Thread: What is "space" in the statistical descriptions used in cosmology?

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What is "space" in the statistical descriptions used in cosmology?

When astronomers speak of distributions like the distribution of hydrogen atoms "in space", what mathematical model of space are they using?

For example, astrological data based on receiving electromagnetic waves is out of date by the time it reaches earth. So if I an astronomer wishes to do statistics about the distribution of something "in space", what convention is used to account for this? Does the astronomer predict what conditions in the rest of the universe will be at the current local time on earth and used 3-D Euclidean space as the model? Or does the astronomer consider a distribution of something "in space" to include things that existed at times in our past? Or is something fancier done, based on the model of 4-D spacetime?

2. Astronomical data. ;-)
The space in the ΛCDM model of the expanding universe is a set of coordinates that expands on a timescale measured by comoving clocks. So the distance to a faraway object can be given in various ways, such as its distance when its emitted light is received on Earth, or its distance when that light was emitted.

Grant Hutchison

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Most of the work I did (some time ago!) would just pick a useful definition of space and make sure it was obvious in the analysis we did. Essentially there was no one answer - you selected the appropriate measure such that the observable was static or quasi-static and not too sparse to draw conclusions from. It was always a trade-off.

So you could correct for expansion, path taken, evolution, look at temporal variations by adjusting for distance etc - or you could look at a constrained area where you could ignore these factors for the data you were interested in. Or some combination of some or all of these (and other corrections). It all depended what you were looking for and the trade-off between the degree of accuracy of the measurement vs the amount of data you needed to get a good answer.

Sorry, that is the classical "Depends" answer. But the truth is ... it depends.

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Originally Posted by grant hutchison
Astronomical data. ;-)
Yes! - not "astrological".

The space in the ΛCDM model of the expanding universe is a set of coordinates that expands on a timescale measured by comoving clocks.
An interesting quote from https://en.wikipedia.org/wiki/Lambda-CDM_model

The model includes an expansion of metric space that is well documented ...
Although this expansion increases the distance between objects that are not under shared gravitational influence, it does not increase the size of the objects (e.g. galaxies) in space.
So any measure of a volume in the lambda-CDM model of space must consider how mass affects that volume?

5. Originally Posted by tashirosgt
Yes! - not "astrological".

An interesting quote from https://en.wikipedia.org/wiki/Lambda-CDM_model

So any measure of a volume in the lambda-CDM model of space must consider how mass affects that volume?
Well, the accelerating expansion of the Universe actually does change the size of "objects in space". The greater the acceleration, the greater the effect, until we reach a hypothetical Big Rip scenario. It's a small effect at present, but you are very slightly taller in a Universe with an increasing rate of expansion than you would be in a Universe with a constant rate of expansion. (See the classic Lineweaver & Davis article from Scientific American for more on that topic.)
What's happening is that expanding space effectively "slides out from under" objects that are held together by gravitational or electromagnetic forces, not that these objects prevent space from expanding locally.
But globally, of course, the average mass density of the Universe is one of the parameters that determines the value of the Hubble parameter (a measure of the expansion rate).

Grant Hutchison

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