  As an illustration of a renormalizable, asymptotically-free model of induced
gravity, we consider an $SO(10)$ gauge theory interacting with a real scalar
multiplet in the adjoint representation. We show that dimensional transmutation
can occur, spontaneously breaking $SO(10)$ to $SU(5){\otimes}U(1),$ while
inducing the Planck mass and a positive cosmological constant, all proportional
to the same scale $v$. All mass ratios are functions of the values of coupling
constants at that scale. Below this scale (at which the Big Bang may occur),
the model takes the usual form of Einstein-Hilbert gravity in de Sitter space
plus calculable corrections. We show that there exist regions of parameter
space in which the breaking results in a local minimum of the effective action,
and a {\bf positive} dilaton $(\hbox{mass})^2$ from two-loop corrections
associated with the conformal anomaly. Furthermore, unlike the singlet case we
considered previously, some minima lie within the basin of attraction of the
ultraviolet fixed point. Moreover, the asymptotic behavior of the coupling
constants also lie within the range of convergence of the Euclidean path
integral, so there is hope that there will be candidates for sensible vacua.
Although open questions remain concerning unitarity of all such renormalizable
models of gravity, it is not obvious that, in curved backgrounds such as those
considered here, unitarity is violated. In any case, any violation that may
remain will be suppressed by inverse powers of the reduced Planck mass.
