Samples from Planck TT+lowP chains in the N_eff–H₀ plane, colour-coded by σ₈. The grey bands show the constraint H₀ = (70.6 ± 3.3) km s^-1Mpc^-1 of Eq. (30). Notice that higher N_eff brings H₀ into better consistency with direct measurements, but increases σ₈. Solid black contours show the constraints from Planck TT,TE,EE+lowP+BAO. Models with N_eff< 3.046 (left of the solid vertical line) require photon heating after neutrino decoupling or incomplete thermalization. Dashed vertical lines correspond to specific fully-thermalized particle models, for example one additional massless boson that decoupled around the same time as the neutrinos (ΔN_eff ≈ 0.57), or before muon annihilation (ΔN_eff ≈ 0.39), or an additional sterile neutrino that decoupled around the same time as the active neutrinos (ΔN_eff ≈ 1).