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I wanted to recalculate the number of atoms in the universe according to What paper can I cite for the estimated number of atoms in the observable universe to be lower than $10^{82}$? .

But in the cited paper Planck 2015 Results XIII Cosmological Parameters.pdf the density of baryons (where it is about $0.025$, page $47$) differs from the one in the calculation above (where it is about $0.048$). Why is that?

MarianD
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Ben
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1 Answers1

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The number "~0.025" is not the baryon density parameter $\Omega_\mathrm{b}$, but $\omega_\mathrm{b} \equiv \Omega_\mathrm{b}h^2$, i.e. scaled by the dimensionless Hubble parameter $h \equiv H_0 \, / \,(100\,\mathrm{km}\,\mathrm{s}^{-1}\,\mathrm{Mpc}^{-1})$.

Using the "TT+lowP+lensing" numbers (which is common; you'll find them in 2nd column of Tab. 4, p. 31, in Planck Collaboration et al. 2016), $$ \begin{array}{rcl} h & = & 0.6781\pm0.0092,\\ \Omega_\mathrm{b}\,h^2 & = & 0.02226\pm0.00023, \end{array} $$ so $$ \Omega_\mathrm{b} = 0.0484\pm0.0014, $$ where I've simply assumed standard error propagation with no covariance.

pela
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  • Ah, ok. I saw the equation with the additional parameter but I thought this is the planck constant :D Thank you for the further information about the numbers! – Ben Oct 31 '17 at 13:22