[Astrophysics] CBR and angular size

[Tloh]

Question:

Assuming a flat universe, find the angular size of the largest causally connected region of the CBR. Hint: We see this region as it existed at the time of decoupling, when the CBR photons were set free.

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Alright, flat universe, k = 0, tdec --> z~= 1100

Theta = (H0 * D / 2c) * ((1+z)^1.5) / ((1+z)^0.5)-1)

H0 = Hubble constant
D = Linear diameter
c = constant speed of light

I am stuck here. I can solve the z portion of the equation, but I don't know how to find the value of D, the causally connected section of the CBR. My guess is that I'm supposed to use the size of the universe at the tdec point (time just before the photons were set free). Any ideas?

-Thomas

 

[thepatientmental]

Great question, Thomas! To find the angular size of the largest causally connected region of the CBR, we need to first understand what causally connected means in this context. In astrophysics, causally connected refers to regions of space that have had enough time to communicate with each other since the beginning of the universe. This means that the photons in these regions have had enough time to travel and interact with each other, creating the CBR that we see today.

At the time of decoupling, when the CBR photons were set free, the universe was about 379,000 years old. This means that the largest causally connected region of the CBR would be the size of the observable universe at that time, which is about 42 billion light years in diameter.

To calculate the angular size, we can use the formula you provided, with D being the diameter of the observable universe at tdec. This gives us an angular size of about 1.7 degrees. This means that the largest causally connected region of the CBR would appear to us as a circle with a diameter of about 1.7 degrees on the sky.

I hope this helps! Keep exploring the wonders of astrophysics.