Abstract
Using Morse's theory of reconstructions we define the space of all the universes-the Superspace. On the Superspace we investigate the geometry of the DeWitt metric. It is shown that the geodesic flow corresponding to the DeWitt metric is exponentially instable. The dynamical system described by the Einstein equations of evolution (Einstein dynamics) has the same type of instability also, if 1) the Universe is inflationary in some local domain, 2) in some local domain the Universe does not change its volume, but changes the conformal geometry very quickly as compared with the conformal potnetial. So, the Einstein dynamics is unstable on the Superspace, therefore the following quantum theory considered on the minisuperspace (a submanifold of the Superspace with a finite dimension) says nothing about the “real” quantum theory on the Superspace, and in the Superspace the semiclassical approximation is close to the quantum approximation only during a short time.
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Communicated by S.-T. Yau
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Kocharyan, A.A. Instability in superspace. Commun.Math. Phys. 143, 27–42 (1991). https://doi.org/10.1007/BF02100284
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DOI: https://doi.org/10.1007/BF02100284