View Full Version : How to calculate Omega_b through time ?

stephaneww

2019-Feb-02, 05:09 AM

Hello,

In the \Lambda CDM model, I have a doubt. Is this true for long duration from now :

\rho_{c_i}=\frac{3H_i^2}{8\pi G} \text{ } kg/m^3

V_i=4/3 \pi R_i^3 where R_i is comoving distance of observable universe

M_{b_i} assumed constant :

\Omega_{b_i} =M_{b_i}/(V_i *\rho_{c_i}) \text{ ?}

If it's wrong, what is the good formula please ?

Reality Check

2019-Feb-04, 12:41 AM

In the \Lambda CDM model, I have a doubt. Is this true for long duration from now :

The answer is not true, stephaneww.

The Lambda-CDM model (https://en.wikipedia.org/wiki/Lambda-CDM_model) uses \Omega_{b_i} because we are limited to what we can see in the observable universe. The amount of baryonic matter in the universe is unknown.

The size of the observable universe is not the size of the universe which may be infinite. An infinite universe is another reason to use densities rather than amounts.

The Friedmann equations (https://en.wikipedia.org/wiki/Friedmann_equations) give the change of the different components of density with time. These are given in terms of the scale factor a(t) (https://en.wikipedia.org/wiki/Scale_factor_(cosmology)). We are currently in a matter-dominated universe so a(t) ~ t2/3. If dark energy dominates then a(t) will be an exponential law.

Also see the PDF Effect of Matter Density in the Evolution of the Universe (https://www.phys.ksu.edu/personal/rprice/Friedmann.pdf) where equation 11 is that the density of matter changes as a(t)-3.

StupendousMan

2019-Feb-05, 01:25 AM

It's not clear to me from your initial question, but perhaps you are interested in computing the value of the scale factor of the universe, or related quantities, as a function of time. If so, a few good references are listed at the end of this lecture:

http://spiff.rit.edu/classes/phys443/lectures/lambda/lambda.html

stephaneww

2019-Feb-08, 09:36 PM

Thanks, but I didn't find what I was looking for. In other words, to move forward a little :

- is the ratio \Omega_b/ \Omega_M constant in the model \Lambda CDM ?

stephaneww

2019-Feb-09, 05:36 PM

to be even more precise, I would like to have values (or how to calculate the values) of \Omega_b (ordinary matter = baryonic) and \Omega_{\Lambda} (density parameter of the cosmological constant) in relation to, or as a function of, the Hubble constant H at different ages of the universe.

thank you in advance

Cougar

2019-Feb-09, 06:08 PM

to be even more precise, I would like to have values (or how to calculate the values) of \Omega_b (ordinary matter = baryonic) and \Omega_{\Lambda} (density parameter of the cosmological constant) in relation to, or as a function of, the Hubble constant H at different ages of the universe.

Well, AFAIK, there's no more baryonic matter being added to the universe. Same for dark matter. But according to current thinking, as the universe expands, the dark energy does not become diluted. If it works like a cosmological constant, the density of dark energy per volume stays constant, even as the volume increases.

So the ratio of \Omega_b to \Omega_{\Lambda} will decrease with time.

stephaneww

2019-Feb-09, 07:06 PM

...

So the ratio of \Omega_b to \Omega_{\Lambda} will decrease with time.

Thank you but I know already that ;). What I need are the numeric values as an example or the calculation formulas. (I already know the formula to calculate \Omega_{\Lambda} from the value of H and the value of the cosmological constant) I need \Omega_b from H please

I'm also interest by the ratio of \Omega_b to \Omega_M or \Omega_\text{dark matter} throught time

stephaneww

2019-Feb-10, 01:50 AM

Hello,

I think I have found the elements of the answer to my question here on page 5 :

http://www.astronomy.ohio-state.edu/~ryden/ast143/Nov_18.pdf

Can someone confirm that it's OK, please?

StupendousMan

2019-Feb-10, 05:40 PM

Sure, now all you need is the relationship for the scale factor a(t). See references provided earlier in this thread.

Reality Check

2019-Feb-11, 12:08 AM

is the ratio \Omega_b/ \Omega_M constant in the model \Lambda CDM ?

See the PDF Effect of Matter Density in the Evolution of the Universe (https://www.phys.ksu.edu/personal/rprice/Friedmann.pdf) where equations 10 to 12 are the densities of radiation, matter and dark energy. Matter (baryonic or dark) has the same scale factor dependence. Their ratio will be constant (but not the densities themselves).

Reality Check

2019-Feb-11, 12:15 AM

...http://www.astronomy.ohio-state.edu/~ryden/ast143/Nov_18.pdf

Can someone confirm that it's OK, please?

That is OK and has similar equations to the PDF Effect of Matter Density in the Evolution of the Universe (https://www.phys.ksu.edu/personal/rprice/Friedmann.pdf) (equations 10 to 12 are the densities of radiation, matter and dark energy).

stephaneww

2019-Feb-11, 12:16 AM

Thank you. I'll try to work with that.

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