Context :

Aims : An interesting question of contemporary cosmology concerns the relation between the spatial distribution of galaxies and dark matter , which is thought to be the driving force behind the structure formation in the Universe .
In this paper , we measure this relation , parameterised by the linear stochastic bias parameters , for a range of spatial scales using the data of the Garching-Bonn Deep Survey ( GaBoDS ) .

Methods : The weak gravitational lensing effect is used to infer matter density fluctuations within the field-of-view of the survey fields .
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 .

Results : Using a flat \Lambda CDM model with \Omega _ { m } = 0.3 , \Omega _ { \Lambda } = 0.7 as fiducial cosmology , we obtain values for the galaxy bias on scales between 1 ^ { \prime } \leq \theta _ { ap } \leq 20 ^ { \prime } .
At 10 ^ { \prime } , the median redshifts of the samples correspond roughly to a typical comoving scale of 3 , 5 , 7 ~ { } h ^ { -1 } Mpc with h = 0.7 , respectively .
We find evidence for a scale-dependence of b .
Averaging the measurements of the bias over the range 2 ^ { \prime } \leq \theta _ { ap } \leq 19 ^ { \prime } yields \bar { b } = 0.81 \pm 0.11 , 0.79 \pm 0.11 , 0.81 \pm 0.11 ( 1 \sigma ) , respectively .
Galaxies are thus less clustered than the total matter on that particular range of scales ( anti-biased ) .
As for the correlation factor r we see no scale-dependence within the statistical uncertainties ; the average over the same range is \bar { r } = 0.61 \pm 0.16 , 0.64 \pm 0.18 , 0.58 \pm 0.19 ( 1 \sigma ) , respectively .
This implies a possible decorrelation between galaxy and dark matter distribution .
An evolution of galaxy bias with redshift is not found , the upper limits are : \Delta b \lesssim 0.2 and \Delta r \lesssim 0.4 ( 1 \sigma ) .

Conclusions :