Semiclassical instability of gravity with positive cosmological constant

Abstract

Construction of a partition function for Euclidean quantum gravity with positive cosmological constant using compact instantons results in imaginary contributions to the partition function. The relevant negative eigenmodes for the differential operator governing the one-loop contributions for the ${S}^{2}\ifmmode\times\else\texttimes\fi{}{S}^{2}$ and the $\mathrm{C}{\mathrm{P}}^{2}#{\stackrel{-}{\mathrm{CP}}}^{2}$ instantons are discussed.