Wormhole in the modified theory of gravity in Kaluza-Klein cosmology

Noether symmetry in the modified theory of gravity with F(R)-term in the action in the background of 5-dimensional Kaluza-Klein cosmology yields F(R) proportional to R-n for arbitrary n. Wormhole is allowed quantum mechanically with both n = 3/2 and 2. Further wormhole is allowed from the Euclidean field equations for n = 3/2 only, however for n = 2 its existence is not clear. Quantum wormholes are also allowed for arbitrary n with n > 1/2 except n = 1 and 13/10 from the Wheeler-DeWitt equation in terms of new canonical variables obtained from Noether symmetry, consistent with solution in terms of old variables. We present concept of time in quantum cosmology with use of Noether constant of motion. We also present an idea of transition from wormhole configuration to the inflationary era.