Possible antigravity regions in $F(R)$ theory?

Understand

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.