Abstract
In this paper, we study the estimation of the effective number of relativistic species from a combination of cosmic microwave background (CMB) and baryon acoustic oscillations (BAO) data. We vary different ingredients of the analysis: the Planck high-ℓ likelihoods, the Boltzmann solvers, and the statistical approaches. The variation of the inferred values gives an indication of an additional systematic uncertainty, which is of the same order of magnitude as the error derived from each individual likelihood. We show that this systematic uncertainty is essentially associated to the assumptions made in the high-ℓ likelihood implementations, in particular for the foreground residuals modellings. We also compare a subset of likelihoods using only the TE power spectra, expected to be less sensitive to foreground residuals.
Highlights
The expansion rate in the early universe depends on the energy density of relativistic particles, which is parameterised by Neff, the effective number of relativistic species or degrees of freedom
We have studied in detail the estimation of the effective number of relativistic species from cosmic microwave background (CMB) Planck data
– If we can safely neglect the impact of the covariance matrix estimation, as suggested by the obtained results, the variation linked to the assumptions on foreground residuals modelling derived from the comparison of the high- likelihoods has been estimated to be of the order of ∆Neff = 0.17, of which a small part may be attributed to a statistical effect
Summary
Neff relates the radiation (Ωrad) and the photon (Ωγ) energy densities relative to the critical density through: Ωrad. Under the assumption that only photons and standard light neutrinos contribute to the radiation energy density, Neff is equal to the effective number of neutrinos: Neff 3.045. This value has been derived from the number of neutrinos constrained by the measurement of the decay width of the Z boson (Beringer 2012), and takes into account residual interactions during the electronpositron annihilation
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