Mathematics – Logic
Scientific paper
Dec 1987
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987phrvd..36.3604j&link_type=abstract
Physical Review D (Particles and Fields), Volume 36, Issue 12, 15 December 1987, pp.3604-3613
Mathematics
Logic
3
Origin And Formation Of The Universe
Scientific paper
We study a quantum cosmological model, using the modified effective-action formalism which produces effective field equations satisfied by an expectation value of the metric operator, as opposed to the usual in-out matrix element. These equations are found to be real and causal. The reality means that the solution can be interpreted as the effective metric during the very early Universe, when quantum corrections were important. The causality of the equations means that they can, in principle, be solved from initial data, without any assumption being made about the final state of the system. However, a new problem is discovered: namely, that there exist solutions which represent exponentially growing perturbations of the classical solution. This instability, which has previously been discovered for a flat background, prevents the numerical solution of the effective field equations. Thus we have been unable to discover the evolution of the expectation value of the metric in this model.
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