 Contribution of a decoupled real scalar to Neff

ID: contribution-of-a-decoupled-real-scalar-to-neff

If a real relativistic scalar decouples when the other coupled particles have entropy degrees of freedom

g_{* s} (T_{d})

, then

Δ N_{eff} = \frac{4}{7} (\frac{43}{4 g _{* s} ( T _{d} )})^{4/3} .

Earlier decoupling and the subsequent annihilation of more coupled species make the scalar colder and suppress its contribution.

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