Wormhole inducing exponential expansion in R2 gravity

Wormholes are considered both from the Wheeler deWitt equation, as well as from the field equations in the Euclidean background of Robertson Walker mini-superspace in $R^2$ gravity. Quantum wormhole satisfies Hawking Page wormhole boundary condition in the Euclidean background of mini-superspace, however, in the Lorentzian background wave functional turns to the usual oscillatory function. The Euclidean field equations for $\kappa =0,\pm 1$ lead to the wormhole configuration, as well as oscillating universe in Euclidean time $\tau$. The oscillating universe in Euclidean time $\tau$ transforms to an expanding universe only for $\kappa =1$ in Lorentz time $t$ under analytic continuation $\tau =it$ and asymptotically leads to an exponential solution. An Euclidean wormhole in the very early era evolves to an oscillating universe in $\tau$, thereafter crossing deSitter radius transition to an inflationary era is evident at later epoch only for $\kappa =1$.