# Force Form of Dark Energy

#### particlemania

Well what is the apparent force applied on two bodies of mass m1 and m2 due to Cosmological Constant?

First of all, what is the meaning of a constantly accelerating expansion of universe? Is the second time derivative of volume constant or that of the diametric size of universe?

Well in a lecture by Leonard Susskind, I remember, he said that the force is of a form similar to elastic spring force, just repulsive in nature. That is, for a universal constant k, the force is kr, in repulsive sense.

But in History Channel Documentary featuring Michio Kaku and Sean Caroll, it said that Expansion preserves proportion, and a mass-independent force will mean a mass-dependent acceleration, which wouldn't preserve proportions.

So what is the force formulation of dark energy?

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#### bapowell

$$\ddot{a} > 0$$