  Recent observations of Type Ia SNe at redshifts 0 < z <1 reveal a progressive
dimming which has been interpreted as evidence for a cosmological constant of
Omega_Lambda ~ 0.7. An alternative explanation of the SN results is an open
universe with Omega_Lambda=0 and the presence of > 0.1 micron dust grains with
a mass density of Omega_dust ~ (few) * 10^{-5} in the intergalactic (IG)
medium. The same dust that dims the SNe absorbs the cosmic UV/optical
background radiation around ~ 1 micron, and re-emits it at far infrared (FIR)
wavelengths. Here we compare the FIR emission from IG dust with observations of
the cosmic microwave (CMB) and cosmic far infrared backgrounds (FIRB) by the
DIRBE/FIRAS instruments. We find that the emission would not lead to measurable
distortion to the CMB, but would represent a substantial fraction (> 75%) of
the measured value of the FIRB in the 300-1000 micron range. This contribution
would be marginally consistent with the present unresolved fraction of the
observed FIRB in an open universe. However, we find that IG dust probably could
not reconcile the standard Omega=1 CDM model with the SN observations, even if
the necessary quantity of dust existed. Future observations able to reliably
resolve the FIRB to a flux limit of ~0.5 mJy, along with a more precise measure
of the coarse-grained FIRB, will provide a definitive test of the IG dust
hypothesis in all cosmologies.
