Undergrad How to solve for the volume of the universe / redshift

[rano jojo]

Hey !

i am having this question to be answered , i am new to the cosmology studies and still a bit confused about some formulas.

the question is:
(a) The greatest redshift known corresponds to the cosmic microwave background
(CMB, CBR) at redshift z 1100 (although the redshift is obtained theoretically
rather than observationally). UDFy-38135539 is a galaxy with the high redshift of
z = 8:555. By what factor did the volume of the universe increase between the
epochs corresponding to z = 1100 and z = 8:555?

what i am thinking of is using the scale factor with the relationship of the redshift for z= 1100

R= 1/1+1100 = 1/1101

then calculate the volume for a dimension universe of the z= 1100

volume = 1/1001*1/1101*1/1001*V (z=8.555)

is that corrects ?

otherwise how i can be solving this question.

thanks

 

[Jorrie]

By what factor did the volume of the universe increase between the
epochs corresponding to z = 1100 and z = 8:555?

Note that you should not talk about the volume of the universe, because that is an unknown. Rather say "what is the ratio of the scale factors for the two redshifts?"
The scale factor a = z+1, where the present a=1. Using this information, the answer to this question is simple to calculate.

 

[rano jojo]

Note that you should not talk about the volume of the universe, because that is an unknown. Rather say "what is the ratio of the scale factors for the two redshifts?"
The scale factor a = z+1, where the present a=1. Using this information, the answer to this question is simple to calculate.

many thanks but i still cannot get it. i thought of solving for the R = 1/1+z of both galaxies and substract the two values to reach the the volume increase between the two epochs.

 

[Jorrie]

The scale factor correlates with distance increase, not volume increase. And sorry, in a hurry, I forgot the divide, because I should have written a = 1/(z+1), not z+1.
The CMB (at redshift 1089) presently is 1090 time farther from us than what it was when those photons were emitted. Your galaxy at z= 8.55 is today 9.55 time farther than what it was when the photons we from it see were emitted.

In order to calculate volumes, you must convert redshifts to distances by means of the Hubble constant, and then calculate volumes. Do you know how to do that? (I see that you have marked the thread "I" for Intermediate, so we assume you already know the basic stuff).

 

[rano jojo]

many thanks for your kindhelp but i tried to convert it but couldn't work , as i am still new to the studies of cosmology . would you elaborate more to help me out please?

thank you again

 

[Jorrie]

Rano, I can just show you how to do it, but that will not help you much. On the other hand, I cannot give you a complete beginner's course here either. If you are just interested in the ratio between the volumes, there is an easy shortcut:

The distance ratio represented by your two redshifts is $$\frac{D_1}{D_2} = \frac{1090+1}{8.55+1} =114.24$$
Now, volumes are proportional to the cubes of distances, so the volume ratio will just be the cube of that.

In order to find the real distances and volumes, you must be able to convert redshift to recession rate and then use the Hubble constant to find the present (comoving) distance. How much of that have you already studied?

 

[rano jojo]

many thanks , but what i believe that i will find the ration then multibly it by 3 times as the universe id 3 dimension and that would be the ratio!

 

[Jorrie]

I hope you mean "multiply it by itself 3 times" - because it needs to be to the power 3.

 

[Chronos]

1+z is not the same as (1+z).

 

[rano jojo]

I hope you mean "multiply it by itself 3 times" - because it needs to be to the power 3.

thank you, this is what i meant multiplying itself by the power of three and not multiplying the number by 3.

so is this correct or not?

 

[rano jojo]

1+z is not the same as (1+z).

really ? how? what is the difference please

 

[Jorrie]

Yes, I think you've got it now.

I think Chronos referred to your first post's R= 1/1+1100 = 1/1101, where the brackets were missing.