Contribution of the first galaxies to the cosmic far-infrared/sub-millimeter background - I. Mean background level

We study the contribution of the first galaxies to the far-infrared/sub-millimeter (FIR/sub-mm) extragalactic background light (EBL) by implementing an analytical model for dust emission. We explore different dust models, assuming different grain size distributions and chemical compositions. According to our findings, observed re-radiated emission from dust in dwarf-size galaxies at $z \sim 10$ would peak at a wavelength of $\sim 500 \mu {\rm m}$ with observed fluxes of $\sim 10^{-3} - 10^{-2}$ nJy, which is below the capabilities of current observatories. In order to be detectable, model sources at these high redshifts should exhibit luminosities of $\gtrsim 10^{12} L_{\odot}$, comparable to that of local ultra-luminous systems. The FIR/sub-mm EBL generated by primeval galaxies peaks at $\sim 500 \mu {\rm m}$, with an intensity ranging from $\sim 10^{-4}$ to $10^{-3} {\rm nW \ m^{-2} \ sr^{-1}}$, depending on dust properties. These values are $\sim 3 - 4$ orders of magnitude below the absolute measured cosmic background level, suggesting that the first galaxies would not contribute significantly to the observed FIR/sub-mm EBL. Our model EBL exhibits a strong correlation with the dust-to-metal ratio, where we assume a fiducial value of $D = 0.005$, increasing almost proportionally to it. Thus, measurements of the FIR/sub-mm EBL could provide constraints on the amount of dust in the early Universe. Even if the absolute signal from primeval dust emission may be undetectable, it might still be possible to obtain information about it by exploring angular fluctuations at $\sim 500 \mu {\rm m}$, close to the peak of dust emission from the first galaxies.