Deep radio observations of the sky have revealed the presence of diffuse radio sources in about 10% of known galaxy clusters. Their emission is not associated to single galaxies, but to the presence of intracluster relativistic particles and magnetic fields. One of the main open questions of modern astrophysics is to understand how this non-thermal intracluster component originates and if it affects the thermo-dynamical evolution of galaxy clusters. A deep understanding of the complex evolutionary physics of these systems is indeed essential if we want to exploit them as cosmological tools through ongoing and upcoming multiwavelength surveys. For this, we need a detailed knowledge of the nature of all the different cluster components (galaxies, thermal and non-thermal intracluster medium - ICM) and of their mutual interactions.
After the huge progress in the last 15 years of our knowledge of galaxy and thermal ICM physics, we are now living in the “golden age” for non-thermal cluster studies: the opening of the few spectral windows largely unexplored by astronomical observations (i.e. the low-frequency radio band) will allow to study the non-thermal physics of galaxy clusters with unprecedented statistics and thoroughness.
One of the main aim of current galaxy cluster studies at radio wavelengths is to test the different theoretical models about the origin of the non-thermal intracluster component and to analyze its effects on the evolutionary physics of galaxy clusters. It is firstly strongly debated how the observed cosmic-rays are accelerated. Two main classes of models have been proposed: primary and secondary models. The former predict that cluster mergers (i.e. the process by which clusters form and evolve) power the mechanisms responsible for the acceleration of intracluster electrons. The latter propose that relativistic electrons are the secondary product of hadronic collisions between relativistic protons and ICM ions. Even more debated are the intracluster magnetic field origin and the effects of the non-thermal intracluster component on the transport processes and pressure of the ICM.
At present we lack the observational means to test these different theories: the low surface brightness and steep power-law spectra of diffuse cluster radio sources make them difficult to be imaged. Only recent developments in technology and computing power are allowing observations of the low frequency window of the electromagnetic spectrum through a new generation of radio telescopes that are the technical and scientific pathfinders (e.g. LOFAR/NenuFAR, JVLA, GMRT, ...) and precursors (ASKAP, MeerKAT, MWA) of one of the most important future international project: the Square Kilometre Array (SKA). These instruments will allow to map diffuse radio emission in clusters through deep and extended surveys.