<p>We are not actually measuring the <span class="math-container">$\Omega_r$</span>,<span class="math-container">$\Omega_m$</span>,<span class="math-container">$\Omega_{\Lambda}$</span>.</p>
<p>At first, we measure the <a href="http://astronomy.swin.edu.au/cosmos/D/Distance+Modulus" rel="nofollow noreferrer">distance modulus</a> to certain celestial objects by using the <a href="http://astronomy.swin.edu.au/cosmos/S/Standard+Candle" rel="nofollow noreferrer">standart candles</a> in the astronomy.</p>
<p>This distance can be calculated from,</p>
<p><span class="math-container">$$d_L=\frac {c} {H_0}z(1+\frac {1-q_0} {2}z)\,\,\, (Eqn.1)$$</span></p>
<p>Here <span class="math-container">$q_0$</span> represents the deceleration parameter. Now I am not going to go in mathematical details but you should now that, using the acceleration equation we can write <span class="math-container">$q_0$</span> in terms of <span class="math-container">$\Omega_r$</span>,<span class="math-container">$\Omega_m$</span>,<span class="math-container">$\Omega_{\Lambda}$</span>.</p>
<p><span class="math-container">$$q_0=1/2 \sum \Omega_{w,0}(1+3w)$$</span>  and for matter ,<span class="math-container">$w=0$</span>, for radiation <span class="math-container">$w=1/3$</span> and for dark energt <span class="math-container">$w=-1$</span> we get,</p>
<p><span class="math-container">$$q_0=\Omega_r+1/2\Omega_m - \Omega_{\Lambda}\,\,\, (Eqn.2)$$</span></p>
<p>And the relationship between distance modulus <span class="math-container">$(m-M)$</span> and <span class="math-container">$d_L$</span> can be written as,</p>
<p><span class="math-container">$$m-M=5log_{10}(d_L/1Mpc)+25\,\,\, (Eqn.3)$$</span></p>
<p>If we combine Eqn.1 and Eqn.3 we get a relationship between distance modulus and z.</p>
<p>We plot the <span class="math-container">$m-M$</span> for distant objects with respect to <span class="math-container">$z$</span>. From the slope of the graph we can determine the <span class="math-container">$H_0$</span> (for <span class="math-container">$z\rightarrow 0$</span>) And for large z,  deviation of the plot from the straight line gives us to determine the <span class="math-container">$q_0$</span>.</p>
<p>Now we have experimental data. Then we put different values for <span class="math-container">$q_0$</span> or equally <span class="math-container">$\Omega_m$</span> and <span class="math-container">$\Omega_{\Lambda}$</span> (with respect to Eqn.2) to determine the best fit for the graph (since we can take <span class="math-container">$\Omega_r=0$</span>)</p>
<p><a href="https://i.sstatic.net/RIu9u.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/RIu9u.png" alt="Distance modulus versus redshift for type Ia supernovae from the Supernova Cosmology Project (Perlmutter et al. 1999, ApJ, 517, 565) and the High-z Supernova Search Team (Riess et al. 1998, AJ, 116, 1009). " /></a></p>
<blockquote>
<p>Edit: I clearly missed the &quot;The Planck data&quot; in the OP's question but its the same general idea. For different density parameters, the CMBR would look different, like the graphs that I shared are different for different density parameters. So by looking at the CMBR, we can determine the density parameters and which one fits well to the CMBR.</p>
</blockquote>
<p>Further Note: I want to also suggest that the <span class="math-container">$\Omega_b$</span> can be calculated from the early universe by measuring the amount of deuterium and other elements present in primordial gas clouds.</p>
<p>And observering the rotational curves on the galaxies we can have approximate values on the <span class="math-container">$\Omega_{dm}$</span>. (finding the dark matter density)</p>
<p>We cannot deduce the <span class="math-container">$\Omega_m$</span> and <span class="math-container">$\Omega_{\Lambda}$</span> just by looking at the Supernova data, for example the supernova data is also consistent with <span class="math-container">$\Omega_m=0$</span> and <span class="math-container">$\Omega_{\Lambda}=0.4$</span> or with <span class="math-container">$\Omega_m=1$</span> and <span class="math-container">$\Omega_{\Lambda}=1.7$</span></p>

CC BY-SA 4.0
2019-01-19T12:49:18.690Z
The question asks about the analysis of Planck data.
ProfRob
CC BY-SA 4.0
2019-01-19T14:03:59.057Z
@I edited my answer
seVenVo1d
CC BY-SA 4.0
2019-01-19T11:56:19.680Z
2019-01-28T16:33:59.247Z
2020-06-17T09:47:40.653Z
seVenVo1d
<p>In 2015 the Planck satellite consortium released an analysis of data collected by the Planck satellite that showed this percentage break down of the universe’s mass/energy.</p>

<p>Ordinary matter: 4.9%</p>

<p>Dark Matter: 26.8%,</p>

<p>Dark Energy: 68.3%</p>

<p>How did they calculate the "stuff" of the observable universe and how did they come to this conclusion?</p>

<p>I assume  this took some tough calculations and some work with a supercomputer but i wonder what the entire process was.</p>

CC BY-SA 4.0
2019-01-19T10:34:50.363Z
It's unclear what form of answer you want. In a sentence, you have a physical model for how the CMB is produced, including its spatial variations, and you compare it with the observations.
ProfRob
CC BY-SA 4.0
2019-01-19T11:16:44.717Z
They didn't just happen to know this. how did they find out? In detail
Tom Sol
CC BY-SA 4.0
2019-01-19T11:28:09.223Z
Didn't happen to know what? The big bang model and indications of dark matter were around long before CMB variations were detected. Your CMB model has (variable) parameters, characterising the things you want to know. And you compare it with what is observed to constrain those parameters.
ProfRob
<universe><dark-matter><observable-universe><dark-energy><matter>
What was the process of calculating how much darkmatter/matter/dark energy the observable universe consists of and how did it come at this conclusion
Tom Sol
# What was the process of calculating how much darkmatter/matter/dark energy the observable universe consists of and how did it come at this conclusion

(Asked by: username_0 on 2019-01-18)

In 2015 the Planck satellite consortium released an analysis of data collected by the Planck satellite that showed this percentage break down of the universe’s mass/energy.

Ordinary matter: 4.9%

Dark Matter: 26.8%,

Dark Energy: 68.3%

How did they calculate the "stuff" of the observable universe and how did they come to this conclusion?

I assume this took some tough calculations and some work with a supercomputer but i wonder what the entire process was.

**Tags:** universe, dark-matter, observable-universe, dark-energy, matter

> **Comments:**
> **username_1**: It's unclear what form of answer you want. In a sentence, you have a physical model for how the CMB is produced, including its spatial variations, and you compare it with the observations.  
> **username_0**: They didn't just happen to know this. how did they find out? In detail  
> **username_1**: Didn't happen to know what? The big bang model and indications of dark matter were around long before CMB variations were detected. Your CMB model has (variable) parameters, characterising the things you want to know. And you compare it with what is observed to constrain those parameters.  

---

## 1 answers

### Answer by username_2 on 2019-01-19. Score: 2 | Accepted answer

We are not actually measuring the $\Omega\_r$,$\Omega\_m$,$\Omega\_{\Lambda}$.

At first, we measure the [distance modulus](http://astronomy.swin.edu.au/cosmos/D/Distance+Modulus) to certain celestial objects by using the [standart candles](http://astronomy.swin.edu.au/cosmos/S/Standard+Candle) in the astronomy.

This distance can be calculated from,

$$d\_L=\frac {c} {H\_0}z(1+\frac {1-q\_0} {2}z)\,\,\, (Eqn.1)$$

Here $q\_0$ represents the deceleration parameter. Now I am not going to go in mathematical details but you should now that, using the acceleration equation we can write $q\_0$ in terms of $\Omega\_r$,$\Omega\_m$,$\Omega\_{\Lambda}$.

$$q\_0=1/2 \sum \Omega\_{w,0}(1+3w)$$ and for matter ,$w=0$, for radiation $w=1/3$ and for dark energt $w=-1$ we get,

$$q\_0=\Omega\_r+1/2\Omega\_m - \Omega\_{\Lambda}\,\,\, (Eqn.2)$$

And the relationship between distance modulus $(m-M)$ and $d\_L$ can be written as,

$$m-M=5log\_{10}(d\_L/1Mpc)+25\,\,\, (Eqn.3)$$

If we combine Eqn.1 and Eqn.3 we get a relationship between distance modulus and z.

We plot the $m-M$ for distant objects with respect to $z$. From the slope of the graph we can determine the $H\_0$ (for $z\rightarrow 0$) And for large z, deviation of the plot from the straight line gives us to determine the $q\_0$.

Now we have experimental data. Then we put different values for $q\_0$ or equally $\Omega\_m$ and $\Omega\_{\Lambda}$ (with respect to Eqn.2) to determine the best fit for the graph (since we can take $\Omega\_r=0$)

[![Distance modulus versus redshift for type Ia supernovae from the Supernova Cosmology Project (Perlmutter et al. 1999, ApJ, 517, 565) and the High-z Supernova Search Team (Riess et al. 1998, AJ, 116, 1009). ](https://i.sstatic.net/RIu9u.png)](https://i.sstatic.net/RIu9u.png)

> Edit: I clearly missed the "The Planck data" in the OP's question but its the same general idea. For different density parameters, the CMBR would look different, like the graphs that I shared are different for different density parameters. So by looking at the CMBR, we can determine the density parameters and which one fits well to the CMBR.

Further Note: I want to also suggest that the $\Omega\_b$ can be calculated from the early universe by measuring the amount of deuterium and other elements present in primordial gas clouds.

And observering the rotational curves on the galaxies we can have approximate values on the $\Omega\_{dm}$. (finding the dark matter density)

We cannot deduce the $\Omega\_m$ and $\Omega\_{\Lambda}$ just by looking at the Supernova data, for example the supernova data is also consistent with $\Omega\_m=0$ and $\Omega\_{\Lambda}=0.4$ or with $\Omega\_m=1$ and $\Omega\_{\Lambda}=1.7$

> **Comments:**
> **username_1**: The question asks about the analysis of Planck data.  
> **username_2**: @I edited my answer  

---

