Five parameters are all you need (in ΛCDM)

Abstract The standard cosmological model successfully describes the Universe with six parameters. One of them, the optical depth to reionization τ reio , empirically depicts the scatterings of Cosmic Microwave Background (CMB) photons off free electrons, as the intergalactic medium transitions from neutral to ionized. τ reio depends on the neutral hydrogen fraction x HI , which ultimately depends on cosmology. We present a novel method to establish such a missing link between physical parameters and reionization timeline using symbolic regression. We discover the timeline has a universal shape well described by the Gompertz mortality law, applicable to any cosmology within our simulated data. Unlike the conventional tanh prescription, our model is asymmetric in time and a good fit to astrophysical constraints on x HI . By combining CMB with astrophysical data and marginalizing over astrophysics, we treat τ reio as a derived parameter, tightening its constraint to < 3%. This approach reduces the error on the amplitude of the primordial fluctuations by a factor of 2.3 compared to Planck's PR3 constraint and provides a commanding constraint on the ionization efficiency ζ UV = 26.9 +2.1 -2.5 . We expect further improvements in the near term as reionization constraints increase and our understanding of reionization advances.