We investigate to what extent future microwave background experiments might
be able to detect a suppression of fluctuation power on large scales in fl
at and open universe models. Such suppression would arise if fluctuations a
re generated by causal processes, and a measurement of a small suppression
scale would be problematic for inflation models, but consistent with many d
efect models. More speculatively, a measurement of a suppression scale of t
he order of the present Hubble radius could provide independent evidence fo
r a fine-tuned inflation model leading to a low-density universe. We find t
hat, depending on the primordial power spectrum, a suppression scale modest
ly larger than the visible Horizon can be detected, but that the detectabil
ity drops very rapidly with increasing scale. For models with two periods o
f inflation, there is essentially no possibility of detecting a causal supp
ression scale.