Finite Conformal Quantum Gravity and Nonsingular Spacetimes
  We explicitly prove that a class of finite quantum gravitational theories (in
odd as well as in even dimension) is actually a range of anomaly-free
conformally invariant theories in the spontaneously broken phase of the
conformal Weyl symmetry. At classical level we show how the Weyl conformal
invariance is likely able to tame the spacetime singularities that plague not
only Einstein gravity, but also local and weakly non-local higher derivative
theories. This latter statement is rigorously proved by a singularity theorem
that applies to a large class of weakly non-local theories. Following the
seminal paper by Narlikar and Kembhavi, we provide an explicit construction of
singularity-free black hole exact solutions conformally equivalent to the
Schwarzschild metric. Furthermore, we show that the FRW cosmological solutions
and the Belinski, Khalatnikov, Lifshitz (BKL) spacetimes, which exactly solve
the classical equations of motion, are conformally equivalent to regular
spacetimes. Finally, we prove that the Oppenheimer-Volkov gravitational
collapse is a an exact (singularity-free) solution of the non-local conformally
invariant theory compatible with the bounce paradigm.
