Cluster Radio Halos at the crossroads between astrophysics and cosmology
  in the SKA era
  Giant Radio Halos (RH) are diffuse, Mpc-sized, synchrotron radio sources
observed in a fraction of merging galaxy clusters. The current scenario for the
origin of RHs assumes that turbulence generated during cluster mergers
re-accelerates pre-existing fossil and/or secondary electrons in the
intra-cluster-medium (ICM) to the energies necessary to produce the observed
radio emission. Moreover, more relaxed clusters could host diffuse "off state"
halos produced by secondary electrons. In this Chapter we use Monte Carlo
simulations, that combine turbulent-acceleration physics and the generation of
secondaries in the ICM, to calculate the occurrence of RHs in the Universe,
their spectral properties and connection with properties of the hosting
clusters. Predictions for SKA1 surveys are presented at low (100-300 MHz) and
mid (1-2 GHz) frequencies assuming the expected sensitivities and spatial
resolutions of SKA1. SKA1 will step into an unexplored territory allowing us to
study the formation and evolution of RHs in a totally new range of cluster
masses and redshift, allowing firm tests of the current theoretical hypothesis.
In particular, the combination of SKA1-LOW and SUR will allow the discovery of
~1000 ultrasteep- spectrum halos and to detect for the very first time "off
state" RHs. We expect that at least ~2500 giant RHs will be discovered by
SKA1-LOW surveys up to z~0.6. Remarkably these surveys will be sensitive to RHs
in a cluster mass range (down to ~10^14 solar masses) and redshifts (up to ~1)
that are unexplored by current observations. SKA1 surveys will be highly
competitive with present and future SZ-surveys in the detection of
high-redshift massive objects.
