Amplitude of Primeval Fluctuations from Cosmological Mass Density Reconstructions

We use the POTENT reconstruction of the mass density field in the nearby universe to estimate the amplitude of the density fluctuation power spectrum for various cosmological models. We find sigma_8\Omega_m^{0.6}= 1.3^{+0.4}_{-0.3}, almost independently of the power spectrum. This value agrees well with the COBE normalization for the standard CDM model, while some alternative models predict an excessive amplitude compared with COBE. Flat low \Omega_m models and tilted models with spectral index n<0.8 are particularly discordant.