Over time, the temperature T of the universe has decreased. (We define this temperature locally, but we average over large enough regions so that local variations don’t matter.) The negative gradi...Over time, the temperature T of the universe has decreased. (We define this temperature locally, but we average over large enough regions so that local variations don’t matter.) The negative gradient of this temperature, −∇T, is a covector that points in a preferred direction in spacetime, and a preferred world-line for an observer is one whose velocity vector v is always parallel to −∇T, in the sense defined in example \PageIndex1 above.
