Wormhole inducing exponential expansion in $R^2$ gravity

TL;DR

This paper explores wormholes within $R^2$ gravity, showing how Euclidean wormholes evolve into oscillating and inflationary universes, with quantum and classical perspectives providing insights into early universe dynamics.

Contribution

It introduces a detailed analysis of wormhole solutions in $R^2$ gravity using both quantum and classical approaches, highlighting their evolution into inflationary universes.

Findings

Euclidean wormholes evolve into oscillating universes.

Oscillating universes can transition to inflationary phases.

Wormhole configurations depend on curvature parameter $b7$.

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 $\kappa=1$.