Antipodal correlation on the meron wormhole and a bang-crunch universe

We present a covariant euclidean wormhole solution to Einstein Yang-Mills system and study scalar perturbations analytically. The fluctuation operator has a positive definite spectrum. We compute the Euclidean Green’s function, which displays maximal antipodal correlation on the smallest three sphere. Upon analytic continuation, it corresponds to the Feynman propagator on a compact bang-crunch universe. We present the connection matrix that relates past and future modes. We thoroughly discuss the physical implications of the antipodal map in both the Euclidean and Lorentzian geometries.