  We constrain the basic comological parameters using the first observations by
the Very Small Array (VSA) in its extended configuration, together with
existing cosmic microwave background data and other cosmological observations.
We estimate cosmological parameters for four different models of increasing
complexity. In each case, careful consideration is given to implied priors and
the Bayesian evidence is calculated in order to perform model selection. We
find that the data are most convincingly explained by a simple flat Lambda-CDM
cosmology without tensor modes. In this case, combining just the VSA and COBE
data sets yields the 68 per cent confidence intervals Omega_b h^2=0.034
(+0.007, -0.007), Omega_dm h^2 = 0.18 (+0.06, -0.04), h=0.72 (+0.15,-0.13),
n_s=1.07 (+0.06,-0.06) and sigma_8=1.17 (+0.25, -0.20). The most general model
considered includes spatial curvature, tensor modes, massive neutrinos and a
parameterised equation of state for the dark energy. In this case, by combining
all recent cosmological data, we find, in particular, 95 percent limit on the
tensor-to-scalar ratio R < 0.63 and on the fraction of massive neutrinos f_nu <
0.11; we also obtain the 68 per cent confidence interval w=-1.06 (+0.20, -0.25)
on the equation of state of dark energy.
