# Baryon density of the universe at recombination epoch

1. Jan 1, 2009

### 2203312

Hi
I am just looking for the formula to calculate the baryon density of the universe at the recombination epoch.

Is it a case of adding the average density of matter + radiation? but this does not take into account the recombination epoch (z=1200).

I do not have a background in physics (that is why I am here)

2. Jan 1, 2009

### marcus

Just for convenience let's say you want the baryon density at z=1199, so that z+1 = 1200.

That means that distances have expanded by a factor of 1200 since that time, and volumes have expanded by the cube, that is by the factor 12003

That means whatever the density is now, to find the density then you multiply by 12003

So your problem is simply to find the PRESENT baryon density.

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In what form, in what units, do you want to know the density? As a number of particles per cubic meter? Or as kilograms of rest mass per cubic meter? Or as the energy equivalent of mass of the baryonic matter, in joules per cubic meter?

And how accurate do you want it?

If you want a rough estimate in joules per cubic meter that is easy. Today the critical density is 0.85 nanojoule per m3, and it is estimated that baryonic matter is about 4% of critical. So today the density if about 0.034 nJ per m3
Then you must simply multiply by 12003

The google calculator would help here. Put this in the box and press return"
1200^3*.034 nJ/m^3/c^2

It will give something like 6.5 x 10-19 kilogram per m3

If you don't insist on kilograms, and joules are OK you can say
1200^3*.034 nJ/m^3
and it will say 0.059 joule per cubic meter.

Last edited: Jan 1, 2009
3. Jan 2, 2009

### 2203312

Many thanks for that