Geared turbofan with three turbines with first two counter-rotating, and third co-rotating with the second turbine

A gas turbine engine comprising:

• a fan rotor, a first compressor rotor and a second compressor rotor, said second compressor rotor compressing air to a higher pressure than said first compressor rotor;
• a first turbine rotor, said first turbine rotor driving said second compressor rotor, and a second turbine rotor, said second turbine driving said first compressor rotor;
• a fan drive turbine positioned downstream of said second turbine rotor, said fan drive turbine driving said fan through a gear reduction;
• said first compressor rotor and said second turbine rotor rotating as an intermediate speed spool, and said second compressor rotor and said first turbine rotor rotating together as a high speed spool, with said high speed spool rotating in an opposed direction to said intermediate speed spool, and said fan drive turbine rotating in the same direction as said intermediate speed spool;
• said fan rotor being driven by said speed reduction to rotate in the same direction as said high speed spool;
• a power density of the engine being greater than or equal to about 1.5 lbf/in3, and less than or equal to about 5.5 lbf/in3;
• and
• said power density defined as a ratio of thrust produced by said engine expressed in pounds force to a volume of a turbine section incorporating each of said first turbine rotor, said second turbine rotor and said fan driving turbine rotor, expressed in cubic inches.