Testing Inflation with the Cosmic Background Radiation

In innation cosmologies, cosmic structure develops through the gravitational instability of the inevitable quantum noise in primordial scalar elds. I show how the acceleration of the universe deenes the shape of the primordial spectrum of gravitational metric and scalar eld uctuations. I assess how we can determine the shape and overall amplitude over the ve decades or so of spatial wavelengths we can probe, and use current data from cosmic background radiation (CMB) anisotropies, large scale clustering and streaming observations, distribution functions of cosmic objects, to show how far we are in this program. Broad-band power amplitudes are given for CMB anisotropy detections up to spring 1994, covering angular scales from all-sky down It may be only a little premature to say that a spectral shape is emerging which is near that of preferred innation models. The cluster-scale density uctuation power derived from the broad-band power for COBE must fall within a narrow range to get the abundance of clusters right. This rules out many structure formation models, in particular restricting the primordial spectral index to be close to the scale invariant one. I show that COBE band-powers found with full Bayesian analysis of the 53; 90; 31 a+b GHz rst year DMR (and FIRS) maps are in good agreement, and are essentially independent of spectral slope and degree of (sharp) signal-to-noise ltering. Further, after (smooth) optimal signal-to-noise ltering (i.e., Wiener-ltering), the diierent 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 ltered: with no ltering whatsoever, the slope is high, but the power is not described by a single-slope law; as ltering is increased, the index moves nearer to innation predictions. 1