  Scalar-tensor theories of gravity that embrace conformal coupling to the
scalar curvature are the focal point of cosmology on discussions of inflation
and late-time accelerating universe. Although there exists a stringent
nucleo-synthesis constraint on conformal gravity, one can formulate how to
evade this difficulty by modifying the standard particle theory action
consistently with the principles of gauge invariant quantum field theory. It is
shown that stronger gravity at early epochs of cosmological evolution than
previously thought of is inevitable in a class of conformal gravity models.
This enhances discovery potentials of primordial gravitational wave emission
and primordial black hole formation. The strong gravity effect may be enormous
if massive clumps are energetically dominated by cold dark matter made of
inflaton field, and created black holes may become a major candidate of cold
dark matter.
