A Semiblind Reconstruction of the History of Effective Number of Neutrinos Using CMB Data

We explore the possibility of redshift-dependent deviations in the contribution of relativistic degrees of freedom to the radiation budget of the cosmos, conventionally parameterized by the effective number of neutrinos $N_{\mathrm{e}\mathrm{f}\mathrm{f}}$, from the predictions of the standard model. We expand the deviations $\mathrm{\Delta }{N}_{\mathrm{e}\mathrm{f}\mathrm{f}}(z)$ in terms of top-hat functions and treat their amplitudes as the free parameters of the theory to be measured alongside the standard cosmological parameters by the Planck measurements of the cosmic microwave background (CMB) anisotropies and Baryonic Acoustic Oscillations, as well as performing forecasts for futuristic CMB surveys such as PICO and CMB-S4. We reconstruct the history of $\mathrm{\Delta }{N}_{\mathrm{e}\mathrm{f}\mathrm{f}}$ and find that with the current data the history is consistent with the standard scenario. Inclusion of the new degrees of freedom in the analysis increases $H_0$ to $68.71\pm 0.44$, slightly reducing the Hubble tension. With the smaller forecasted errors on the $\mathrm{\Delta }{N}_{\mathrm{e}\mathrm{f}\mathrm{f}}(z)$ parametrization modes from future CMB surveys, very accurate bounds are expected within the possible range of dark radiation models.