The scope of Volkswagen’s diesel scandal broadened on Tuesday, when the company said that 11 million of its diesel cars worldwide were equipped with the same software that was used to cheat on emissions tests in the United States. The number of cars involved suggests that the scale of the damage to Volkswagen’s reputation and its financial standing may be even greater than thought. The E.P.A. has ordered Volkswagen to recall almost a half-million vehicles sold in the United States from 2009 to 2015. The affected Golf, Passat, Jetta and Beetle cars were equipped with 2-liter diesel engines. Some Audi models also use the same diesel engine.