Euclidean Wormhole with k-essence field in the presence of Gauss–Bonnet term

In this paper, we present some analytical solutions of wormhole in four-dimensional Robertson–Walker Euclidean background considering Einstein–Gauss–Bonnet dilaton interaction with a [Formula: see text]-essence field for [Formula: see text]. The solutions are obtained assuming some restrictions on coupling function with a form of potential or with the ratio of kinetic to potential energy of the dilaton field. Euclidean wormhole, in one case, evolves through early transient inflationary era and after graceful exit from inflation, it asymptotically yields a radiation dominated era or a matter dominated era. In another solution, initial Euclidean wormhole is accompanied by oscillation of scale factor in Euclidean time at some late era which asymptotically yields exponential expansion. The violation of the null energy condition can be avoided asymptotically. The potential is also found to decay sharply.