Cosmic Flatness Deduced from CMB

[XilOnGlennSt]

TL;DR

Cosmic Background Radiation studies by the WMAP project, concluded that the Universe has basically Euclidian flat curvature. Can someone sketch the reasoning behind this?

The Wilkinson Microwave Anisotropy Probe (WMAP) measured temperature differences across the sky in the cosmic microwave background (CMB). See --->(Wikipedia: https://en.wikipedia.org/wiki/Wilkinson_Microwave_Anisotropy_Probe#Main_result)

From these observations researchers concluded that the curvature of space is basically flat. I would love to gain insight into their reasoning. Maybe I can make this easier by exposing major points of my ignorance. Q1: How can spatial curvature be deduced from temperature variation? Q1A: Couldn't all sorts of uniform curvatures also produce uniform temperature variations?

So, the CMB witnessed by WMAP during nine years, took 13.8 billion years to catch up to 'us'. This despite the idea that the CMB pattern was formed at a time when the Universe, including our "position" in it, was much smaller. From this I imagine that the observed radiation would have originated only from a thin 'spherical' section of the original plasma at that time, consisting of points equidistant from our position. Q2: How can overall spatial curvature be deduced from such a select small sample.

Related questions:
Q3: Can we suppose that a similar CMB has been and will continue to be present in our skies?
Q4: We now witness gravitational lensing around black holes and stars. These would seem to be smaller-scale examples of non-flat space. Why wouldn't we expect that larger collective masses could have large-scale effects?
Q5: Wouldn't black holes themselves be examples of high-curvature spaces?

Thanks for your help!

 

[XilOnGlennSt]

As soon as I posted this, I was guided to all sorts of information on this subject. I'll start there.

Still, comments are welcome. Thanks

 

[PeterDonis]

As soon as I posted this, I was guided to all sorts of information on this subject.

Can you provide a link for other readers of this thread?

 

[Orodruin]

Basically it is about drawing triangles and measuring the angles of those triangles. The scale of variations can be inferred so that together with the travel distance gives you three legs of a triangle. Measuring the angular size of variations gives you an angle. Compare with what the angle would be in Euclidean space for the same side lengths. A larger angle means closed universe, a smaller open.

 

[XilOnGlennSt]

bapowell submitted a new PF Insights post

A Poor Man's CMB Primer. Part 4: Cosmic Acoustics

View attachment 190669Continue reading the Original PF Insights Post.

So, this post helped me appreciate the depth of theory around this question. Here are my take-aways:

• Acoustic modeling can be accomplished based on assumptions about the primordial-plasma universe.
• Such models give different values for dominate sound wavelengths based on its spatial curvature.
• Observation of the CMB shows dominate wave forms which match those predicted for flat curvature.

This is all news to me, and I'm glad to have a better mental sketch.

If the theory was all settled prior to the observations, then I would say that this is a marvelous triumph for the theorists! Horay!

In any case, congratulations to these researchers. Thanks for the information.