Limits on arcsecond-scale fluctuations in the cosmic microwave background

We used the NRAO Very Large Array in its C configuration at a wavelength of 6 cm to set upper limits on the rms fluctuation of sky brightness on angular scales of 6''--18'' from sources too weak to be detected individually. At the highest resolution, we establish a limit of 8 μJy per beam area on the rms sky fluctuation. If this fluctuation level is the result of a Poisson distribution of unresolved sources, each of flux density S0 Jy, then the number density of such sources per steradian must be less than 0.08 S0-2 sr-1. For alternative models in which all sources are resolved, we derive less stringent limits. Our limits on the rms sky fluctuation also establish limits on the rms temperature fluctuation ΔT for simple models of fluctuations in the cosmic microwave background: (ΔT/2.7 K)<3.2 x 10-3 and (ΔT/2.7 K)<1.2 x 10-3 for Gaussian temperature fluctuations of angular scale 6'' and 18'', respectively