The top four U.S. carriers American Airlines Group Inc (AAL.O), Delta Air Lines Inc (DAL.N), United Continental Holdings Inc (UAL.N) and Southwest Airlines Co (LUV.N) control some 80 percent of the domestic air travel market. The four confirmed receipt of the regulator's letter and said they are cooperating fully with the investigation. News of the probe sent the Dow Jones U.S. airlines index (.DJUSAR) down 2 percent. Shares of the U.S. carriers have gyrated in recent weeks as investors questioned whether they were planning to add capacity at a pace faster than overall economic growth, which could put downward pressure on fares. Southwest fueled investor jitters about declining profit margins in May when it unveiled plans to boost capacity by as much as 8 percent this year from 2014, although it later revised the expected increase to 7 percent.