# Since the universe is expanding, does anything ever occupy the same point in space?

Let's say we can observe expansion in a supercluster.
We define origin of our frame of reference at the center of the supercluster.
We observe an object/atom at point A at time T. The object is motionless relative to the origin.
We wait for expansion until T+ΔT and again observe the object.
Is the object at A or somewhere else?

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In the classical description of general relativity, the spacetime points constitute a smooth manifold with local coordinates $x^{\mu}$. In order to compute distances and intervals between points, an extra piece of information is needed, namely the metric tensor field $g_{\mu\nu}$(x). Space expansion can be thought of as not moving the points around, but rather as simply a change of the spatial part of the metric tensor with time.
For example, if we write the spacetime coordinates as $x^{\mu}$ = (t, $x^i$) where i=1,2,3 then we can write the metric of a spatially expanding universe as $$ds^2 = c^2dt^2-a(t)^2g_{ij}dx^idx^j$$ where the spatial metric components $g_{ij}$ do not depend on time.