# How to calculate age of universe with a certain redshift?

1. Mar 30, 2005

### detty_hk

Hi i am confused as to how to calculate the age of the universe with redshift
say for example

The age of the universe now is 13 billion years old (and a critical universe).
How do i find the age of the universe if it was a redshift at say 10??

Do i have to find the scale factor first?

2. Mar 30, 2005

### marcus

two good online cosmology calculators:

Ned Wright's
http://www.astro.ucla.edu/~wright/CosmoCalc.html

Siobahn Morgan's
http://www.earth.uni.edu/~morgan/ajjar/Cosmology/cosmos.html

homepage for Siobahn in case you want to see who she is
http://www.earth.uni.edu/smm.html
homepage for Ned in case you want to see who he is
http://www.astro.ucla.edu/~wright/intro.html

the answer you should get, if you put in today's best estimates of the parameters, is 0.48 billion years

that is, if you see light from a galaxy and that light is redshift 10
then it was emitted by the galaxy when the universe was only about half
a billion years old

Last edited: Mar 30, 2005
3. Mar 30, 2005

### detty_hk

can you teach me how you actually do it?
I would like to do it myself and check, thx.

4. Mar 30, 2005

### marcus

If you need help using the calculators, just say.

they are both put up by astronomy professors to help their students.

the easiest to use is ned wright's

just go there, put 10 into the z box, dont change anything else
and press "general"
this will give the answer 0.482 billion years

however siobhan morgan's is fun to play with because she gives recession speeds too, which ned does not.
with her calculator you must type in 0.27 for Omega (matter fraction) and 0.73 for Lambda (cosmological constant or dark energy fraction) and 71 for the Hubble parameter. then put in z = 10.

ned wright already has these default values of the cosmological parameters set for you so he makes you do less work.
both calculators give the same answer, as you might expect

5. Mar 30, 2005

### marcus

I already gave some pointers, now I will wait until you try and say if it came out

if you put in z = 10 then it should come out 0.48 billion years

6. Mar 30, 2005

### detty_hk

nono I know how to play with the calculator
what i want to know is how to do the Calculations by hand.
thx

7. Mar 30, 2005

### marcus

bravo!

Lineweaver's article "Inflation and the Cosmic Microwave Background" has formulas. Look it up in arxiv.

or the Astronomy Reference thread here at PF has a link to Lineweaver.

8. Mar 30, 2005

### detty_hk

argh there's too many to it
can someone teach me plz?

9. Mar 30, 2005

### detty_hk

why don't you try to solve a question for me and see if u guys can help:
if you can, please show it step by step

The current age of the universe is 13billion years old and assume that the univers is a flat universe (critical universe). What is the age of the universe at redshift 10?

sorry for all the fuss

10. Mar 30, 2005

### matt.o

it is not a simple calculation. the integral needs to be solved numerically.

11. Mar 30, 2005

### detty_hk

would it help if i tell you that R(t) is proportional to t^(2/3)
and that
t = 2/3H^-1

where t = now and H = hubble constant

12. Mar 30, 2005

### marcus

but detty! that formula is not right, it applies only to a simple case

for the real universe it is not true that the scale factor R(t) is proportional to t^(2/3)

Give us an online source for that formula, and i bet we can show you where it says that the formula only applies to a special (artificially simple) case.

this figure shows that the R(t) curve is not simply what you say but can be shaped different ways depending on the assumptions about the cosmological constant etc.

http://nedwww.ipac.caltech.edu/level5/March03/Lineweaver/Figures/figure14.jpg

here is the context in his "Inflation and the CMB"
http://nedwww.ipac.caltech.edu/level5/March03/Lineweaver/Lineweaver7_7.html

here is the TOC for that article
http://nedwww.ipac.caltech.edu/level5/March03/Lineweaver/Lineweaver_contents.html

here is the abstract, which has a link to a more legible PDF copy
http://lanl.arxiv.org/abs/astro-ph/0305179

I have helped all I can. have to go

Last edited: Mar 30, 2005
13. Mar 30, 2005

### detty_hk

I know
but assume that it is, would i be able to solve it?
cos i'm stuck in a question and these are all the assumptions

14. Mar 30, 2005

### marcus

You want to assume the wrong formula is right? then it is easy

you asked WHAT IS THE AGE AT REDSHIFT Z = 10

z = 10 means a ratio of 11 in the scale factor

the oversimplified formula says the scale factor R(t) is proportional to the age^(2/3)

so clearly 11 = age ratio ^(2/3)

so age ratio = 11^(3/2) = 36.5

to get the age of the universe at z = 10 you would therefore have to divide the age now, by the factor 36.5

but remember using this oversimplified model the present age of the universe is equal to 2/3 of the Hubble time, which works out to 9.2 billion years!

So, divide 9.2 billion years by 36.5 and you get

0.25 billion years

I think you could force Ned Wright's calculator to follow this wrong oversimplified formula by making the cosmological constant Lambda be zero and selecting the flat case, where Omega_matter = 1

Last edited: Mar 30, 2005
15. Mar 30, 2005

### marcus

you said "assume that formula is right and do it by hand" OK I did, assuming the formula is right is the same as saying Lambda = 0
and Omega_matter = 1.
I did it by hand AND checked it with Siobhan Morgan calculator and it came out the same both times: age = 0.25 billion years.

That's all I have time for. I suggest you assume more realistic parameters like Lambda = 0.73 and Omega_matter = 0.27 and experiment with the calculators yourself

16. Mar 31, 2005

### hellfire

If you neglect the energy density of radiation and consider that the universe is currently flat, you can make use of the following formula (which you can derive from the Friedmann equation):

$$dt = \frac{da}{H_0 \left(\frac{\Omega_{m,0}}{a} + a^2 \Omega_{\Lambda,0}\right)^{\frac{1}{2}}}$$

The subindices mean current values for the Hubble parameter (= 71 Km /s Mpc), Omega matter (= 0.27), Omega cosmological constant (= 0.73).

To get the age at a given redshift z, you have to integrate from a = 0, to a = 1/(1+z).

Last edited: Mar 31, 2005
17. Mar 31, 2005

### SpaceTiger

Staff Emeritus
If this is a question from a class, then I suspect your professor is asking you to consider a flat universe with only matter (i.e. no cosmological constant). The reason they have you make this simplifying assumption is that the equations are harder to solve for other situations. This simple model for the universe was considered for a long time before the acceleration was discovered, so it shouldn't be wildly off.