Constraints on CMBR flux due to high-z dust emission

Gjergo & Kroupa (2025) have proposed a new foreground CMBR component produced by dust associated with the progenitor clouds at $z=15-20$ that led to the formation of massive early-type galaxies, calculating that a minimum of 1.4% and a maximum of 100% of the whole CMBR radiation would be produced by this mechanism. Here, I check how much dust emission is compatible with the spectrum of the CMBR monopole flux measurements within the corresponding errors. COBE-FIRAS monopole is fitted to different models with different dust emissivity spectral indexes ($\beta$) and dispersion of redshifts of the progenitor clouds ($\sigma _d$). Within the realistic values of $\beta \ge 0.5$, $\sigma _d\ge 0.8$, the contamination of CMBR flux by high $z$ dust should be $<1.3$% (95% CL).