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.
