Is the metric basis for space expanding as the universe expands?

[Jim Hasty]

I have read that as the universe expands that the "fabric" of spacetime expands. Does this mean that the metric basis for a given space is expanding? Also, does this mean the distances between the atoms in the lattice of matter is also increasing proportional to the expansion of the cosmos?

 

[Jorrie]

Nope. Things that are atomically or gravitationally bound do not expand with the cosmos. Even at cluster-size distances, the effect of the cosmological constant is so small that even feeble gravitational forces overwhelm it. All that happens at those scales is that the orbits are a tiny bit larger than it would have been without lambda.

 

[phyzguy]

I have read that as the universe expands that the "fabric" of spacetime expands. Does this mean that the metric basis for a given space is expanding? Also, does this mean the distances between the atoms in the lattice of matter is also increasing proportional to the expansion of the cosmos?

I think Jorrie answered your second question about the distances between atoms. Let me answer the first question about the metric basis for space. The answer is yes, the metric basis for space is expanding. The derivation of the Friedmann equation, which is what describes the expanding universe, assumes a metric of this form:
$$ds^2 = -c^2 dt^2 + a(t)^2 ds_3^2$$
Here $ds_3^2$ is the 3 dimensional spatial metric. So you can view it as a 3 dimensional metric that is growing with time.