Wormhole-Induced cosmic scenario in f(G) gravity with a k-essence field

In this paper, we present some analytic solutions of wormhole in four-dimensional Robertson–Walker Euclidean background with a function [Formula: see text], where G is Gauss–Bonnet curvature and a k-essence field for [Formula: see text] = 0. The solutions are obtained assuming an ansatz on [Formula: see text] with some additional assumptions on potential of the dilaton field and energy density of Gauss–Bonnet term. The Euclidean wormhole, in one case, asymptotically yields oscillating universe in Lorentzian time. In another solution, stable wormhole evolves through early transient inflationary era and after graceful exit from inflation, it yields a stable radiation dominated era asymptotically. The deceleration parameter, jerk and snap parameters are studied with cosmic time and they support observational data. The function [Formula: see text] obtained from the solution is consistent with earlier works. We also have another wormhole configuration, which is accompanied by oscillation of the scale factor in Euclidean time at an intermediate era and yields exponential expansion in the asymptotic domain. The magnitude of potential is found to decay. The violation of the null energy condition can be avoided asymptotically in all cases.