Re: After the swarm leaves ... ?
If you are sure it was that hive that swarmed and it was 20 days ago, something is not right if no cells have emerged. Typically the new queen will have emerged about 9-10 days after the swarm and by day 24 you should be seeing eggs. By this time one cell should be opened with a round hole and all the others should be getting torn down. Did you have any real cold nights in the past three weeks? At this point, wait another week. You may have missed seeing the properly emerged from queen cell. You can also take one or two of the capped cells and cut them open to see if the larvae are viable. There are other situations that could explain what you are seeing.
Thankfully, the bees are smarter than I am. They are doing well, in spite of my efforts to help them.