The first CMB peak - Flat Universe

In summary, the size of bouncing lumps of charged particles, DM and photons in the primordial universe is supposed to be around 220,000 lyr. If we then calculate the angle A subtended at Earth by a lump of this size W, some 13.8 Glyr away D (back at recombination when t=380,000 yrs), then we are supposed to get A=1 degree. However, if we convert this to degrees, the result is suspiciously out by a factor of z=1100. This is most likely why curved spacetime is the short answer.
  • #1
tonyp1001
5
0
The size of bouncing lumps of charged particles, DM and photons in the primordial universe is supposed to be around 220,000 lyr (= sound horizon since the acoustic speed is approx 0.6c). If we then calculate the angle A subtended at Earth by a lump of this size W, some 13.8 Glyr away D (back at recombination when t=380,000 yrs), then we are supposed to get A=1 degree. This is the fundamental size of the first acoustic peak in the CMB power spectrum.

If I put A=W/D radians, I don't get 1 degree when converting to degrees - why? It is suspiciously out by a factor of z=1100 - is this why
 
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  • #2
Curved spacetime is the short answer.
 
  • #3
Chronos said:
Curved spacetime is the short answer.

? How? Thought the answer was 'flat' but it has to be curved to get the flat result ?

Isn't it 'stretched' instead of curved?
 
  • #4
tonyp1001 said:
The size of bouncing lumps of charged particles, DM and photons in the primordial universe is supposed to be around 220,000 lyr (= sound horizon since the acoustic speed is approx 0.6c). If we then calculate the angle A subtended at Earth by a lump of this size W, some 13.8 Glyr away D (back at recombination when t=380,000 yrs), then we are supposed to get A=1 degree. This is the fundamental size of the first acoustic peak in the CMB power spectrum.

If I put A=W/D radians, I don't get 1 degree when converting to degrees - why? It is suspiciously out by a factor of z=1100 - is this why

Very good question. We should try to answer a bit quantitatively. Back at recomb time, the surface of last scattering (the emitting matter) was about 41 million lightyears from here.

The hot fog we are seeing was 41 million lightyears at that time from the hot fog that became us. That is the actual distance, if you could have frozen expansion it would have taken that long for light to travel here from the emitting matter.

So let's see what one degree is, on a circle of that radius. Divide 41 million lightyears by the number of degrees in a radian.
I get 716,000 light years.

So I think your figure of 220,000 is wrong. It should be more like 720,000. Suspicious factor of a bit over 3. Maybe there is a units problem or a problem involving the definitions of distance.
================

Tony one danger signal is you saying that the distance to the surface of last scattering (the matter that emitted the CMB we are now receiving) is 13.7 billion light years. That is not the current distance. The presentday distance to that matter is 45 billion lightyears. In other words, if you would freeze expansion it would take 45 billion years for us to get a signal to them out there, where that matter is now. this is just standard cosmology. the standard LCDM model everybody (or almost everybody) uses.

You can see the factor of 1090 between the 41 million I told you and this 45 billion. That 1090 is the expansion factor or the redshift z +1 associated with the CMB 13.7 billion year light travel time.

Because of the expansion history of the universe there is no simple relation between light travel time and distance. So try not to confuse travel time with distance--it causes a muddle. Use what is called the proper distance, where you freeze expansion. Proper distance as of today is the same as current or now distance. where did you get that 220,000 lightyear figure? I'm curious.
 
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  • #5
So let's see what one degree is, on a circle of that radius. Divide 41 million lightyears by the number of degrees in a radian.
I get 716,000 light years.

you are dividing the radius rather than the circumference by the number of degrees in a radian? that doesn't seem right somehow but maybe I just need to brush up on geometry
 
  • #6
TalonD said:
So let's see what one degree is, on a circle of that radius. Divide 41 million lightyears by the number of degrees in a radian.
I get 716,000 light years.

you are dividing the radius rather than the circumference by the number of degrees in a radian? that doesn't seem right somehow but maybe I just need to brush up on geometry

Yes I want to see what original distance (at the "recomb" moment) corresponds to one degree of the sky today.

Dividing the circumference by 360 is arithmetically the same as dividing the radius by 57 point something. You get the same answer.
===============

Talon there is another way to do this, that you should try. I think you know that the microwave background redshift is z = 1090. So google "wright calculator" and plug 1090 into the online calculator and see what you get.

See what lightyears per arc-second you get!

This is a nice quickie exercise in astro grits. Besides all the other info, the calculator tells you what is the angular equivalent, in terms of lightyears/"
You know that " is the symbol for arc-second which is 1/3600 of a degree.
So you look down the list of outputs that the calculator gives.
If it says parsecs/" then multiply by 3.26 to get lightyears.
Then multiply that by 3600 to get lightyears per degree.

It will come out to be around 727,000 lightyears per degree.

That is, one degree in our CMB sky represented, in the very old times, a distance of 727,000 lightyears across the last scattering surface.

I did a rough calculation earlier and got 716,000 but the Wright calculator says 727,000 so I take that for better.
 
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  • #7
marcus said:
Yes I want to see what original distance (at the "recomb" moment) corresponds to one degree of the sky today.

Dividing the circumference by 360 is arithmetically the same as dividing the radius by 57 point something. You get the same answer.

ok, now I get it. I had to go look up radian. It's been a long time since I did any geometry.
 
  • #8
An estimate of the age of the universe: 13.3B
Degrees in a radian (57.296)
Estimate of subtended arc= 13.3B/57.296=232k lyr

220k lyr doesn't seem far off

(I'm a 50 year old insurance guy so don't yell at me)
 

What is the first CMB peak?

The first CMB peak refers to the first peak observed in the cosmic microwave background (CMB) radiation spectrum. This peak represents the maximum intensity of the CMB radiation and is a key feature used to study the properties of the universe.

What does the first CMB peak tell us about the universe?

The first CMB peak is an important indicator of the geometry and composition of the universe. Its position and height can provide information about the curvature of space and the amount of matter and energy in the universe. In a flat universe, the first CMB peak is expected to be the highest and occur at a specific angular scale.

How does the first CMB peak support the idea of a flat universe?

In a flat universe, the first CMB peak is predicted to occur at a specific angular scale which has been confirmed by observations. This supports the idea of a flat universe as it is consistent with the predictions of the inflationary theory, which suggests that the universe should have a flat geometry.

What is the significance of the first CMB peak in understanding the early universe?

The first CMB peak is a key feature of the CMB radiation, which is the oldest light in the universe. Studying the first peak can provide insights into the conditions of the early universe, such as the density and temperature of matter and radiation. It can also help us understand the processes that took place during the Big Bang.

How has the measurement of the first CMB peak changed our understanding of the universe?

The accurate measurement of the first CMB peak has greatly advanced our understanding of the universe. It has confirmed the predictions of the inflationary theory and provided evidence for a flat universe with a specific density of matter and energy. This has also helped to refine our understanding of the age, size, and composition of the universe.

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