Eternal inflation and swampland conjectures

We study if eternal inflation is realized while satisfying the recently proposed string swampland criteria concerning the range of scalar field excursion, vertical bar Delta phi vertical bar < D . M-P, and the potential gradient, vertical bar del V vertical bar > c . V/M-P, where D and c are constants of order unity and MP is the reduced Planck mass. We find that only the eternal inflation of chaotic type is possible for c similar to O(0.01) and 1/ D similar to O(0.01) and that the Hubble parameter during the eternal inflation is parametrically close to the Planck scale and is in the range of 2 pi c <= H-inf = M-P < 1 root 3.