We explore the possibility of planet formation in the carbon-rich protoplanetary disks of carbon-enhanced metal-poor (CEMP) stars, possible relics of the early Universe. The chemically anomalous abundance patterns ([C/Fe] $geq$ 0.7) in this subset of low-mass stars suggest pollution by primordial core-collapsing supernovae (SNe) ejecta that are particularly rich in carbon dust grains. By comparing the dust-settling timescale in the protoplanetary disks of CEMP stars to the expected disk lifetime (assuming dissipation via photoevaporation), we determine the maximum distance $r_{max}$ from the host CEMP star at which carbon-rich planetesimal formation is possible, as a function of the host stars [C/H] abundance. We then use our linear relation between $r_{max}$ and [C/H], along with the theoretical mass-radius relation derived for a solid, pure carbon planet, to characterize potential planetary transits across host CEMP stars. Given that the related transits are detectable with current and upcoming space-based transit surveys, we suggest initiating an observational program to search for carbon planets around CEMP stars in hopes of shedding light on the question of how early planetary systems may have formed after the Big Bang.
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