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Mock catalogues are a crucial tool in the analysis of galaxy surveys data, both for the accurate computation of covariance matrices, and for the optimisation of analysis methodology and validation of data sets. In this paper, we present a set of 1800 galaxy mock catalogues designed to match the Dark Energy Survey Year-1 BAO sample (Crocce et al. 2017) in abundance, observational volume, redshift distribution and uncertainty, and redshift dependent clustering. The simulated samples were built upon HALOGEN (Avila et al. 2015) halo catalogues, based on a $2LPT$ density field with an exponential bias. For each of them, a lightcone is constructed by the superposition of snapshots in the redshift range $0.45, Comment: 18 pages, 15 figures, 1 table, published in MNRAS

The Fourier-space galaxy bispectrum is complex, with the imaginary part arising from leading-order relativistic corrections, due to Doppler, gravitational redshift and related line-of-sight effects in redshift space. The detection of the imaginary part of the bispectrum is potentially a smoking gun signal of relativistic contributions. We investigate whether next-generation spectroscopic surveys could make such a detection. For a Stage IV spectroscopic $H\alpha$ survey similar to Euclid, we find that the cumulative signal to noise of this relativistic signature is $\mathcal{O}(10)$. Long-mode relativistic effects couple to short-mode Newtonian effects in the galaxy bispectrum, but not in the galaxy power spectrum. This is the basis for detectability of relativistic effects in the bispectrum of a single galaxy survey, whereas the power spectrum requires multiple galaxy surveys to detect the corresponding signal., Comment: 13 pages, 10 figures, Typo in equation (3.8) corrected - results unchanged

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 angular power spectrum is a gauge-independent observable that is in principle the natural tool for analysing galaxy number counts. In practice, the problem is that the computational requirements for next-generation spectroscopic surveys such as Euclid and the Square Kilometre Array are currently unfeasible. We propose a new method to save computational time for spectroscopic angular power spectra. This hybrid method is modelled on the Fourier power spectrum approach of treating relatively thick redshift bins (redshift width ~0.1) as separate surveys. In the hybrid method, each thick bin is further subdivided into thin bins (redshift width ~0.01); all the correlations within each thick bin are computed, while cross-bin correlations beyond the thick bins are neglected. Constraints on cosmological parameters from the hybrid method are comparable to those from the standard galaxy power spectrum analysis - but they have the advantage that cosmic evolution, wide-angle and lensing effects are naturally included, while no Alcock-Paczynski correction is needed. The hybrid method delivers much tighter constraints than a 2D tomographic approach that is typical for photometric surveys, which considers only thick bins and the correlations between them. Furthermore, for standard cosmological parameters our method is not biased by neglecting the effects of lensing on number counts, while the tomographic method is strongly biased., 11 pages, 7 figures, 4 tables. Typo in Eq. (2) fixed

We study synergies between HI 21cm and H$\alpha$ intensity map observations, focusing on SKA1-like and SPHEREx-like surveys. We forecast how well such a combination can measure features in the angular power spectrum on the largest scales, that arise from primordial non-Gaussianity and from general relativistic effects. For the first time we consider Doppler, Sachs-Wolfe and integrated SW effects separately. We confirm that the single-tracer surveys on their own cannot detect general relativistic effects and can constrain the non-Gaussianity parameter $f_{\rm NL}$ only slightly better than Planck. Using the multi-tracer technique, constraints on $f_{\rm NL}$ can be pushed down to $\sim1$. Amongst the general relativistic effects, the Doppler term is detectable with the multi-tracer. The Sachs-Wolfe terms and the integrated SW effect are still not detectable., Comment: 9 pages, 7 figures, 2 tables, version accepted by MNRAS

We present measurements of the Baryon Acoustic Oscillation (BAO) scale in redshift-space using the clustering of quasars. We consider a sample of 147 000 quasars from the extended Baryon Oscillation Spectroscopic Survey (eBOSS) distributed over 2044 square degrees with redshifts 0.8 < z < 2.2 and measure their spherically averaged clustering in both configuration and Fourier space. Our observational data set and the 1400 simulated realizations of the data set allow us to detect a preference for BAO that is greater than 2.8σ. We determine the spherically averaged BAO distance to z = 1.52 to 3.8 per cent precision: D (z = 1.52) = 3843 ± 147 (r/r) Mpc. This is the first time the location of the BAO feature has been measured between redshifts 1 and 2. Our result is fully consistent with the prediction obtained by extrapolating the Planck flatΛCDMbest-fitting cosmology. All of our results are consistent with basic large-scale structure (LSS) theory, confirming quasars to be a reliable tracer of LSS, and provide a starting point for numerous cosmological tests to be performed with eBOSS quasar samples. We combine our result with previous, independent, BAO distance measurements to construct an updated BAO distance-ladder. Using these BAO data alone and marginalizing over the length of the standard ruler, we find Ω > 0 at 6.6s significance when testing a ΛCDM model with free curvature.C 2017 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society, AJR is grateful for support from the Ohio State University Center for Cosmology and ParticlePhysics. HGM acknowledges support from the Labex ILP (reference ANR-10-LABX-63) part of the Idex SUPER, and received financial state aid managed by the Agence Nationale de la Recherche, as part of the programme Investissements d'avenir under the reference ANR-11-IDEX-0004-02. GBZ is supported by NSFC Grant No. 11673025, and by a Royal Society Newton Advanced Fellowship. RT acknowledges support from the Science and Technology Facilities Council via an Ernest Rutherford Fellowship (grant number ST/K004719/1) CHC is grateful for support from Leibniz-Institut fur Astrophysik Potsdam (AIP). EB and PZ acknowledge support from the P2IO LabEx (ANR-10-LABX-0038). JLT acknowledges support from National Science Foundation grant AST-1615997. YW is supported by the NSFC grant number 11403034. WJP acknowledges support from the UK Space Agency through grant ST/K00283X/1, and WJP acknowledges support from the European Research Council through grant Darksurvey, and the UK Science & Technology Facilities Council through the consolidated grant ST/K0090X/1. ADM was partially supported by the NSF through grant numbers 1515404 and 1616168. IP acknowledges the support of the OCEVU Labex (ANR-11-LABX-0060) and the A*MIDEX project (ANR-11-IDEX-0001-02) funded by the 'Investissements d'Avenir French government program managed by the AN. JPK acknowledges support from the ERC advanced grant LIDA. GR acknowledges support from the National Research Foundation of Korea (NRF) through NRF-SGER 2014055950 funded by the Korean Ministry of Education, Science and Technology (MoEST), and from the faculty research fund of Sejong University in 2016. Funding for SDSS-III and SDSS-IV has been provided by the Alfred P. Sloan Foundation and Participating Institutions. Additional funding for SDSS-III comes from the National Science Foundation and the U.S. Department of Energy Office of Science. Further information about both projects is available at www.sdss.org. SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions in both collaborations. In SDSS-III, these include the University of Arizona, the Brazilian Participation Group, Brookhaven National Laboratory, Carnegie Mellon University, University of Florida, the French Participation Group, the German Participation Group, Harvard University, the Instituto de Astrofisica de Canarias, the Michigan State/Notre Dame/JINA Participation Group, Johns Hopkins University, Lawrence Berkeley National Laboratory, Max Planck Institute for Astrophysics, Max Planck Institute for Extraterrestrial Physics, New Mexico State University, New York University, Ohio State University, Pennsylvania State University, University of Portsmouth, Princeton University, the Spanish Participation Group, University of Tokyo, University of Utah, Vanderbilt University, University of Virginia, University of Washington, and Yale University. The Participating Institutions in SDSS-IV are Carnegie Mellon University, Colorado University, Boulder, Harvard-Smithsonian Center for Astrophysics Participation Group, Johns Hopkins University, Kavli Institute for the Physics and Mathematics of the Universe Max-Planck-Institut fuer Astrophysik (MPA Garching), Max-Planck-Institut fuer Extraterrestrische Physik (MPE), Max-Planck-Institut fuer Astronomie (MPIA Heidelberg), National Astronomical Observatories of China, New Mexico State University, New York University, The Ohio State University, Penn State University, Shanghai Astronomical Observatory, United Kingdom Participation Group, University of Portsmouth, University of Utah, University of Wisconsin and Yale University. This work made use of the facilities and staff of the UK Sciama High Performance Computing cluster supported by the ICG, SEP-Net and the University of Portsmouth. This research used resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231.

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

We determine an optimized clustering statistic to be used for galaxy samples with significant redshift uncertainty, such as those that rely on photometric redshifts. To do so, we study the baryon acoustic oscillation (BAO) information content as a function of the orientation of galaxy clustering modes with respect to their angle to the line-of-sight (LOS). The clustering along the LOS, as observed in a redshift-space with significant redshift uncertainty, has contributions from clustering modes with a range of orientations with respect to the true LOS. For redshift uncertainty $\sigma_z \geq 0.02(1+z)$ we find that while the BAO information is confined to transverse clustering modes in the true space, it is spread nearly evenly in the observed space. Thus, measuring clustering in terms of the projected separation (regardless of the LOS) is an efficient and nearly lossless compression of the signal for $\sigma_z \geq 0.02(1+z)$. For reduced redshift uncertainty, a more careful consideration is required. We then use more than 1700 realizations (combining two separate sets) of galaxy simulations mimicking the Dark Energy Survey Year 1 sample to validate our analytic results and optimized analysis procedure. We find that using the correlation function binned in projected separation, we can achieve uncertainties that are within 10 per cent of those predicted by Fisher matrix forecasts. We predict that DES Y1 should achieve a 5 per cent distance measurement using our optimized methods. We expect the results presented here to be important for any future BAO measurements made using photometric redshift data., Comment: Matches version accepted by MNRAS, should be clearer

The low statistical errors on cosmological parameters promised by future galaxy surveys will only be realised with the development of new, fast, analysis methods that reduce potential systematic problems to low levels. We present an efficient method for measuring the evolution of the growth of structure using Redshift Space Distortions (RSD), that removes the need to make measurements in redshift shells. We provide sets of galaxy-weights that cover a wide range in redshift, but are optimised to provide differential information about cosmological evolution. These are derived to optimally measure the coefficients of a parameterisation of the redshift-dependent matter density, which provides a framework to measure deviations from the concordance $\Lambda$CDM cosmology, allowing for deviations in both geometric and/or growth. We test the robustness of the weights by comparing with alternative schemes and investigate the impact of galaxy bias. We extend the results to measure the combined anisotropic Baryon Acoustic Oscillation (BAO) and RSD signals., Comment: 10 pages, 5 figures, submitted to MNRAS

The Astrophysical Journal 151.2 (2016): 44 reproduced by permission of the AAS, In a six-year program started in 2014 July, the Extended Baryon Oscillation Spectroscopic Survey (eBOSS) will conduct novel cosmological observations using the BOSS spectrograph at Apache Point Observatory. These observations will be conducted simultaneously with the Time Domain Spectroscopic Survey (TDSS) designed for variability studies and the Spectroscopic Identification of eROSITA Sources (SPIDERS) program designed for studies of X-ray sources. In particular, eBOSS will measure with percent-level precision the distance-redshift relation with baryon acoustic oscillations (BAO) in the clustering of matter. eBOSS will use four different tracers of the underlying matter density field to vastly expand the volume covered by BOSS and map the large-scale-structures over the relatively unconstrained redshift range 0.6 < z < 2.2. Using more than 250,000 new, spectroscopically confirmed luminous red galaxies at a median redshift z = 0.72, we project that eBOSS will yield measurements of the angular diameter distance dA(z) to an accuracy of 1.2% and measurements of H(z) to 2.1% when combined with the z > 0.6 sample of BOSS galaxies. With ∼195,000 new emission line galaxy redshifts, we expect BAO measurements of dA(z) to an accuracy of 3.1% and H(z) to 4.7% at an effective redshift of z = 0.87. A sample of more than 500,000 spectroscopically confirmed quasars will provide the first BAO distance measurements over the redshift range 0.9 < z < 2.2, with expected precision of 2.8% and 4.2% on dA(z) and H(z), respectively. Finally, with 60,000 new quasars and re-observation of 60,000 BOSS quasars, we will obtain new Lyα forest measurements at redshifts z > 2.1; these new data will enhance the precision of dA(z) and H(z) at z > 2.1 by a factor of 1.44 relative to BOSS. Furthermore, eBOSS will provide improved tests of General Relativity on cosmological scales through redshift-space distortion measurements, improved tests for non-Gaussianity in the primordial density field, and new constraints on the summed mass of all neutrino species. Here, we provide an overview of the cosmological goals, spectroscopic target sample, demonstration of spectral quality from early data, and projected cosmological constraints from eBOSS, K.D. acknowledges support from the U.S. Department of Energy under Grant DE-SC000995. J.P.K. and T.D. acknowledge support from the ERC advanced grant LIDA. W.J.P. acknowledges support from the UK STFC through the consolidated grant ST/K0090X/1, and from the European Research Council through grant Darksurvey

It has recently been shown that second-order corrections to the background distance-redshift relation can build up significantly at large redshifts, due to an aggregation of gravitational lensing events. This shifts the expectation value of the distance to the CMB by 1%. In this paper we show that this shift is already properly accounted for in standard CMB analyses. We clarify the role that the area distance to the CMB plays in the presence of second-order lensing corrections., 15 pages, no figure; v2: some typos and an error in eq. (20) (v1) corrected. Conclusion unchanged; v3: reference added, minor changes to the text, matches published version

The observed galaxy power spectrum acquires relativistic corrections from lightcone effects, and these corrections grow on very large scales. Future galaxy surveys in optical, infrared and radio bands will probe increasingly large wavelength modes and reach higher redshifts. In order to exploit the new data on large scales, an accurate analysis requires inclusion of the relativistic effects. This is especially the case for primordial non-Gaussianity and for extending tests of dark energy models to horizon scales. Here we investigate the latter, focusing on models where the dark energy interacts non-gravitationally with dark matter. Interaction in the dark sector can also lead to large-scale deviations in the power spectrum. If the relativistic effects are ignored, the imprint of interacting dark energy will be incorrectly identified and thus lead to a bias in constraints on interacting dark energy on very large scales., 12 pages, 6 figures. Minor corrections. Version accepted by Physical Review D

Non-Gaussianity in the primordial fluctuations that seeded structure formation produces a signal in the galaxy power spectrum on very large scales. This signal contains vital information about the primordial Universe, but it is very challenging to extract, because of cosmic variance and large-scale systematics - especially after the Planck experiment has already ruled out a large amplitude for the signal. Cosmic variance and experimental systematics can be alleviated by the multi-tracer method. Here we address another systematic - introduced by not using the correct relativistic analysis of the power spectrum on very large scales. In order to reduce the errors on fNL, we need to include measurements on the largest possible scales. Failure to include the relativistic effects on these scales can introduce significant bias in the best-fit value of fNL from future galaxy surveys., 5 pages, 1 figure. Version published on MNRAS Letters

Next-generation cosmological surveys will probe ever larger volumes of the Universe, including the largest scales, near and beyond the horizon. On these scales, the galaxy power spectrum carries signatures of local primordial non-Gaussianity (PNG) and horizon-scale general relativistic (GR) effects. However, cosmic variance limits the detection of horizon-scale effects. Combining different surveys via the multi-tracer method allows us to reduce the effect down cosmic variance. This method benefits from large bias differences between two tracers of the underlying dark matter distribution, which suggests a multi-wavelength combination of large volume surveys that are planned on a similar timescale. We show that the combination of two contemporaneous surveys, a large neutral hydrogen intensity mapping survey in SKA Phase1 and a Euclid-like photometric survey, will provide unprecedented constraints on PNG as well as detection of the GR effects. We forecast that the error on local PNG will break through the cosmic variance limit on cosmic microwave background surveys and achieve $\sigma(f_{NL})\simeq1.4-0.5$, depending on assumed priors, bias, and sky coverage. GR effects are more robust to changes in the assumed fiducial model, and we forecast that they can be detected with a signal-to-noise of about $14$., Comment: Typos corrected; Accepted for publication by the Astrophysical Journal Letters; 5 pages, 3 figures, 2 tables

Employing a nonparametric approach of the principal component analysis (PCA), we forecast the future constraint on the equation of state $w(z)$ of dark energy, and on the effective Newton constant $\mu(k,z)$, which parameterise the effect of modified gravity, using the planned SKA HI galaxy survey. Combining with the simulated data of Planck and Dark Energy Survey (DES), we find that SKA Phase 1 (SKA1) and SKA Phase 2 (SKA2) can well constrain $3$ and $5$ eigenmodes of $w(z)$ respectively. The errors of the best measured modes can be reduced to 0.04 and 0.023 for SKA1 and SKA2 respectively, making it possible to probe dark energy dynamics. On the other hand, SKA1 and SKA2 can constrain $7$ and $20$ eigenmodes of $\mu(k,z)$ respectively within 10\% sensitivity level. Furthermore, 2 and 7 modes can be constrained within sub percent level using SKA1 and SKA2 respectively. This is a significant improvement compared to the combined datasets without SKA., Comment: 13 pages, 5 figures. The wrongly generated last page was removed. This article is part of the 'SKA Cosmology Chapter, Advancing Astrophysics with the SKA (AASKA14), Conference, Giardini Naxos (Italy), June 9th-13th 2014'

If dark energy and dark matter interact via exchange of energy and momentum, then this may affect the galaxy power spectrum on large scales. When this happens, it may be degenerate with the signal from primordial non-Gaussianity via scale-dependent bias. We consider a class of interacting dark energy models and show that the matter overdensity is scale-dependent on large scales. We estimate the effective non-Gaussianity arising from the large-scale effects of interaction in the dark sector. The signal of dark sector interaction can be disentangled from a primordial non-Gaussian signal by measuring the power at two redshifts., Comment: Minor changes. Version accepted by Phys Rev D

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 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