Possible antigravity regions in $F(R)$ theory?
  We construct an $F(R)$ gravity theory corresponding to the Weyl invariant two
scalar field theory. We investigate whether such $F(R)$ gravity can have the
antigravity regions where the Weyl curvature invariant does not diverge at the
Big Bang and Big Crunch singularities. It is revealed that the divergence
cannot be evaded completely but can be much milder than that in the original
Weyl invariant two scalar field theory.
