The VIMOS VLT deep survey -: Evolution of the non-linear galaxy bias up to z=1.5

We present the first measurements of the Probability Distribution Function (PDF) of galaxy fluctuations in the four-passes, first-epoch VIMOS-VLT Deep Survey (VVDS) cone, covering 0.4 x 0.4 deg between 0.4 < z < 1.5. We show that the PDF of density contrasts of the VVDS galaxies is an unbiased tracer of the underlying parent distribution up to redshift z = 1.5, on scales R = 8 and 10 h(-1) Mpc. The second moment of the PDF, i.e., the rms fluctuations of the galaxy density field, is to a good approximation constant over the full redshift baseline investigated: we find that, in redshift space, sigma(8) for galaxies brighter than M-B(c) = - 20 + 5 log h has a mean value of 0.94 +/- 0.07 in the redshift interval 0.7 < z < 1.5. The third moment, i.e., the skewness, increases with cosmic time: we find that the probability of having underdense regions is greater at z similar to 0.7 than it was at z similar to 1.5. By comparing the PDF of galaxy density contrasts with the theoretically predicted PDF of mass fluctuations we infer the redshift-, density- and scale-dependence of the biasing function b(z, delta, R) between galaxy and matter overdensities up to redshift z = 1.5. Our results can be summarized as follows: i) the galaxy bias is an increasing function of redshift: evolution is marginal up to z similar to 0.8 and more pronounced for z greater than or similar to 0.8; ii) the formation of bright galaxies is inhibited below a characteristic mass-overdensity threshold whose amplitude increases with redshift and luminosity; iii) the biasing function is non linear in all the redshift bins investigated with non-linear effects of the order of a few to similar to 10% on scales > 5 h(-1) Mpc. By subdividing the sample according to galaxy luminosity and colors, we also show that: iv) brighter galaxies are more strongly biased than less luminous ones at every redshift and the dependence of biasing on luminosity at z similar to 0.8 is in good agreement with what is observed in the local Universe; v) red objects are systematically more biased than blue objects at all cosmic epochs investigated, but the relative bias between red and blue objects is constant as a function of redshift in the interval 0.7 < z < 1.5, and its value (b(rel) similar to 1.4) is similar to what is found at z similar to 0.