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We assess and develop techniques to remove contaminants when calculating the 3D galaxy power spectrum. We separate the process into three separate stages: (i) removing the contaminant signal, (ii) estimating the uncontaminated cosmological power spectrum, (iii) debiasing the resulting estimates. For (i), we show that removing the best-fit contaminant mode subtraction), and setting the contaminated components of the covariance to be infinite (mode deprojection) are mathematically equivalent. For (ii), performing a Quadratic Maximum Likelihood (QML) estimate after mode deprojection gives an optimal unbiased solution, although it requires the manipulation of large $N_{\rm mode}^2$ matrices ($N_{\rm mode}$ being the total number of modes)}, which is unfeasible for recent 3D galaxy surveys. Measuring a binned average of the modes for (ii) as proposed by \citet*[FKP]{Feldman} is faster and simpler, but is sub-optimal and gives rise to a biased solution. We present a method to debias the resulting FKP measurements that does not require any large matrix calculations. We argue that the sub-optimality of the FKP estimator compared with the QML estimator, caused by contaminants is less severe than that commonly ignored due to the survey window., Comment: 10 pages, 4 figures; version equivalent to accepted article

We consider the shape of the posterior distribution to be used when fitting cosmological models to power spectra measured from galaxy surveys. At very large scales, Gaussian posterior distributions in the power do not approximate the posterior distribution $\mathcal{P}_R$ we expect for a Gaussian density field $\delta_k$, even if we vary the covariance matrix according to the model to be tested. We compare alternative posterior distributions with $\mathcal{P}_R$, both mode-by-mode and in terms of expected measurements of primordial non-Gaussianity parameterised by $f_\mathrm{NL}$. Marginalising over a Gaussian posterior distribution $\mathcal{P}_f$ with fixed covariance matrix yields a posterior mean value of $f_\mathrm{NL}$ which, for a data set with the characteristics of Euclid, will be underestimated by $\triangle f_\mathrm{NL}=0.4$, while for the data release 9 (DR9) of the Sloan Digital Sky Survey (SDSS)-III Baryon Oscillation Spectroscopic Survey (BOSS) it will be underestimated by $\triangle f_\mathrm{NL}=19.1$. Adopting a different form of the posterior function means that we do not necessarily require a different covariance matrix for each model to be tested: this dependence is absorbed into the functional form of the posterior. Thus, the computational burden of analysis is significantly reduced., Comment: 9 pages, 7 figures

The observed distribution of galaxies has local transverse isotropy around the line-of- sight (LOS) with respect to the observer. The difference in the statistical clustering signal along and across the line-of-sight encodes important information about the ge- ometry of the Universe, its expansion rate and the rate of growth of structure within it. Because the LOS varies across a survey, the standard Fast Fourier Transform (FFT) based methods of measuring the Anisotropic Power-Spectrum (APS) cannot be used for surveys with wide observational footprint, other than to measure the monopole moment. We derive a simple analytic formula to quantify the bias for higher-order Legendre moments and we demonstrate that it is scale independent for a simple sur- vey model, and depends only on the observed area. We derive a similar numerical correction formula for recently proposed alternative estimators of the APS that are based on summing over galaxies rather than using an FFT, and can therefore in- corporate a varying LOS. We demonstrate that their bias depends on scale but not on the observed area. For a quadrupole the bias is always less than 1 per cent for k > 0.01h/Mpc at z > 0.32. For a hexadecapole the bias is below 5 per cent for k>0.05h/Mpc at z>0.32., 6 pages, 3 figures. Minor revisions to match published version

The Square Kilometre Array (SKA) will conduct the biggest spectroscopic galaxy survey ever, by detecting the 21cm emission line of neutral hydrogen (HI) from around a billion galaxies over 3/4 of the sky, out to a redshift of z~2. This will allow the redshift-space matter power spectrum, and corresponding dark energy observables, to be measured with unprecedented precision. In this paper, we present an improved model of the HI galaxy number counts and bias from semi-analytic simulations, and use it to calculate the expected yield of HI galaxies from surveys with a variety of Phase 1 and 2 SKA configurations. We illustrate the relative performance of the different surveys by forecasting errors on the radial and transverse scales of the baryon acoustic oscillation (BAO) feature, finding that the full "billion galaxy survey" with SKA2 will deliver the largest dark energy figure of merit of any current or future large-scale structure survey., 11 pages, 7 figures, 5 tables. Minor revisions for improved clarity. Version accepted by MNRAS

The Square Kilometre Array (SKA) will produce spectroscopic surveys of tens to hundreds of millions of HI galaxies, eventually covering 30,000 sq. deg. and reaching out to redshift z~2. The huge volumes probed by the SKA will allow for some of the best constraints on primordial non-Gaussianity, based on measurements of the large-scale power spectrum. We investigate various observational set-ups for HI galaxy redshift surveys, compatible with the SKA Phase 1 and Phase 2 (full SKA) configurations. We use the corresponding number counts and bias for each survey from realistic simulations and derive the magnification bias and the evolution of source counts directly from these. For the first time, we produce forecasts that fully include the general relativistic effects on the galaxy number counts. These corrections to the standard analysis become important on very large scales, where the signal of primordial non-Gaussianity grows strongest. Our results show that, for the full survey, the non-Gaussianity parameter fNL can be constrained down to an accuracy of 1.54. This improves the current limit set by the Planck satellite by a factor of five, using a completely different approach., 10 pages, 5 figures, 3 tables. Errors corrected in the magnification bias and plot of evolution bias; these errors do not change our main results

Reconstructing an estimate of linear Baryon Acoustic Oscillations (BAO) from an evolved galaxy field has become a standard technique in recent analyses. By partially removing non-linear damping caused by bulk motions, the real-space BAO peak in the correlation function is sharpened, and oscillations in the power spectrum are visible to smaller scales. In turn these lead to stronger measurements of the BAO scale. Future surveys are being designed assuming that this improvement has been applied, and this technique is therefore of critical importance for future BAO measurements. A number of reconstruction techniques are available, but the most widely used is a simple algorithm that decorrelates large-scale and small-scale modes approximately removing the bulk-flow displacements by moving the overdensity field (Eisenstein et al. 2007; Padmanabhan, White & Cohn 2009). We consider the practical implementation of this algorithm, looking at the efficiency of reconstruction as a function of the assumptions made for the bulk-flow scale, the shot noise level in a random catalogue used to quantify the mask and the method used to estimate the bulk-flow shifts. We also examine the efficiency of reconstruction against external factors including galaxy density, volume and edge effects, and consider their impact for future surveys. Throughout we make use of the mocks catalogues created for the Baryon Oscillation Spectroscopic Survey (BOSS) Date Release 11 samples covering 0.43 < z < 0.7 (CMASS) and 0.15 < z < 0.43 (LOWZ), to empirically test these changes., 19 pages, 18 figures. Minor modifications to match version accepted by MNRAS. Erratum added in Appendix, conclusions unchanged

We show that at second order, ensemble averages of observables and directional averages do not commute due to gravitational lensing -- observing the same thing in many directions over the sky is not the same as taking an ensemble average. In principle this non-commutativity is significant for a variety of quantities that we often use as observables and can lead to a bias in parameter estimation. We derive the relation between the ensemble average and the directional average of an observable, at second order in perturbation theory. We discuss the relevance of these two types of averages for making predictions of cosmological observables, focusing on observables related to distances and magnitudes. In particular, we show that the ensemble average of the distance in a given observed direction is increased by gravitational lensing, whereas the directional average of the distance is decreased. For a generic observable, there exists a particular function of the observable that is not affected by second-order lensing perturbations. We also show that standard areas have an advantage over standard rulers, and we discuss the subtleties involved in averaging in the case of supernova observations., Comment: 11 pages, 2 figures; v2: discussion about supernovae extended, eq. (8) detailed, minor typos corrected, matches published version

We present the galaxy number overdensity up to second order in redshift space on cosmological scales for a concordance model. The result contains all general relativistic effects up to second order that arise from observing on the past light cone, including all redshift effects, lensing distortions from convergence and shear, and contributions from velocities, Sachs-Wolfe, integrated SW and time-delay terms. This result will be important for accurate calculation of the bias on estimates of non-Gaussianity and on precision parameter estimates, introduced by nonlinear projection effects., Comment: 7 pages, 1 figure. In the previous v4 (and in the published paper), we mistakenly omitted some post-Born terms. This error has been corrected here and in the companion paper 1406.0319v4. Our results are now in agreement, in the appropriate limit, with those of arXiv:1606.02113