The second law of thermodynamics, together with the nature of the cosmic microwave background (CMB), imply that the Big Bang must have had a very particular structure. Conformal cyclic cosmology (CCC) posits that this structure comes about from an assumption that our Big Bang is the conformal continuation of the remote future of a previous aeon of the universe, this process continuing indefinitely. The geometrical consistency of this picture is made possible only by the presence of a positive cosmological constant (or equivalent) and some scalar material (dark matter?) produced at the Big Bang. Physical consistency also demands that there is very significant loss of information (in the sense of phase-space volume) in the Hawking evaporation and ultimate disappearance of large black holes. Galactic black-hole encounters in the previous aeon, involving much energy loss in the form of gravitational radiation, should, according to CCC, lead to statistically discernable circles in the CMB sky, either of slightly higher than average temperature or else of slightly lower than average (depending upon the location of the source). The observational situation is currently under examination.