The Justice Department is investigating whether Standard & Poor’s rated mortgage securities improperly leading up to the financial crisis. The investigation began before Standard & Poor’s cut the United States’ AAA credit rating this month, but it is likely to add fuel to the political firestorm that has surrounded that action. Lawmakers and some administration officials have since questioned the agency’s secretive process, its credibility and the competence of its analysts, claiming to have found an error in its debt calculations.