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The amount of dark energy in the universe is pinned down fairly precisely by fluctuations in the cosmic microwave background, if I understand correctly. So in that sense there's very good evidence of its existence.

What I'm wondering is, could there ever be a laboratory-sized experiment that demonstrates its effects? For comparison, Pound and Rebka demonstrated the existence of gravitational redshift over the height of a five-storey building. What would be the smallest equivalent for showing the existence of dark energy?

For instance, suppose I have two super-light ping pong balls floating in space. (On the ISS, say, or on board Voyager 1.) Would dark energy make them drift apart?

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Dark energy at the level it is understood now comes as an observation of a global "distortion" of space that can be measured at cosmic scales, because at even within galactic distances it is too slight to be measurable. Galaxies retain their form because the percentage of change in the volume they occupy is not measurable at our level of observations.

The Virgo cluster which is not strongly bound has been used to observe/estimate the effects of dark energy:

Conclusions. The phase and dynamical similarity of the systems on the scales of 1–30 Mpc suggests that a two-component pattern may be universal for groups and clusters: a quasi-stationary bound central component and an expanding outflow around it, caused by the nonlinear gravity-antigravity interplay with the dark energy dominating in the flow component.

It is a matter of current research.

Ping pong balls do not fall in the scale. So the answer is no, they cannot be used to detect the effects of dark energy because they will be very very small.

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