GaBoDS: The Garching-Bonn Deep Survey: VII. Probing galaxy bias using weak gravitational lensing

[ABRIDGED] The weak gravitational lensing effect is used to infer matter density fluctuations within the field-of-view of the Garching-Bonn Deep Survey (GaBoDS). This information is employed for a statistical comparison of the galaxy distribution to the total matter distribution. The result of this comparison is expressed by means of the linear bias factor, b, the ratio of density fluctuations, and the correlation factor $r$ between density fluctuations. The total galaxy sample is divided into three sub-samples using R-band magnitudes and the weak lensing analysis is applied separately for each sub-sample. Together with the photometric redshifts from the related COMBO-17 survey we estimate the typical mean redshifts of these samples with $\bar{z}=0.35, 0.47, 0.61$, respectively. For all three samples, a slight galaxy anti-bias, b~0.8+-0.1, on scales of a few Mpc/h is found; the bias factor shows evidence for a slight scale-dependence. The correlation between galaxy and (dark) matter distribution is high, r~0.6+-0.2, indicating a non-linear or/and stochastic biasing relation between matter and galaxies. Between the three samples no significant evolution with redshift is found.