Towards a precision calculation of the effective number of neutrinos Neff in the Standard Model: the QED equation of state

• Published in: Journal of cosmology and astroparticle physics 2020-03, Vol.2020 (3)
• Main Authors: Bennett, Jack J, Buldgen, Gilles, Drewes, Marco, Wong, Yvonne YY
• Format: Article
• Language: eng ; jpn
• Subjects: Approximation; Astronomical models; Cosmology; Decoupling; Electron mass; Equations of state; Neutrinos; Plasma (physics); Temperature; Transport
• ISSN: 1475-7516; 1475-7516
• DOI: 10.1088/1475-7516/2020/03/003

We revisit and quantify in this work several aspects of Standard Model physics at finite temperature that drive the theoretical value of the cosmological parameter, the effective number of neutrinos Neff, away from 3 in the early universe. Our chief focus is finite-temperature corrections to the equation of state of the QED plasma in the vicinity of neutrino decoupling at T∼1 MeV, where T is the photon temperature. Working in the instantaneous decoupling approximation, we recover at (e2), where e is the elementary electric charge, the well-established correction of δNeff(2)≃0.010 across a range of plausible neutrino decoupling temperatures, in contrast to an erroneous claim in the recent literature which found twice as large an effect. At (e3) we find a new and significant correction of δNeff(3)≃−0.001 that has so far not been accounted for in any precision neutrino decoupling calculation of Neff, significant because this correction is in fact larger than—or at least comparable to—the change in Neff induced between including and excluding neutrino oscillations in the transport modelling. In addition to the QED equation of state, we make a first pass at quantifying finite-temperature QED corrections to the weak interaction rates that directly affect the neutrino decoupling process, and find in this connection that the (e2) thermal electron mass correction induces a change of δNeffmth≲10−4. A complete assessment of the various effects considered in this work on the final value of Neff will necessitate an account of neutrino energy transport beyond the instantaneous decoupling approximation. However, relative to Neff=3.044 obtained in the most recent such calculation, we expect the new effects found in this work to lower the number to Neff=3.043.