-model as examples to show that the models pass all the constraints. The Gauss−Bonnet coupling seems a way out of the swampland issue for single-field inflationary models.
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