The big bang cosmology - enigmas and nostrums

Some outstanding problems in connection with the big bang cosmology and relativity theory are reviewed under the headings: enigmas; nostrums and elixirs (the universe as Phoenix (an oscillating universe), the anthropomorphic universe (existence of observers in the present universe), reproducing universes (could a mini big bang bounce, perhaps adding entropy and matter and eventually developing into a suitable home for observers), variable strength of the gravitational interaction and oscillating universes (possible bounce models that have led eventually to the present hospitable environment). (U.K.)