# How are dark energy and matter quantified?

1. Feb 8, 2016

### gnnmartin

To quote http://science.nasa.gov/astrophysics/focus-areas/what-is-dark-energy/, "It turns out that roughly 68% of the Universe is dark energy. Dark matter makes up about 27%. The rest - everything on Earth, everything ever observed with all of our instruments, all normal matter - adds up to less than 5% of the Universe. "

I know (roughly) where these estimates come from, but I don't see how we quantify them. My best guess is that viewing the universe as a spacial 3 sphere (ie everywhere similar) with time running at the same rate everywhere, we can estimate the amount of 'ordinary' matter per unit volume, assuming pressure is a negligible, and we can estimate the 'mass equivalence' of any dark matter (ie the extra mass suggested by the speed of rotation of galaxies), and then the 'negative mass equivalence' suggested by the rate of acceleration of expansion of the universe.

Is that roughly how the percentages are calculated? Is there an authoritative source to quote?

2. Feb 8, 2016

### Staff: Mentor

Roughly, yes.

3. Feb 10, 2016

### gnnmartin

Thanks. I'd still like a quotable authority that I can reference when writing something relevant.

4. Feb 10, 2016

### Bandersnatch

You can use PLANCK mission's data release papers. Such as these latest ones: http://www.cosmos.esa.int/web/planck/publications
You'll most easily find results for baryonic matter/dark matter/dark energy densities in the overview (first) paper. There are also various methods used listed there (baryon acoustic oscillations power spectrum, gravitational lensing, etc.).
If nothing in those papers rings any bells (they are highly technical), you want to look for $Ω_b$ for baryonic matter density, $Ω_c$ for dark matter, and $Ω_Λ$ for dark energy. There's usually a table or two in there. For various reasons, those values are often given in the form of $Ω_{whatever}h^2$, where $h$ is the Hubble constant ($H_0$ always also given) divided by 100.
The densities Ω are given as fractions of unity (i.e. 10% is 0.1 and so on).

As an example of a method of getting those values, lots of information can be gleaned by observing the anisotropies in CMBR (the clumpiness of deviations from homogeneity). The page listed below has some nice animations showing how changing the parameters of the model (densities of various components) changes the expected power spectrum. It can then be compared with observations of CMBR to see which set of parameters fits best to what is seen.
http://background.uchicago.edu/~whu/metaanim.html (switch between the tabs on the left)
The tutorial section will walk you through the reasoning behind those measurements, and why they are a proxy for those densities.

Last edited: Feb 11, 2016
5. Feb 11, 2016

### gnnmartin

Many thanks, very useful. I'll study that.

I was aware of the pivotal role of Ω, but it is hard to look for that, even in the index of a text book. Does this value have a name other than omega that one can expect to find in an index?

6. Feb 11, 2016

### Bandersnatch

It's called density parameter(s). The problem with looking for it in an index as a phrase is that many papers don't even bother writing it in any other form than Ω, because it was defined some place earlier or is obvious from the context (obvious to those at whom the paper is aimed, that is). Quick skimming of the 2015 PLANCK overview paper seems to indicate that they didn't bother with naming the terms they list in tables (they did in earlier releases - e.g. the 2013 one)

Note: I made a mistake above (now edited out) - I listed $Ω_m$ for dark energy, whereas that's the total matter content (baryonic+dark). Dark energy will be listed either as $Ω_Λ$, $1-Ω_m$ or left out completely since for present values and a critical density universe it's whatever is left after deducting matter density and the now-negligible radiation density from unity (so it's obvious; e.g. 30% matter density implies 70% DE density).

7. Feb 11, 2016

Thanks.