  As an alternative explanation of the dimming of distant supernovae it has
recently been advocated that we live in a special place in the Universe near
the centre of a large void described by a Lemaitre-Tolman-Bondi (LTB) metric.
The Universe is no longer homogeneous and isotropic and the apparent late time
acceleration is actually a consequence of spatial gradients in the metric. If
we did not live close to the centre of the void, we would have observed a
Cosmic Microwave Background (CMB) dipole much larger than that allowed by
observations. Hence, until now it has been argued, for the model to be
consistent with observations, that by coincidence we happen to live very close
to the centre of the void or we are moving towards it. However, even if we are
at the centre of the void, we can observe distant galaxy clusters, which are
off-centre. In their frame of reference there should be a large CMB dipole,
which manifests itself observationally for us as a kinematic Sunyaev-Zeldovich
(kSZ) effect. kSZ observations give far stronger constraints on the LTB model
compared to other observational probes such as Type Ia Supernovae, the CMB, and
baryon acoustic oscillations. We show that current observations of only 9
clusters with large error bars already rule out LTB models with void sizes
greater than approximately 1.5 Gpc and a significant underdensity, and that
near future kSZ surveys like the Atacama Cosmology Telescope, South Pole
Telescope, APEX telescope, or the Planck satellite will be able to strongly
rule out or confirm LTB models with giga parsec sized voids. On the other hand,
if the LTB model is confirmed by observations, a kSZ survey gives a unique
possibility of directly reconstructing the expansion rate and underdensity
profile of the void.
