Eternal inflation and swampland conjectures

Abstract

We study if eternal inflation is realized while satisfying the recently proposed string swampland criteria concerning the range of scalar field excursion, |Δϕ| < D·M[subscript P], and the potential gradient, |∇V|>c·V/M[subscript P], where D and c are constants of order unity and M[subscript P] is the reduced Planck mass. We find that only the eternal inflation of chaotic type is possible for c∼O(0.01) and 1/D∼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 2πc≲H[subscript inf]/M[subscript P]< 1/√3.