  We investigate the cosmological implications of studying galaxy clustering
using a tomographic approach applied to the final BOSS DR12 galaxy sample,
including both auto- and cross-correlation functions between redshift shells.
We model the signal of the full shape of the angular correlation function,
$\omega(\theta)$, in redshift bins using state-of-the-art modelling of
non-linearities, bias and redshift-space distortions. We present results on the
redshift evolution of the linear bias of BOSS galaxies, which cannot be
obtained with traditional methods for galaxy-clustering analysis. We also
obtain constraints on cosmological parameters, combining this tomographic
analysis with measurements of the cosmic microwave background (CMB) and type Ia
supernova (SNIa). We explore a number of cosmological models, including the
standard $\Lambda$CDM model and its most interesting extensions, such as
deviations from $w_\rm{DE} = -1$, non-minimal neutrino masses, spatial
curvature and deviations from general relativity using the growth-index
$\gamma$ parametrisation. These results are, in general, comparable to the most
precise present-day constraints on cosmological parameters, and show very good
agreement with the standard model. In particular, combining CMB,
$\omega(\theta)$ and SNIa, we find a value of $w_\rm{DE}$ consistent with $-1$
to a precision better than 5\% when it is assumed to be constant in time, and
better than 6\% when we also allow for a spatially-curved Universe.
