  An exact solution is obtained for a massive scalar field conformally coupled
with the curvature in a cosmological model with the scale factor $a(t) = a_0 /
|t|$, corresponding to background matter with the equation of state $ p = - 5
\varepsilon /3 $. An expression for the number density of created particles is
obtained, and its behavior is studies as the model approached the instant of a
Big Rip. Renormalization of the energy-momentum tensor is considered, and it is
shown that back reaction of the quantum effects of a conformally coupled scalar
field on the space-time metric can be neglected if the field mass is much
smaller than the Planck mass and if the time left to the Big Rip is greater
than the Planck time.
