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On large scales, the higher order moments of the mass distribution,$S_J=\xibar_J/\xibar_2^{J-1}$, e.g., the skewness $S_3$ and kurtosis $S_4$, canbe predicted using non-linear perturbation theory. Comparison of thesepredictions with moments of the observed galaxy distribution probes the biasbetween galaxies and mass. Applying this method to models with initiallyGaussian fluctuations and power spectra $P(k)$ similar to that of galaxies inthe APM survey, we find that the predicted higher order moments $S_J(R)$ are ingood agreement with those directly inferred from the APM survey {\it in theabsence of bias}. We use this result to place limits on the linear andnon-linear bias parameters. Models in which the extra power observed on largescales (with respect to standard CDM) is produced by scale-dependent bias matchthe APM higher order amplitudes only if non-linear bias (rather than non-lineargravity) generates the observed higher order moments. When normalized to COBEDMR, these models are significantly ruled out by the $S_3$ observations. Thecold plus hot dark matter model normalized to COBE can reproduce the APM higherorder correlations if one introduces non-linear bias terms, while thelow-density CDM model with a cosmological constant does not require any bias tofit the large-scale amplitudes.Comment: 8 pages, 2 figures included, uuencoded postscript file (100 kB),  Fermilab-Pub-94/207-

Bias and high-order galaxy correlation functions in the APM galaxy survey