Motion vs space expansion Let us consider two particles A and B in empty space, and let us assume that I am an observer attached to particle A. Also let us assume that, according to my measurements, I see that the distance from particle A to particle B increases over time.
According to General relativity, this could happen in two ways:

*

*The two particles are moving through space

*The two particles are still in space, but the space itself is expanding

If all information I have is how the distance between A and B increases with respect to proper time measured in A, how can I tell in which scenario I am?
 A: 
Motion vs space expansion

The two body situation cannot separated the two hypothesis you offer. Either can be assumed. Actually in order to establish with data that the space in our universe is expanding, astrophysicists needed data from the galaxies all around the earth

In 1912, Vesto Slipher discovered that light from remote galaxies was redshifted. which was later interpreted as galaxies receding from the Earth. In 1922, Alexander Friedmann used Einstein field equations to provide theoretical evidence that the universe is expanding. In 1927, Georges Lemaître independently reached a similar conclusion to Friedmann on a theoretical basis, and also presented the first observational evidence for a linear relationship between distance to galaxies and their recessional velocity. Edwin Hubble observationally confirmed Lemaître's findings two years later.Assuming the cosmological principle, these findings would imply that all galaxies are moving away from each other.

Without introducing general relativity (four dimensional spacetime ) and the expansion of space in order to interpret the measurements/observations, one would have to conclude  that the earth, or our galaxy,  was the center of the universe from where a large explosion started!
