  We explore how local, cosmology-independent measurements of the Hubble
constant and the age of the Universe help to provide a powerful consistency
check of the currently favored cosmological model (flat LambdaCDM) and
model-independent constraints on cosmology. We use cosmic microwave background
(CMB) data to define the model-dependent cosmological parameters, and add local
measurements to assess consistency and determine whether extensions to the
model are justified. At current precision, there is no significant tension
between the locally measured Hubble constant and age of the Universe (with
errors of 3% and 5% respectively) and the corresponding parameters derived from
the CMB. However, if errors on the local measurements could be decreased by a
factor of two, one could decisively conclude if there is tension or not. We
also compare the local and CMB data assuming simple extensions of the flat,
$\Lambda$CDM model (including curvature, dark energy with a constant equation
of state parameter not equal to -1, non-zero neutrino masses and a non-standard
number of neutrino families) and find no need for these extra parameters; in
particular, we constrain the effective number of neutrino species to be Neff <
4 at 95% confidence. We show that local measurements provide constraints on the
curvature and equation of state of dark energy nearly orthogonal to those of
the CMB. We argue that cosmology-independent measurements of local quantities
at the percent level would be very useful to explore cosmology in a
model-independent way.
