Constraining exotic high-$z$ reionization histories with Gaussian processes and the Cosmic Microwave Background

The large-angle polarization anisotropies in the Cosmic Microwave Background (CMB) arise from Thomson scattering of CMB photons off free electrons in the post-recombination Universe. In the standard $\Lambda$ cold dark matter cosmological model, the free electron density increases at redshifts $z \lesssim 10$ as the first stars form, reionizing the intergalactic medium. We use \emph{Gaussian processes} to perform a model-independent reconstruction of the cosmic reionization history constrained by \textit{Planck} CMB data. Our approach recovers the standard reionization at $z \lesssim 10$ and places stringent limits on any additional high-$z$ reionization. From this reconstruction, we define a new derived parameter, the high-redshift contribution to the CMB optical depth, $\tau_{\mathrm{highz}}$, whose posterior distribution provides robust constraints on exotic energy injection scenarios. We demonstrate this for decaying dark matter with particle masses in the range $\mathcal{O}(1\,\text{MeV})$. A companion paper applies this framework to multi-axion models. All data and code are publicly available at: \href{https://github.com/Cheng-Hanyu/CLASS_reio_gpr}{github.com/Cheng-Hanyu/CLASS\_reio\_gpr}.