2023-08-08 18:04:04
As you well know, the standard cosmological model ΛCDM allows us to predict the effective number of neutrino species, Neff; actually, the ratio between the energy density of low-mass fermions moving at ultrarelativistic speeds and the energy density of photons (Neff ∝ pn/RG). In 2009 it was estimated to be 3,046, in 2016 it was lowered to 3,045 and in 2019 to 3,044; work has continued to reduce the uncertainty of this calculation. The last estimated value is published in arXiv, Neff = 3.0432 ± 0.0002 ≈ 3.043, which includes QED corrections to second order (NLO) in the scattering between an electron and a positron that gives rise to a neutrino-antineutrino pair. A technically complicated calculation relevant to future ultra-precision cosmology (the figure shows the relative error of the NLO correction with respect to the LO). Remember that the Planck space telescope precision estimate published in 2020 is Neff = 2.99 ± 0.17, but is expected to drop by a factor of ten from 0.17 to 0.014 over the next few decades. The first firm signal of physics beyond the Standard Model can come from anywhere, including ultra-precision cosmology.
The prediction of the cosmological model ΛCDM is Neff = (8/7) (11/4)4/3 (pn/RG), where pn y RG are the energy densities of fermions with a mass less than that of the electron (we only know neutrinos) and of photons for temperatures less than that associated with the mass of the electron (T ≪ me). For more than forty years, the theoretical estimate of the value of Neff, including different effects associated with the uncoupling of neutrinos from the primordial plasma via their annihilation and scattering into electron-positron pairs, that is, the eν→eν, ee→νν, and ee→νν(γ) interactions. The NLO calculation is very complicated because the parameter space is very large, since it has fifteen dimensions, which makes it impossible to solve the Liouville equation that describes the thermodynamic equilibrium during the decoupling of neutrinos. Additional hypotheses about the thermal distribution of neutrinos are required, which skew said space and allow a feasible calculation. I don’t have enough knowledge to assess whether the new NLO calculation will be definitive, or if more rigorous alternative calculations will be published in the next few years, but as far as I can tell, the calculation seems reasonable and robust to me.
A new number to remember, 3,043. I predict that the new calculation will end up published in Physical Review Letters. The new calculation has been published in Mattia Cielo, Miguel Escudero, …, Ofelia Pisanti, “Neff in the Standard Model at NLO is 3.043,” arXiv:2306.05460 [hep-ph] (08 Jun 2023), two: https://doi.org/10.48550/arXiv.2306.05460.
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