Wormhole inducing exponential expansion in $R^2$ gravity

Abstract

Wormholes are considered both from the Wheeler deWitt equation, as well as from the field equations in the Euclidean background of Roberson 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 $\kappa=0, \pm1$ lead to the wormhole configuration; as well as oscillating universe in Euclidean time $\tau$. The oscillating universe is equivalent to expanding universe under analytic continuation $\tau=it$ and asymptotically leads to 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 $\kappa=1$.