The cosmological constant acts like a repulsive force which grows stronger with distance. Let's consider Newtonian mechanics and specify the force as

For simplicity let's imagine an object in orbit with a radius of 100 AU (twice the radius of pluto). If we work in the corotating frame of that object the only force is due to . So we have

or

Since > 0, the repulsive acceleation increase. Of course, if < 0 we recover the equation for a simple harmonic oscillator.

The solution is

;

The velocity is given by

A reasonably upper bound on is that its the same as the critial density now. This means

< 10^-35s^-2

With this we have

or 10^-2.5 cm/s repulsive velocity. So one can not test for on the scale of the solar system.

So What About These 120 Orders of Magnitude

Inflation strongly predicts:

vac + matter = 1

It can be shown, but not easily, that

H_ot_o = 2/3(vac)^-1/2 * ln[A]

where A = ln [1+(vac)^1/2)/ (1-vac)^1/2]

H_ot_o > 1 implies vac > 0.74 and hence we are now at the period of exponential expansion (again)

Initially, the vacuum energy density scaled as M_pl⁴ = 10⁷⁶ Gev⁴

If now the vacuum energy density equals the critical density then that is order /G which is 10^-47 Gev⁴.

So to satisfy inflation and the present day age of the Universe, has had to decrease by 120 orders of magnitude but remain non-zero.

So what, nothing in inflation predicts that should be equal to zero. Only that some minimum amount of vacuum energy will be present after inflation ends.

With non-zero the Universe becomes radiation dominated, then matter dominated then vacuum energy dominated once the critical density reaches some point. Observations indicate that we may be there now and that the vacuum energy associated with the true vacuum determines the large scale dynamics of the Universe.

Tests for non-zero :

• H_ot_o (seems to indicate)
• Power spectrum of the Galaxy Distribution (very consistent)
• Number density of luminous X-ray clusters (yes)
• Statistics of gravitational lenses (no but not enough data yet)

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