We measure the evolution of clustering for galaxies with different spectral types from 6495 galaxies with 17.5<=I_AB<=24 and measured spectroscopic redshift in the first epoch VIMOS-VLT Deep Survey. We classify our sample into 4 classes, based on the fit of well-defined galaxy spectral energy distributions on observed multi-color data. We measure the projected function wp(rp) and estimate the best-fit parameters for a power-law real-space correlation function. We find the clustering of early-spectral-type galaxies to be markedly stronger than that of late-type galaxies at all redshifts up to z<=1.2. At z~0.8, early-type galaxies display a correlation length r_0=4.8+/-0.9h^{-1}Mpc, while late types have r_0=2.5+/-0.4h^{-1}Mpc. The clustering of these objects increases up to r_0=3.42+/-0.7h^{-1}Mpc for z~1.4. The relative bias between early- and late-type galaxies within our magnitude-limited survey remains approximately constant with b~1.7-1.8 from z~=0.2 up to z~=1, with indications for a decrease at z>1.2, due to the growth in clustering of the star-forming population. We find similar results when splitting the sample into `red and `blue galaxies using the observed color bi-modality. When compared to the expected linear growth of mass fluctuations, a natural interpretation of these observations is that: (a) the assembly of massive early type galaxies is already mostly complete in the densest dark matter halos at z~=1; (b) luminous late-type galaxies are located in higher-density, more clustered regions of the Universe at z~=1.5 than at present, indicating that star formation activity is progressively increasing, going back in time, in the higher-density peaks that today are mostly dominated by old galaxies.
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