We present a detailed overview of the cosmological surveys that we aim to carry out with Phase 1 of the Square Kilometre Array (SKA1) and the science that they will enable. We highlight three main surveys: a medium-deep continuum weak lensing and low-redshift spectroscopic HI galaxy survey over 5 000 deg2; a wide and deep continuum galaxy and HI intensity mapping (IM) survey over 20 000 deg2 from $z = 0.35$ to 3; and a deep, high-redshift HI IM survey over 100 deg2 from $z = 3$ to 6. Taken together, these surveys will achieve an array of important scientific goals: measuring the equation of state of dark energy out to $z \sim 3$ with percent-level precision measurements of the cosmic expansion rate; constraining possible deviations from General Relativity on cosmological scales by measuring the growth rate of structure through multiple independent methods; mapping the structure of the Universe on the largest accessible scales, thus constraining fundamental properties such as isotropy, homogeneity, and non-Gaussianity; and measuring the HI density and bias out to $z = 6$ . These surveys will also provide highly complementary clustering and weak lensing measurements that have independent systematic uncertainties to those of optical and near-infrared (NIR) surveys like Euclid, LSST, and WFIRST leading to a multitude of synergies that can improve constraints significantly beyond what optical or radio surveys can achieve on their own. This document, the 2018 Red Book, provides reference technical specifications, cosmological parameter forecasts, and an overview of relevant systematic effects for the three key surveys and will be regularly updated by the Cosmology Science Working Group in the run up to start of operations and the Key Science Programme of SKA1.

According to the Cosmological Principle, the matter distribution on very large scales should have a kinematic dipole that is aligned with that of the CMB. We determine the dipole anisotropy in the number counts of two all-sky surveys of radio galaxies. For the first time, this analysis is presented for the TGSS survey, allowing us to check consistency of the radio dipole at low and high frequencies by comparing the results with the well-known NVSS survey. We match the flux thresholds of the catalogues, with flux limits chosen to minimise systematics, and adopt a strict masking scheme. We find dipole directions that are in good agreement with each other and with the CMB dipole. In order to compare the amplitude of the dipoles with theoretical predictions, we produce sets of lognormal realisations. Our realisations include the theoretical kinematic dipole, galaxy clustering, Poisson noise, simulated redshift distributions which fit the NVSS and TGSS source counts, and errors in flux calibration. The measured dipole for NVSS is ∼ 2 times larger than predicted by the mock data. For TGSS, the dipole is almost ∼ 5 times larger than predicted, even after checking for completeness and taking account of errors in source fluxes and in flux calibration. Further work is required to understand the nature of the systematics that are the likely cause of the anomalously large TGSS dipole amplitude.

We investigate the validity of the Cosmological Principle by mapping the cosmological parameters H 0 and q 0 through the celestial sphere. In our analysis, performed in a low-redshift regime to follow a model-independent approach, we use two compilations of type Ia Supernovae (SNe Ia), namely the Union2.1 and the JLA datasets. Firstly, we show that the angular distributions for both SNe Ia datasets are statistically anisotropic at high confidence level (p-value < 0.0001), in particular the JLA sample. Then we find that the cosmic expansion and acceleration are mainly of dipolar type, with maximal anisotropic expansion [acceleration] for the Union2.1 and JLA data, respectively. Secondly, we use a geometrical method to test the hypothesis that the non-uniformly distributed SNe Ia events could introduce anisotropic imprints on the cosmological expansion and acceleration. For the JLA compilation, we found significant correlations between the celestial distribution of data points and the directional studies of H 0 and q 0 , suggesting that these results can be attributed to the intrinsic anisotropy of the sample. In the case of the Union2.1 data, nonetheless, these correlations are less pronounced, and we verify that the dipole asymmetry found in the H 0 analyses coincides with the well-known bulk-flow motion of our local group. From these analyses, we conclude that the directional asymmetry on the cosmological parameters maps are mainly either of local origin or due to celestial incompleteness of current SNe Ia samples.

The dipole anisotropy seen in the cosmic microwave background radiation is interpreted as due to our peculiar motion. The Cosmological Principle implies that this cosmic dipole signal should also be present, with the same direction, in the large-scale distribution of matter. Measurement of the cosmic matter dipole constitutes a key test of the standard cosmological model. Current measurements of this dipole are barely above the expected noise and unable to provide a robust test. Upcoming radio continuum surveys with the SKA should be able to detect the dipole at high signal to noise. We simulate number count maps for SKA survey specifications in Phases 1 and 2, including all relevant effects. Nonlinear effects from local large-scale structure contaminate the cosmic (kinematic) dipole signal, and we find that removal of radio sources at low redshift (z 0.5) leads to significantly improved constraints. We forecast that the SKA could determine the kinematic dipole direction in Galactic coordinates with an error of (∆l, ∆b) ∼ (9 • , 5 • ) to (8 • , 4 • ), depending on the sensitivity. The predicted errors on the relative speed are ∼ 10%. These measurements would significantly reduce the present uncertainty on the direction of the radio dipole, and thus enable the first critical test of consistency between the matter and CMB dipoles.where the direction is given in Galactic coordinates.This dipole is expected to be dominated by the kinematic contribution, which is O(10 2 ) larger than the intrinsic fluctuations in the standard ΛCDM model. Since the cosmic variance of the dipole is very large, significant non-kinematic contributions remain possible and need to be tested by other means. Probing the dipole of the matter distribution in addition to that of the CMB will help to tighten constraints on putative non-kinematic contributions.The extragalactic radio sky offers an excellent opportunity to perform an independent test of the Cosmological Principle. The radio continuum dipole is expected to be dominated by the kinematic dipole. This is not the case for galaxy surveys at visible or infrared wavebands: the number counts in wide area surveys in those wavebands are dominated by objects at redshifts well below unity, so that the large-scale structure dominates over the kinematic signal. By contrast, radio continuum surveys have median redshifts above one, which suppresses the effect of local large-scale structure. Another advantage is that radio waves are not subject to extinction and thus the sky area that can be reliably observed by radio surveys exceeds that of optical and infrared surveys.The largest available wide-area radio continuum surveys include the NRAO VLA Sky Survey (NVSS) (Condon et al. 1998) and the TIFR GMRT Sky Survey (TGSS) (Intema et al. 2016).