Gauss-Bonnet inflation and swampland
  The two swampland criteria are generically in tension with the single field
slow-roll inflation because the first swampland criterion requires small tensor
to scalar ratio while the second swampland criterion requires large tensor to
scalar ratio. The challenge to the 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 swampland criteria may imply Gauss-Bonnet
coupling.
