In recent years cosmology has undergone a revolution, with precise measurements of the microwave background radiation, large galaxy redshift surveys, and the discovery of the recent accelerated expansion of the Universe using observations of distant supernovae. All these groundbreaking observations have boosted our understanding of the Cosmos and its evolution. Because of this detailed understanding, more detailed tests of cosmological models require unprecedented precision that is only available with the next generation of astronomical observatories. Radio observations in particular will be able to access more independent modes than optical, infrared or X-ray facility and will show very different systematics compared to these other wavebands. The SKA enables us to do an ultimate test in cosmology by measuring the expansion rate of the Universe in real time. This can be done by a rather simple experiment of observing the neutral hydrogen (HI) signal of galaxies at two different epochs. The signal will encounter a change in frequency imprinted as the Universe expands over time and thus monitoring the drift in frequencies will provide a real time measure of the cosmic acceleration. Over a period of 12 years one would expected a frequency shift of the order of 0.1 Hz assuming a standard ΛCDM cosmology. However, monitoring such changes would require some modifications to the current baseline design of the SKA. In particular, the design needs to be adapted to achieve higher spectral resolution, at least within sub-bands (strong requirement), and to allow for a well monitored distribution of the local oscillator signal, preferably at milli-Hz accuracy over a period of 12 years (weaker requirement, which could be circumvented by pulsar observations). Based on the sensitivity estimates of the SKA and the number counts of the expected HI galaxies, it is shown that the number counts are sufficiently high to compensate for the observational uncertainties of the measurements and hence allow a statistical detection of the frequency shift. In addition, depending on the observational setup, it is shown that the evolution of the frequency shift in redshift space can be estimated to a precision of a percent. Although technically challenging, the direct measurement of the frequency shift and hence the cosmic acceleration can provide a model independent confirmation of dark energy. At highest precision it can distinguish between some competing cosmological models and combined with probes at other wavelength can break degeneracies and improving the figure of merit of cosmological parameters.

The Square Kilometer Array (SKA) has the potential to produce galaxy redshift surveys which will be competitive with other state of the art cosmological experiments in the next decade. In this chapter we summarise what capabilities the first and the second phases of the SKA will be able to achieve in its current state of design. We summarise the different cosmological experiments which are outlined in further detail in other chapters of this Science Book. The SKA will be able to produce competitive Baryonic Oscillation (BAOs) measurements in both its phases. The first phase of the SKA will provide similar measurements in optical and IR experiments with completely different systematic effects whereas the second phase being transformational in terms of its statistical power. The SKA will produce very accurate Redshift Space Distortions (RSD) measurements, being superior to other experiments at lower redshifts, due to the large number of galaxies. Cross correlations of the galaxy redshift data from the SKA with radio continuum surveys and optical surveys will provide extremely good calibration of photometric redshifts as well as extremely good bounds on modifications of gravity. Basing on a Principle Component Analysis (PCA) approach, we find that the SKA will be able to provide competitive constraint on dark energy and modified gravity models. Due to the large area covered the SKA it will be a transformational experiment in measuring physics from the largest scales such as non-Gaussian signals from f nl. Finally, the SKA might produce the first real time measurement of the redshift drift. The SKA will be a transformational machine for cosmology as it grows from an early Phase 1 to its full power.

Galaxies and supermassive black holes (SMBHs) are believed to evolve through a process of hierarchical merging and accretion. Through this paradigm, multiple SMBH systems are expected to be relatively common in the Universe. However, to date there are poor observational constraints on multiple SMBHs systems with separations comparable to a SMBH gravitational sphere of influence (« 1 kpc). In this chapter, we discuss how deep continuum observations with the SKA will make leading contributions towards understanding how multiple black hole systems impact galaxy evolution. In addition, these observations will provide constraints on and an understanding of stochastic gravitational wave background detections in the pulsar timing array sensitivity band (nHz -µHz). We also discuss how targets for pointed gravitational wave experiments (that cannot be resolved by VLBI) could potentially be found using the large-scale radio-jet morphology, which can be modulated by the presence of a close-pair binary SMBH system. The combination of direct imaging at high angular resolution; low-surface brightness radio-jet tracers; and pulsar timing arrays will allow the SKA to trace black hole binary evolution from separations of a galaxy virial radius down to the sub-parsec level. This large dynamic range in binary SMBH separation will ensure that the SKA plays a leading role in this observational frontier.Advancing Astrophysics with the Square Kilometre Array

The SKA will be a transformational instrument in the study of our local Universe. In particular, by virtue of its high sensitivity (both to point sources and diffuse low surface brightness emission), angular resolution and the frequency ranges covered, the SKA will undertake a very wide range of astrophysical research in the field of nearby galaxies. By surveying vast numbers of nearby galaxies of all types with µJy sensitivity and sub-arcsecond angular resolutions at radio wavelengths, the SKA will provide the cornerstone of our understanding of star-formation and accretion activity in the local Universe. In this chapter we outline the key continuum and molecular line science areas where the SKA, both during phase-1 and when it becomes the full SKA, will have a significant scientific impact.Advancing Astrophysics with the Square Kilometre Array