Clustering of the Diffuse Infrared Light from the COBE DIRBE maps. An all-sky survey of $C(0)$

We measure the smoothness of the infrared sky using the COBE DIRBE maps, and obtain interesting limits on the production of the diffuse cosmic infrared background (CIB) light by matter clustered like galaxies. The predicted fluctuations of the CIB with the DIRBE beam size of 0.7\deg\ are of the order of 10%, and the maps are smooth at the level of $\delta \nu I_{\nu }\sim$ a few \nwm2sr rms from 2.2 to 100 \um. The lowest numbers are achieved at mid- to far-IR where the foreground is bright but smooth; they are $\sqrt{C(0)}$$\le$$(1-1.5)$ \nwm2sr at $\lambda =$ 10-100 \um. If the CIB comes from clustered matter evolving according to typical scenarios, then the smoothness of the maps implies CIB levels less than $\sim (10-15)$ \nwm2sr over this wavelength range.