Probing the epoch of pre-reionization by cross-correlating cosmic
  microwave and infrared background anisotropies
  The epoch of first star formation and the state of the intergalactic medium
(IGM) at that time are not directly observable with current telescopes. The
radiation from those early sources is now part of the Cosmic Infrared
Background (CIB) and, as these sources ionize the gas around them, the IGM
plasma would produce faint temperature anisotropies in the Cosmic Microwave
Background (CMB) via the thermal Sunyaev-Zeldovich (TSZ) effect. While these
TSZ anisotropies are too faint to be detected, we show that the
cross-correlation of maps of source-subtracted CIB fluctuations from {\it
Euclid}, with suitably constructed microwave maps at different frequencies can
probe the physical state of the gas during reionization and test/constrain
models of the early CIB sources. We identify the frequency-combined
CMB-subtracted microwave maps from space and ground-based instruments to show
that they can be cross-correlated with the forthcoming all-sky {\it Euclid} CIB
maps to detect the cross-power at scales $\sim 5'-60'$ with the signal/noise of
up to $S/N\sim 4-8$ depending on the contribution to the Thomson optical depth
during those pre-reionization epochs ($\Delta \tau\simeq 0.05$) and the
temperature of IGM (up to $\sim10^4$K). Such a measurement would offer a new
window to explore emergence and physical properties of these first light
sources.
