  We present forecasts for constraints on cosmological models which can be
obtained by forthcoming radio continuum surveys: the wide surveys with the LOw
Frequency ARray (LOFAR), Australian Square Kilometre Array Pathfinder (ASKAP)
and the Westerbork Observations of the Deep APERTIF Northern sky (WODAN). We
use simulated catalogues appropriate to the planned surveys to predict
measurements obtained with the source auto-correlation, the cross-correlation
between radio sources and CMB maps (the Integrated Sachs-Wolfe effect), the
cross-correlation of radio sources with foreground objects due to cosmic
magnification, and a joint analysis together with the CMB power spectrum and
supernovae. We show that near future radio surveys will bring complementary
measurements to other experiments, probing different cosmological volumes, and
having different systematics. Our results show that the unprecedented sky
coverage of these surveys combined should provide the most significant
measurement yet of the Integrated Sachs-Wolfe effect. In addition, we show that
using the ISW effect will significantly tighten constraints on modified gravity
parameters, while the best measurements of dark energy models will come from
galaxy auto-correlation function analyses. Using the combination of EMU and
WODAN to provide a full sky survey, it will be possible to measure the dark
energy parameters with an uncertainty of \{$\sigma (w_0) = 0.05$, $\sigma (w_a)
= 0.12$\} and the modified gravity parameters \{$\sigma (\eta_0) = 0.10$,
$\sigma (\mu_0) = 0.05$\}, assuming Planck CMB+SN(current data) priors.
Finally, we show that radio surveys would detect a primordial non-Gaussianity
of $f_{\rm NL}$ = 8 at 1-$\sigma$ and we briefly discuss other promising
probes.
