AGN feedback with the Square Kilometer Array (SKA) and implications for
  cluster physics and cosmology
  AGN feedback is regarded as an important non-gravitational process in galaxy
clusters, providing useful constraints on large-scale structure formation. It
modifies the structure and energetics of the intra-cluster medium (ICM) and
hence its understanding is crucially needed in order to use clusters as high
precision cosmological probes. In this context, particularly keeping in mind
the upcoming high quality radio data expected from radio surveys like SKA with
its higher sensitivity, high spatial and spectral resolutions, we review our
current understanding of AGN feedback, its cosmological implications and the
impact that SKA can have in revolutionizing our understanding of AGN feedback
in large-scale structures. Recent developments regarding the AGN outbursts and
its possible contribution to excess entropy in the hot atmospheres of groups
and clusters, its correlation with the feedback energy in ICM, quenching of
cooling flows and the possible connection between cool core clusters and radio
mini-halos, are discussed. We describe current major issues regarding modeling
of AGN feedback and its impact on the surrounding medium. With regard to the
future of AGN feedback studies, we examine the possible breakthroughs that can
be expected from SKA observations. In the context of cluster cosmology, for
example, we point out the importance of SKA observations for cluster mass
calibration by noting that most of $z>1$ clusters discovered by eROSITA X-ray
mission can be expected to be followed up through a 1000 hour SKA-1 mid
programme. Moreover, approximately $1000$ radio mini halos and $\sim 2500$
radio halos at $z<0.6$ can be potentially detected by SKA1 and SKA2 and used as
tracers of galaxy clusters and determination of cluster selection function.
