We investigate how well future large-scale radio surveys could measure different shapes of primordial non-Gaussianity; in particular we focus on angle-dependent non-Gaussianity arising from primordial anisotropic sources, whose bispectrum has an angl
e dependence between the three wavevectors that is characterized by Legendre polynomials $mathcal{P}_L$ and expansion coefficients $c_L$. We provide forecasts for measurements of galaxy power spectrum, finding that Large-Scale Structure (LSS) data could allow measurements of primordial non-Gaussianity competitive or improving upon current constraints set by CMB experiments, for all the shapes considered. We argue that the best constraints will come from the possibility to assign redshift information to radio galaxy surveys, and investigate a few possible scenarios for the EMU and SKA surveys. A realistic (futuristic) modeling could provide constraints of $f_{rm NL}^{rm loc} approx 1 (0.5)$ for the local shape, $f_{rm NL}$ of $mathcal{O}(10) (mathcal{O}(1))$ for the orthogonal, equilateral and folded shapes, and $c_{L=1} approx 80 (2)$, $c_{L=2} approx 400 (10)$ for angle-dependent non-Gaussianity. The more futuristic forecasts show the potential of LSS analyses to considerably improve current constraints on non-Gaussianity, and so on models of the primordial Universe. Finally, we find the minimum requirements that would be needed to reach $sigma(c_{L=1})=10$, which can be considered as a typical (lower) value predicted by some (inflationary) models.
We investigate the cosmological dependence and the constraining power of large-scale galaxy correlations, including all redshift-distortions, wide-angle, lensing and gravitational potential effects on linear scales. We analyze the cosmological inform
ation present in the lensing convergence and in the gravitational potential terms describing the so-called relativistic effects, and we find that, while smaller than the information contained in intrinsic galaxy clustering, it is not negligible. We investigate how neglecting them does bias cosmological measurements performed by future spectroscopic and photometric large-scale surveys such as SKA and Euclid. We perform a Fisher analysis using the CLASS code, modified to include scale-dependent galaxy bias and redshift-dependent magnification and evolution bias. Our results show that neglecting relativistic terms introduces an error in the forecasted precision in measuring cosmological parameters of the order of a few tens of percent, in particular when measuring the matter content of the Universe and primordial non-Gaussianity parameters. Therefore, we argue that radial correlations and integrated relativistic terms need to be taken into account when forecasting the constraining power of future large-scale number counts of galaxy surveys.
The peculiar motion of galaxies can be a particularly sensitive probe of gravitational collapse. As such, it can be used to measure the dynamics of dark matter and dark energy as well the nature of the gravitational laws at play on cosmological scale
s. Peculiar motions manifest themselves as an overall anisotropy in the measured clustering signal as a function of the angle to the line-of-sight, known as redshift-space distortion (RSD). Limiting factors in this measurement include our ability to model non-linear galaxy motions on small scales and the complexities of galaxy bias. The anisotropy in the measured clustering pattern in redshift-space is also driven by the unknown distance factors at the redshift in question, the Alcock-Paczynski distortion. This weakens growth rate measurements, but permits an extra geometric probe of the Hubble expansion rate. In this chapter we will briefly describe the scientific background to the RSD technique, and forecast the potential of the SKA phase 1 and the SKA2 to measure the growth rate using both galaxy catalogues and intensity mapping, assessing their competitiveness with current and future optical galaxy surveys.
We investigate optimization strategies to measure primordial non-Gaussianity with future spectroscopic surveys. We forecast measurements coming from the 3D galaxy power spectrum and compute constraints on primordial non-Gaussianity parameters f_NL an
d n_NG. After studying the dependence on those parameters upon survey specifications such as redshift range, area, number density, we assume a reference mock survey and investigate the trade-off between number density and area surveyed. We then define the observational requirements to reach the detection of f_NL of order 1. Our results show that while power spectrum constraints on non-Gaussianity from future spectroscopic surveys can be competitive with current CMB limits, measurements from higher-order statistics will be needed to reach a sub unity precision in the measurements of the non-Gaussianity parameter f_NL.
The Planck CMB experiment has delivered the best constraints so far on primordial non-Gaussianity, ruling out early-Universe models of inflation that generate large non-Gaussianity. Although small improvements in the CMB constraints are expected, the
next frontier of precision will come from future large-scale surveys of the galaxy distribution. The advantage of such surveys is that they can measure many more modes than the CMB -- in particular, forthcoming radio surveys with the SKA will cover huge volumes. Radio continuum surveys deliver the largest volumes, but with the disadvantage of no redshift information. In order to mitigate this, we use two additional observables. First, the integrated Sachs-Wolfe effect -- the cross-correlation of the radio number counts with the CMB temperature anisotropies -- helps to reduce systematics on the large scales that are sensitive to non-Gaussianity. Second, optical data allows for cross-identification in order to gain some redshift information. We show that, while the single redshift bin case can provide a sigma(fNL) ~ 20, and is therefore not competitive with current and future constraints on non-Gaussianity, a tomographic analysis could improve the constraints by an order of magnitude, even with only two redshift bins. A huge improvement is provided by the addition of high-redshift sources, so having cross-ID for high-z galaxies and an even higher-z radio tail is key to enabling very precise measurements of fNL. Our results show that SKA continuum surveys could provide constraints competitive with CMB and forthcoming optical surveys, potentially allowing a measurement of sigma(fNL) ~ 1 to be made. Moreover, these measurements would act as a useful check of results obtained with other probes at other redshift ranges with other methods.
Galaxy clustering on very large scales can be probed via the 2-point correlation function in the general case of wide and deep separations, including all the lightcone and relativistic effects. Using our recently developed formalism, we analyze the b
ehavior of the local and integrated contributions and how these depend on redshift range, linear and angular separations and luminosity function. Relativistic corrections to the local part of the correlation can be non-negligible but they remain generally sub-dominant. On the other hand, the additional correlations arising from lensing convergence and time-delay effects can become very important and even dominate the observed total correlation function. We investigate different configurations formed by the observer and the pair of galaxies, and we find that the case of near-radial large-scale separations is where these effects will be the most important.
We investigate the properties of the 2-point galaxy correlation function at very large scales, including all geometric and local relativistic effects -- wide-angle effects, redshift space distortions, Doppler terms and Sachs-Wolfe type terms in the g
ravitational potentials. The general three-dimensional correlation function has a nonzero dipole and octupole, in addition to the even multipoles of the flat-sky limit. We study how corrections due to primordial non-Gaussianity and General Relativity affect the multipolar expansion, and we show that they are of similar magnitude (when f_NL is small), so that a relativistic approach is needed. Furthermore, we look at how large-scale corrections depend on the model for the growth rate in the context of modified gravity, and we discuss how a modified growth can affect the non-Gaussian signal in the multipoles.
We present forecasts for constraints on cosmological models which can be obtained by forthcoming radio continuum surveys: the wide surveys with the LOw Frequency ARray (LOFAR), Australian Square Kilometre Array Pathfinder (ASKAP) and the Westerbork O
bservations of the Deep APERTIF Northern sky (WODAN). We use simulated catalogues appropriate to the planned surveys to predict measurements obtained with the source auto-correlation, the cross-correlation between radio sources and CMB maps (the Integrated Sachs-Wolfe effect), the cross-correlation of radio sources with foreground objects due to cosmic magnification, and a joint analysis together with the CMB power spectrum and supernovae. We show that near future radio surveys will bring complementary measurements to other experiments, probing different cosmological volumes, and having different systematics. Our results show that the unprecedented sky coverage of these surveys combined should provide the most significant measurement yet of the Integrated Sachs-Wolfe effect. In addition, we show that using the ISW effect will significantly tighten constraints on modified gravity parameters, while the best measurements of dark energy models will come from galaxy auto-correlation function analyses. Using the combination of EMU and WODAN to provide a full sky survey, it will be possible to measure the dark energy parameters with an uncertainty of {$sigma (w_0) = 0.05$, $sigma (w_a) = 0.12$} and the modified gravity parameters {$sigma (eta_0) = 0.10$, $sigma (mu_0) = 0.05$}, assuming Planck CMB+SN(current data) priors. Finally, we show that radio surveys would detect a primordial non-Gaussianity of $f_{rm NL}$ = 8 at 1-$sigma$ and we briefly discuss other promising probes.
The analysis of Redshift-Space Distortions (RSD) within galaxy surveys provides constraints on the amplitude of peculiar velocities induced by structure growth, thereby allowing tests of General Relativity on extremely large scales. The next generati
on of galaxy redshift surveys, such as the Baryon Oscillation Spectroscopic Survey (BOSS), and the Euclid experiment will survey galaxies out to z=2, over 10,000--20,000 sq deg. In such surveys, galaxy pairs with large comoving separation will preferentially have a wide angular separation. In standard plane-parallel theory the displacements of galaxy positions due to RSD are assumed to be parallel for all galaxies, but this assumption will break down for wide-angle pairs. Szapudi 2004 and Papai & Szapudi 2008 provided a methodology, based on tripolar spherical harmonics expansion, for computing the redshift-space correlation function for all angular galaxy pair separations. In this paper we introduce a new procedure for analysing wide-angle effects in numerical simulations. We are able to separate, demonstrate, and fit each of the effects described by the wide-angle RSD theory. Our analysis highlights some of the nuances of dealing with wide-angle pairs, and shows that the effects are not negligible even for relatively small angles. This analysis will help to ensure the full exploitation of future surveys for RSD measurements, which are currently confined to pair separations less than sim80 Mpc/h out to zsimeq 0.5.
