B Why do we use expanding metric?

[stoper]

TL;DR

Why do we use spatially expanding metric to measure the size of the expanding universe?

Being material observers, we do not expand with the universe. Our ruler for measuring its increasing size does not expand either - its scale does not change. If I identify the ruler with a metric, then from my perspective it should be invariant both spatially and temporally. If it expanded with the universe, then its size measured with this ruler would be constant.

Why then do we use a metric with the spatial scale expanding with the universe and constant temporal scale to measure the increasing size of the universe?

 

[jbriggs444]

TL;DR: Why do we use spatially expanding metric to measure the size of the expanding universe?

Being material observers, we do not expand with the universe. Our ruler for measuring its increasing size does not expand either - its scale does not change. If I identify the ruler with a metric, then from my perspective it should be invariant both spatially and temporally. If it expanded with the universe, then its size, as measured by this ruler, would be constant.

Why then do we use a metric with the spatial scale expanding with the universe and constant temporal scale to measure the increasing size of the universe?

What do you mean when you say that the "spatial scale" expands with the universe?

 

[stoper]

What do you mean when you say that the "spatial scale" expands with the universe?

Scale factor.

 

[Ibix]

Why then do we use a metric with the spatial scale expanding with the universe and constant temporal scale to measure the increasing size of the universe?

You don't have to. You can rescale your length scale to match the expansion - this is called co-moving coordinates. And then you can further rescale your time coordinate to make light have constant coordinate velocity - this is called conformal time.

However, it's very common to want to identify spatial coordinate differences with ruler measures and temporal coordinate differences with clock measures, so the default description used in most texts is the one where we measure time with our clocks and distance with our rulers.