Renegade time travelers meddle in the outcome of the Second Punic War, bringing about the premature deaths of Publius Cornelius Scipio and Scipio Africanus at the Battle of Ticinus in 218 BC and so creating a new timeline in which Hannibal destroys Rome in 210 BC. That made Western European civilization come to be based on a Celtic-Carthaginian cultural synthesis (rather than a Greco-Roman, as in actual history). This civilization discovered the Western Hemisphere and created certain inventions (such as the steam engine) long before the corresponding events happened in actual history (partly since there was nothing corresponding to the fall of the Roman Empire), but overall technological progress has been slow since most developments are arrived at through ad hoc tinkering, and there is no scientific methodology of empirically testing rigorous theories.
Manse Everard, a 20th-century Time Patrol agent, finds himself in the new timeline, in Catavellaunan (approximately New York), facing the moral dilemma. If he returns to the past before the events that led to Carthaginian victory and restores his original timeline by negating the assassinations and military upset that have led to the new alternative timeline, he would wipe out its billions of inhabitants when the course of human history reverts to his own.
Similar themes in other works
John Barnes's The Timeline Wars series has the same basic assumption: an alternative history timeline starting from Hannibal winning the Second Punic War. However, Anderson assumes that the Carthaginians would not have been able to fill the Roman niche and create something similar to the Roman Empire and that it would have been the Celts who would have become central to the successor culture. Conversely, Barnes assumes that the victorious Carthaginians would have succeeded in creating a world empire, an extremely cruel, aggressive and oppressive one, which is the undoubted villain of his books.