# The first CMB peak - Flat Universe

by tonyp1001
Tags: flat, peak, universe
 P: 5 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
 Sci Advisor PF Gold P: 9,087 Curved spacetime is the short answer.
P: 182
 Quote by Chronos 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?

Astronomy
PF Gold
P: 22,671

## The first CMB peak - Flat Universe

 Quote by tonyp1001 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.
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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.
 P: 177 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
Astronomy
PF Gold
P: 22,671
 Quote by TalonD 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.
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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.
P: 177
 Quote by marcus 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.
 P: 1 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)

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