Towards a precision calculation of the effective number of neutrinos $N_{\rm eff}$ in the Standard Model I: The QED equation of state
(2020) Journal of Cosmology and Astroparticle Physics — Vol. 2003, p. 3 (2020)
Files
191104504.pdf
Open Access - Adobe PDF
- 1004.19 KB
Details
- Authors
- Abstract
- We revisit several aspects of Standard Model physics at finite temperature that drive the theoretical value of the cosmological parameter $N_{\rm eff}$, the effective number of neutrinos in the early universe, away from 3. Our chief focus is finite-temperature corrections to the equation of state of the QED plasma in the vicinity of neutrino decoupling at $T \sim 1$ MeV, where $T$ is the photon temperature. Working in the instantaneous decoupling approximation, we recover at ${\cal O}(e^2)$, where $e$ is the elementary electric charge, the well-established correction of $\delta N_{\rm eff}^{(2)} \simeq 0.010$ 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 ${\cal O}(e^3)$ we find a new and significant correction of $\delta N_{\rm eff}^{(3)} \simeq -0.001$ that has so far not been accounted for in any precision calculation of $N_{\rm eff}$, significant because this correction is potentially larger than the change in $N_{\rm eff}$ 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 that the ${\cal O}(e^2)$ thermal electron mass correction induces a change of $\delta N_{\rm eff}^{m_{\rm th}} \lesssim 10^{-4}$. A complete assessment of the various effects considered in this work on the final value of $N_{\rm eff}$ will necessitate an account of neutrino energy transport beyond the instantaneous decoupling approximation. However, relative to $N_{\rm eff} = 3.044$ obtained in the most recent such calculation, we expect the new effects found in this work to lower the number to $N_{\rm eff} = 3.043$.
- Affiliations
Citations
Bennett, J. J., Buldgen, G., Drewes, M., & Wong, Y. Y. Y. (2020). Towards a precision calculation of the effective number of neutrinos $N_{\rm eff}$ in the Standard Model I: The QED equation of state. Journal of Cosmology and Astroparticle Physics, 2003, 3. https://doi.org/10.1088/1475-7516/2020/03/003 (Original work published 2020)