A Jetblue Airbus A321-200, registration N905JB performing flight B6-1468 from Punta Cana (Dominican Republic) to New York JFK,NY (USA), was climbing out of Punta Cana when the crew decided to return to Punta Cana due to problems with the cabin pressure. The aircraft landed safely back. A passenger reported the crew explained the avionics compartment door didn't close properly causing the cabin to not properly pressurize. After landing back the passengers . . .