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The tunneling rate, with exact prefactor, is calculated to first order in
$h$ for an empty closed Friedmann-Robertson-Walker (FRW) universe with
decaying cosmological term $\Lambda \sim R^{-m}$ ($R$ is the scale factor
and $m$ is a parameter $0\leq m \leq 2)$. This model is equivalent to a
cosmology with the equation of state $p_{\chi}=(m/3-1)_{\rho\chi}$. The
calculations are performed by applying the diluteinstanton approximation
on the corresponding Duru-Kleinert path integral. It is shown that the
highest tunneling rate occurs for $m=2$ corresponding to the cosmic
string matter universe. The obtained most probable cosmological term,
like one obtained by Strominger, accounts for a possible solution to the
cosmological constant problem.
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