We give an explanation for the origin of various properties observed in local infrared galaxies, and make predictions for galaxy counts and cosmic background radiation (CBR), by a new model extended from that for optical/near-infrared galaxies. Important new characteristics of this study are that (1) mass scale dependence of dust extinction is introduced based on the size-luminosity relation of optical galaxies, and that (2) the big grain dust temperature T_dust is calculated based on a physical consideration for energy balance, rather than using the empirical relation between T_dust and total infrared luminosity L_IR found in local galaxies, which has been employed in most of previous works. Consequently, the local properties of infrared galaxies, i.e., optical/infrared luminosity ratios, L_IR-T_dust correlation, and infrared luminosity function are outputs predicted by the model. Our model indeed reproduces these local properties reasonably well. We then found considerably different results for MIR-submm counts and CBR from most of previous works based on the empirical L_IR-T_dust relation; especially, it is shown that the dust temperature of starbursting primordial elliptical galaxies is expected to be very high (40-80K). This indicates that intense starbursts of forming elliptical galaxies should have occurred at z~2-3, in contrast to the previous results that significant starbursts beyond z~1 tend to overproduce the far-infrared (FIR) CBR detected by COBE/FIRAS. On the other hand, our model predicts that the mid-infrared (MIR) flux from warm/nonequilibrium dust is relatively weak in such galaxies making FIR CBR, and this effect reconciles the prima facie conflict between the upper limit on MIR CBR from TeV gamma-ray observations and the COBE detections of FIR CBR. (abridged)

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