  In the Big Rip cosmological scenario, a FRW universe containing dark energy
with $w < -1$ in its equation of state (phantom energy) expands in such way
that, in a finite time span, the scale factor diverges to infinity and the size
of the cosmic horizon goes to zero. Here we revisit this scenario in light of
the fact that Hawking radiation is expected to be generated at the apparent
horizon of a FRW universe, and show that the energy density and temperature of
that radiation both diverge at the Big Rip. We then use this fact to propose a
new variant of Penrose's conformal cyclic cosmology model in which the future
spacetime metric becomes conformally invariant at the Big Rip instead of in the
remote future of a de Sitter universe; this removes the need for mass decay
from the model and makes it consistent with current physical laws.
