Unitary and nonunitary evolution in quantum cosmology - art. no. 123519.

We analyze when and why unitarily violations might occur in quantum cosmolo gy restricted to minisuperspace. To this end we discuss in detail backscatt ering transitions between expanding and contracting solutions of the Wheele r-DeWitt equation. We first show that upon neglecting only backscattering, one obtains an intermediate regime in which matter evolves unitarily but wh ich does not correspond to any Schrodinger equation in a given geometry sin ce gravitational back. reaction effects are taken into account at the quant um level. We then show that backscattering amplitudes are exponentially sma ller than matter transition amplitudes. Both results follow from an adiabat ic treatment valid for macroscopic universes. To understand how backscatter ing and the intermediate regime should be interpreted, we review the proble m of electronic transitions induced by nuclear motion since it is mathemati cally very similar. In this problem, transition amplitudes are obtained fro m the conserved current. The same applies to quantum cosmology and indicate s that probability amplitudes should be based on the current when backscatt ering is neglected. We then review why, in a relativistic context, backscat tering is interpreted as pair production whereas it is not in the nonrelati vistic case. In each example the correct interpretation is obtained by coup ling the system to an external quantum device. From the absence of such ext ernal systems in cosmology, we conclude that backscattering does not have a unique consistent interpretation in quantum cosmology. [S0556-2821(99)0331 2-3].