ok, so if i understand you correctly, aside from the derivative of acceleration being used to calculate by definition the rate of change in acceleration, it is in this context being used to infer the rate of change in the energy density of dark energy?
i'm still trying to wrap my head around what a change in acceleration means in the physical world. given that its referred to as "the jerk," i have to assume that it is an even more abrupt change in velocity than that which is caused by a constant, unchanging acceleration. is this at all accurate?
TIA,
Eric
First no one is able to measure the change in the rate of acceleration of the universe yet. There just isn't enough data.
1. Standing still (constant position)
2. Moving in one direction at a constant speed (constant velocity)
3. Accelerating uniformly (constant acceleration)
4. Starting to accelerate (jerk)
1 and 2 you are familiar with so I will leave them alone. With 3, you are accelerating constantly at a uniform rate. You will feel a constant and unchanging force propelling you forward (F=ma, m and a are constant, so F is constant). You feel this constant force when your car is in the middle of a turn, when a plane accelerates down the runway, and when an elevator stops. By the equivalence principle (google it), constant acceleration feels exactly like constant gravity.
Jerk is exactly what it sounds like. You get jerked around.
Imagine you are in a drag race car. At the start line your position, velocity, acceleration, and jerk are all 0. You're just sitting there. Then you hit the gas and start to move. Your head snaps back as you begin to accelerate. This is jerk. Your acceleration goes from 0 to some relatively constant level (say 8 m/s^2) quite quickly. During the ramp up to this acceleration level, you experience jerk.
Once the engine is applying its force to the road through the wheels and is established, jerk goes to zero (for simplicity) and you just feel a constant force pushing you back in the seat. This is constant acceleration.
