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We present wormhole as a solution of Euclidean field equations as well as the solution of Wheeler–DeWitt equation in (4 + 1)-dimensional Kaluza–Klein cosmology minimally coupled with scalar field. A simple analytic solution of the Euclidean field equations enlightens classical forbidden domain in the wormhole configuration under analytic continuation in the Euclidean space by [Formula: see text]. Numerical solutions of the field equations allow wormhole configuration with some standard potentials. The wormhole solution triggers decay of potential and reduction of internal space. Cosmic evolution of a wormhole shows an inflationary era away from the classical forbidden domain introducing aforesaid analytic continuation. Analytic and numerical solution of the Wheeler–DeWitt equation also supports Hawking–Page wormhole boundary conditions.

In this paper, we present some wormhole configurations using analytic and numerical solutions of the Euclidean field equations considering Einstein–Gauss–Bonnet dilaton coupled interaction in the Robertson–Walker metric. Analytic solutions invoking slow-roll type approximation for some potentials yield identical wormholes in the early era. Eventually, in later era, the universe enters to an expanding era much faster than usual inflation accompanied by oscillations with analytic continuation [Formula: see text]. The numerical solutions of wormholes in terms of the scale factor [Formula: see text] are almost identical for some standard potentials of the dilaton field, except for the evolution of potentials. The Hubble parameter and deceleration parameter obtained by curve fit of [Formula: see text] of the numerical solution of wormhole yield an inflationary era away from the throat of the wormhole using [Formula: see text]. A sharp decay of the potential is also observed.

We present wormhole as a solution of Euclidean field equations as well as the solution of the Wheeler–deWitt (WD) equation satisfying Hawking–Page wormhole boundary conditions in (4 + 1)-dimensional Kaluza–Klein cosmology. The wormholes are considered in the cases of pure gravity, minimally coupled scalar (imaginary) field and with a positive cosmological constant assuming dynamical extra-dimensional space. In above cases, wormholes are allowed both from Euclidean field equations and WD equation. The dimensional reduction is possible.