  In inflation cosmologies, cosmic structure develops through the gravitational
instability of the inevitable quantum noise in primordial scalar fields. I show
how the acceleration of the universe defines the shape of the primordial
spectrum of gravitational metric and scalar field fluctuations. I assess how we
can determine the shape and overall amplitude over the five decades or so of
spatial wavelengths we can probe, and use current data ... to show how far we
are in this program. Broad-band power amplitudes are given for CMB anisotropy
detections up to spring 1994 ... I show that COBE band-powers found with full
Bayesian analysis of the $53,90,31$ $a$+$b$ GHz first year DMR (and FIRS) maps
are in good agreement, and are essentially independent of spectral slope and
degree of (sharp) signal-to-noise filtering. Further, after (smooth) optimal
signal-to-noise filtering (\ie Weiner-filtering), the different DMR maps reveal
the same large scale features and correlation functions with little dependence
upon slope. However, the most probable slope depends upon how the maps are
filtered: with no filtering whatsoever, the slope is high, but the power is not
described by a single-slope law; as filtering is increased, the index moves
nearer to inflation predictions. in {\it Relativistic Cosmology}, ed. M.
Sasaki, Academic Press (1994) Proc. 8th Nishinomiya-Yukawa Memorial Symposium,
Japan, October 1993
