Minimal cosmic background fluctuations implied by streaming motions

The minimal cosmic background radiation (CBR) anisotropy implied by the presence of peculiar motions of a given amplitude on some specified scale is calculated using a new, power spectrum-independent approach. If the tentative evidence for deviations from the Hubble flow of magnitude delta V/V roughly 0.1 at V roughly 5000 km/s is confirmed, microwave background fluctuations with a coherence scale of about 2 deg and dispersion delta T/T greater than 10 to the -5th are predicted. It is found that the existing upper limits on delta T/T are not inconsistent with v(r) = 500 km/s at r = 50/h Mpc. A reduction of the observational limits on the CBR anisotropy below the authors' minimal predictions for delta T/T would challenge the current interpretation of measurements of deviations from the Hubble flow. Gravitational instability without reheating as a mechanism for generation of the large-scale structure of the universe would be in severe difficulty.