The origin of dark energy driving the accelerated expansion of the universe
is still mysterious. We explore the possibility that dark energy fluctuates,
resulting in spatial correlations. Due to these fluctuations, the Hubble rate
itself becomes a fluctuating quantity. We discuss the effect this has on
measurements of type Ia supernovae, which are used to constrain the luminosity
distance. We show that the luminosity distance is affected by spatial
correlations in several ways. First, the luminosity distance becomes dressed by
the fluctuations, thereby differing from standard $\mathrm{\Lambda}$ CDM. Second, angular
correlations become visible in the two-point correlation function of the
luminosity distance. To investigate the latter we construct the angular power
spectrum of luminosity distance fluctuations. We then perform a forecast for
two supernova surveys, the ongoing Dark Energy Survey (DES) and the upcoming
Legacy Survey of Space and Time (LSST), and compare this effect with
relativistic lensing effects from perturbed $\mathrm{\Lambda}$ CDM. We find that the
signal can rise above the lensing effects and that LSST could test this effect
for a large part of the parameter space. As an example, a specific realisation
of such a scenario is that quantum fluctuations of some field in the early
universe imprint spatial correlations with a predictable form in the dark
energy density today. In this case, the Hubble rate fluctuates due to the
intrinsic quantum nature of the dark energy density field. We study whether the
signal of this specific model would be measurable, and conclude that testing
this model with LSST would be challenging. However, taking into account a speed
of sound ${c}_{s}<1$ of the dark energy fluid can make this model observable.