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How can I calculate the density of the Universe at recombination?

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Recombination occurred at a red shift of about Z = 1100 i.e. the length scale has increased by a factor of 1100 (strictly speaking 1100 + 1) since then. So if you take the current density and multiply by $1100^3$ you'll get the density at recombination.

However your question isn't as simple as it seems. Do you mean the baryon density, the baryon + dark matter density or the total density? The current total density is pretty close to the critical density, and Wikipedia gives this as about five hydrogen atoms per cubic meter. The baryon density is about 4% of this and the dark matter density is about 21% of this. Five hydrogen atoms weigh $8.3 \times 10^{-24}$g, and multiplying this by $1100^3$ makes the total density at recombination about $10^{-14}$gm$^{-3}$.

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Yes, I want to calculate total recombination density but how five hydrogen atom comes in equation. – sknphy Jun 8 '12 at 13:23
The five hydrogen atoms per m$^3$ is the current critical density. The cosmic microwave background tells us the universe is flat, and for a flat universe the critical density can be calculated from the Hubble constant. If you do this it comes out as about $8.3 \times 10^{-24}$gm$^{-3}$, which is the same as 5 hydrogen atoms per m$^3$. Using five hydrogen atoms as the unit of weight is just a good way to visualise the density and relate it to something easy to remember. – John Rennie Jun 8 '12 at 13:49

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