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.
