Relativistic SZ maps and electron gas temperature spectroscopy

While third-generation CMB experiments have allowed to release the first maps of Compton-$y$ distortion due to thermal Sunyaev-Zeldovich (SZ) effect, next-generation CMB experiments should allow us to map also the electron gas temperature, $T_{\rm e}$, across the sky through the detection of relativistic corrections to the thermal SZ effect. We discuss about experimental requirements to break the $y$-$T_{\rm e}$ degeneracy of the observed SZ intensity, and propose a new component separation approach based on moment expansion to disentangle the $y$ and $T_{\rm e}$ observables of the relativistic SZ effect while mitigating foregrounds. We show how our approach offers a new spectroscopic view of the clusters not only across frequencies but now also across temperatures. We also show how the relativistic electron temperature power spectrum provides a new cosmological observable which may complement the Compton-$y$ map power spectrum to break some of the parameter degeneracies in future cosmological SZ analyses.