  The standard concordance model of the Universe is based on the cosmological
constant as the driver of accelerating expansion. This concordance model is
being subjected to a growing range of inter-locking observations. In addition
to using generic observational tests, one can also design tests that target the
specific properties of the cosmological constant. These null tests do not rely
on parametrisations of observables, but focus on quantities that are constant
only if dark energy is a cosmological constant. We use supernova data in null
tests that are based on the luminosity distance. In order to extract
derivatives of the distance in a model-independent way, we use Gaussian
Processes. We find that the concordance model is compatible with the Union 2.1
data, but the error bars are fairly large. Simulated datasets are generated for
the DES supernova survey and we show that this survey will allow for a sharper
null test of the cosmological constant if we assume the Universe is flat.
Allowing for spatial curvature degrades the power of the null test.
