2021/09/07 We live in an expanding universe whose expansion rate is governed by the Hubble parameter. That, at least, is the picture we see on very large length scales of the universe, beyond the super-galaxy clusters, and it agrees perfectly well with very precise measurements of the cosmic microwave background and redshifts of distant galaxys. Whether this cosmic expansion should be visible also on a much smaller scale, notably within in our solar system, is another question. Einstein and Strauß answered it to the negative already in the mid 1940s, but their work was criticized later as making too restrictive assumptions. Over the last few decades the question has been studied again many times, but no consenus has emerged even from the theoretical side. It appears just too difficult to solve Einstein´s field equations with sources of gravity clustering on length scales that differ by many orders of magnitude.

So could experiments answer the question?

Interestingly, the current value of the Hubble parameter H is, in SI units, of order 10 ^-18 /s --- which means that the proper distance between two objects that follow the Hubble flow grows in 1 second by a relative amount of order 10^-18. That is definitely a small number, but on the other hand, if you compare it with the relative changes of length on the order 10^-22 detected by LIGO when hit by gravitational waves from far away mergers of astronomical objects, it is roughly a factor 10,000 larger! Moreover, modern optical clocks have reached a precision of about 10^-18 Hz ^-1/2, i.e. after averaging for 1s they reach a relative uncertainty of order 10^-18. So shouldn´t that make it possible to measure the expansion of the universe even with a table-top experiment using an optical clock, maybe in an interferometric measurement scheme? Or at least with some satellite experiment?

The answer, so we found out, hinges on that condition "follow the Hubble flow"... What does that mean, and can the condition be satisfied? Learn more about it in our new preprint.