Question: If the current CMB temperature was (27 mathrm{~K}) rather than (2.7 mathrm{~K}), the baryonto-photon ratio would be (10^{3}) times smaller. Equation (9.7.8) implies that the

If the current CMB temperature was \(27 \mathrm{~K}\) rather than \(2.7 \mathrm{~K}\), the baryonto-photon ratio would be \(10^{3}\) times smaller. Equation (9.7.8) implies that the nucleosynthesis temperature would have been about \(20 \%\) lower which would have delayed the nucleosynthesis by an extra two minutes. This would have given the neutrons a longer time to decay leading to \(q \approx 0.10\) rather than 0.12 , leading to a helium content in the universe of about \(20 \%\) by weight. If the current CMB temperature were \(0.27 \mathrm{~K}\), that would have increased the baryon-to-photon ratio by a factor of \(10^{3}\). Fewer photons per baryon would have led to an earlier nucleosynthesis, less time for neutrons to decay and an increase of the neutron fraction to \(q \approx 0.135\) leading to about \(27 \%\) helium content.

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