Constraints on the amplitude of primordial density fluctuations from the large-scale cosmic microwave background temperature distribution

A general method for evaluating the maximum amplitude eta(H) of density fluctuations at their horizon crossing is presented that is consistent with all the available observations of the cosmic microwave background (CMB) large-scale temperature distribution. Flat universes with Gaussian, adiabatic, scale-invariant primordial density fluctuations are considered. The theoretical predictions are compared with the upper bounds on the CMB quadrupole anisotropy, the CMB anisotropy on intermediate angular scales, and the CMB autocorrelation function. It is found that the Fixen et al. (1983) upper limit on 10 degrees implies, at the 95 percent confidence level, eta(H) less than 0.00003. 25 refs