Induced Gravity and Quantum Cosmology
  We study the Wheeler-DeWitt equation for a class of induced gravity models in
the minisuperspace approximation. In such models a scalar field nonminimally
coupled to gravity determines the effective Newton's constant. For simplicity
our analysis is limited to power-law potentials for the scalar field which have
exact classical solutions. We show that these models have exact solutions also
when quantised. Finally the Einstein Frame form of these solutions is obtained
and a classical-quantum correspondence is found. Realistic induced gravity
models also must include a symmetry breaking term which is needed in order to
obtain a gravitational constant, successful inflation and a subsequent standard
cosmological evolution. Nonetheless the potentials considered are important as
they may describe the inflationary phase when the symmetry breaking part of the
potential is negligible.
