Dark Energy Figure Of Merit Research Articles

Improved Tomographic Binning of 3 × 2 pt Lens Samples: Neural Network Classifiers and Optimal Bin Assignments

Large imaging surveys, such as the Legacy Survey of Space and Time, rely on photometric redshifts and tomographic binning for 3 × 2 pt analyses that combine galaxy clustering and weak lensing. In this paper, we propose a method for optimizing the tomographic binning choice for the lens sample of galaxies. We divide the CosmoDC2 and Buzzard simulated galaxy catalogs into a training set and an application set, where the training set is nonrepresentative in a realistic way, and then estimate photometric redshifts for the application sets. The galaxies are sorted into redshift bins covering equal intervals of redshift or comoving distance, or with an equal number of galaxies in each bin, and we consider a generalized extension of these approaches. We find that bins of equal comoving distance produce the highest dark energy figure of merit of the initial binning choices, but that the choice of bin edges can be further optimized. We then train a neural network classifier to identify galaxies that are either highly likely to have accurate photometric redshift estimates or highly likely to be sorted into the correct redshift bin. The neural network classifier is used to remove poor redshift estimates from the sample, and the results are compared to the case when none of the sample is removed. We find that the neural network classifiers are able to improve the figure of merit by ∼13% and are able to recover ∼25% of the loss in the figure of merit that occurs when a nonrepresentative training sample is used.

Constraints on Dark Energy from the CSST Galaxy Clusters

We study the potential of the galaxy cluster sample expected from the Chinese Space Station Telescope (CSST) survey to constrain dark energy properties. By modeling the distribution of observed cluster mass for a given true mass to be log-normal and adopting a selection threshold in the observed mass M 200m ≥ 0.836 × 1014 h −1 M ⊙, we find about 4.1 × 105 clusters in the redshift range 0 ≤ z ≤ 1.5 can be detected by the CSST. We construct the Fisher matrix for the cluster number counts from CSST, and forecast constraints on dark energy parameters for models with constant (w 0CDM) and time dependent (w 0 w a CDM) equation of state. In the self-calibration scheme, the dark energy equation of state parameter w 0 of the w 0CDM model can be constrained to Δw 0 = 0.036. If w a is added as a free parameter, we obtain Δw 0 = 0.077 and Δw a = 0.39 for the w 0 w a CDM model, with a Figure of Merit for (w 0, w a ) of 68.99. Should we have perfect knowledge of the observable-mass scaling relation (“known SR” scheme), we would obtain Δw 0 = 0.012 for the w 0CDM model, and Δw 0 = 0.062 and Δw a = 0.24 for the w 0 w a CDM model. The dark energy Figure of Merit of (w 0, w a ) increases to 343.25. This indicates again the importance of calibrating the observable-mass scaling relation for optically selected galaxy clusters. By extending the maximum redshift of the clusters from to , the dark energy Figure of Merit for (w 0, w a ) increases to 89.72 (self-calibration scheme) and 610.97 (“known SR” scheme), improved by a factor of ∼1.30 and ∼1.78, respectively. We find that the impact of clusters’ redshift uncertainty on the dark energy constraints is negligible as long as the redshift error of clusters is smaller than 0.01, achievable by CSST. We also find that the bias in logarithm mass must be calibrated to be 0.30 or better to avoid significant dark energy parameter bias.

Double source lensing probing high redshift cosmology

Double source lensing, with two sources lensed by the sameforeground galaxy, involves the distance between each sourceand the lens and hence is a probe of the universe away fromthe observer. The double source distance ratio also reduces sensitivity tothe lens model and has good complementarity with standarddistance probes. We show that using this technique at highredshifts z > 1, to be enabled by data from the Euclid satellite and other surveys, can give insights on dark energy, both in terms of w 0–w a and redshift binned density. We find a dark energy figure of merit of 245 from combination of 256 double source systems with moderate quality cosmic microwave background and supernova data. Using instead five redshift bins between z = 1.1–5, we could detect the dark energy density out to z ≈ 5, or make measurements ranging between 31σ and 2.5σ of its values in the bins.

Cosmology from clustering, cosmic shear, CMB lensing, and cross correlations: combining Rubin observatory and Simons Observatory

ABSTRACT In the near future, the overlap of the Rubin Observatory Legacy Survey of Space and Time (LSST) and the Simons Observatory (SO) will present an ideal opportunity for joint cosmological data set analyses. In this paper, we simulate the joint likelihood analysis of these two experiments using six two-point functions derived from galaxy position, galaxy shear, and CMB lensing convergence fields. Our analysis focuses on realistic noise and systematics models and we find that the dark energy Figure of merit (FoM) increases by 53 per cent (92 per cent) from LSST-only to LSST+SO in Year 1 (Year 6). We also investigate the benefits of using the same galaxy sample for both clustering and lensing analyses, and find the choice improves the overall signal to noise by ${\sim}30{-}40{{\ \rm per\ cent}}$, which significantly improves the photo-z calibration and mildly improves the cosmological constraints. Finally, we explore the effects of catastrophic photo-z outliers finding that they cause significant parameter biases when ignored. We develop a new mitigation approach termed ‘island model’, which corrects a large fraction of the biases with only a few parameters while preserving the constraining power.

Euclid: Constraining dark energy coupled to electromagnetism using astrophysical and laboratory data

In physically realistic, scalar-field-based dynamical dark energy models (including, e.g., quintessence), one naturally expects the scalar field to couple to the rest of the model’s degrees of freedom. In particular, a coupling to the electromagnetic sector leads to a time (redshift) dependence in the fine-structure constant and a violation of the weak equivalence principle. Here we extend the previous Euclid forecast constraints on dark energy models to this enlarged (but physically more realistic) parameter space, and forecast how well Euclid, together with high-resolution spectroscopic data and local experiments, can constrain these models. Our analysis combines simulated Euclid data products with astrophysical measurements of the fine-structure constant, α, and local experimental constraints, and it includes both parametric and non-parametric methods. For the astrophysical measurements of α, we consider both the currently available data and a simulated dataset representative of Extremely Large Telescope measurements that are expected to be available in the 2030s. Our parametric analysis shows that in the latter case, the inclusion of astrophysical and local data improves the Euclid dark energy figure of merit by between 8% and 26%, depending on the correct fiducial model, with the improvements being larger in the null case where the fiducial coupling to the electromagnetic sector is vanishing. These improvements would be smaller with the current astrophysical data. Moreover, we illustrate how a genetic algorithms based reconstruction provides a null test for the presence of the coupling. Our results highlight the importance of complementing surveys like Euclid with external data products, in order to accurately test the wider parameter spaces of physically motivated paradigms.

Euclid: Forecasts for k-cut 3×2 Point Statistics

Modelling uncertainties at small scales, i.e. high $k$ in the power spectrum $P(k)$, due to baryonic feedback, nonlinear structure growth and the fact that galaxies are biased tracers poses a significant obstacle to fully leverage the constraining power of the Euclid wide-field survey. $k$-cut cosmic shear has recently been proposed as a method to optimally remove sensitivity to these scales while preserving usable information. In this paper we generalise the $k$-cut cosmic shear formalism to $3 \times 2$ point statistics and estimate the loss of information for different $k$-cuts in a $3 \times 2$ point analysis of the {\it Euclid} data. Extending the Fisher matrix analysis of Euclid Collaboration: Blanchard et al. (2019), we assess the degradation in constraining power for different $k$-cuts. We find that taking a $k$-cut at $2.6 \ h \ {\rm Mpc} ^{-1}$ yields a dark energy Figure of Merit (FOM) of 1018. This is comparable to taking a weak lensing cut at $\ell = 5000$ and a galaxy clustering and galaxy-galaxy lensing cut at $\ell = 3000$ in a traditional $3 \times 2$ point analysis. We also find that the fraction of the observed galaxies used in the photometric clustering part of the analysis is one of the main drivers of the FOM. Removing $50 \% \ (90 \%)$ of the clustering galaxies decreases the FOM by $19 \% \ (62 \%)$. Given that the FOM depends so heavily on the fraction of galaxies used in the clustering analysis, extensive efforts should be made to handle the real-world systematics present when extending the analysis beyond the luminous red galaxy (LRG) sample. <em>This paper is published on behalf of the Euclid Consortium</em>: http://euclid-ec.org

Cosmological parameter forecasts by a joint 2D tomographic approach to CMB and galaxy clustering

The cross-correlation between the cosmic microwave background (CMB) fields and matter tracers carries important cosmological information. In this paper, we forecast by a signal-to-noise ratio analysis the information contained in the cross-correlation of the CMB anisotropy fields with source counts for future cosmological observations and its impact on cosmological parameters uncertainties, using a joint tomographic analysis. We include temperature, polarization and lensing for the CMB fields and galaxy number counts for the matter tracers. By restricting ourselves to quasi-linear scales, we forecast by a Fisher matrix formalism the relative importance of the cross-correlation of source counts with the CMB in the constraints on the parameters for several cosmological models. We obtain that the CMB-number counts cross-correlation can improve the dark energy Figure of Merit (FoM) at most up to a factor $\sim 2$ for LiteBIRD+CMB-S4 $\times$ SKA1 compared to the uncorrelated combination of both probes and will enable the Euclid-like photometric survey to reach the highest FoM among those considered here. We also forecast how CMB-galaxy clustering cross-correlation could increase the FoM of the neutrino sector, also enabling a statistically significant ($\gtrsim$ 3$\sigma$ for LiteBIRD+CMB-S4 $\times$ SPHEREx) detection of the minimal neutrino mass allowed in a normal hierarchy by using quasi-linear scales only. Analogously, we find that the uncertainty in the local primordial non-Gaussianity could be as low as $\sigma (f_{\rm NL}) \sim 1.5-2$ by using two-point statistics only with the combination of CMB and radio surveys such as EMU and SKA1. Our results highlight the additional constraining power of the cross-correlation between CMB and galaxy clustering from future surveys which is mainly based on quasi-linear scales and therefore sufficiently robust to non-linear effects.

The Roman Space Telescope Relative Calibration System and the Dark Energy Figure of Merit

Abstract One of the Roman Space Telescopes principal science objectives is to measure dark energy's equation-of-state using a strategic combination of imaging and spectroscopic surveys at high galactic latitude. Type Ia Supernovae survey requirements demand 0.3% photometric accuracy and calibration of key systematic effects. One of these is count rate dependent nonlinearity (CRNL) that if uncorrected affects the accuracy of SNe Ia distance measurements. Romans Relative Calibration System (RCS) enables on-orbit measurement and tracking of CRNL, through a direct illumination mode and a simultaneous lamp plus scene mode. We present results on the impact of CRNL calibration on the dark energy figure of merit (FoM), for a specific reduction of RCS capabilities. We examined many combinations of illumination and passbands, finding that only six meet the requirements. No RCS at all results in a factor of 5 degradation in the FoM.

Joint cosmology and mass calibration from thermal Sunyaev-Zel’dovich cluster counts and cosmic shear

We present a new method for joint cosmological parameter inference and cluster mass calibration from a combination of weak lensing measurements and the abundance of thermal Sunyaev-Zel'dovich (tSZ) selected galaxy clusters. We combine cluster counts with the spherical harmonic cosmic shear power spectrum and the cross-correlation between cluster overdensity and cosmic shear. These correlations constrain the cluster mass-observable relation. We model the observables using a halo model framework, including their full non-Gaussian covariance. Forecasting constraints on cosmological and mass calibration parameters for a combination of LSST cosmic shear and Simons Observatory tSZ cluster counts, we find competitive constraints for cluster cosmology, with a factor two improvement in the dark energy figure of merit compared to LSST cosmic shear alone. We find most of the mass calibration information will be in the large and intermediate scales of the cross-correlation between cluster overdensity and cosmic shear. Finally, we find broadly comparable constraints to traditional analyses based on calibrating masses using stacked cluster lensing measurements, with the benefit of consistently accounting for the correlations with cosmic shear.

Euclid preparation

Aims. The Euclid space telescope will measure the shapes and redshifts of galaxies to reconstruct the expansion history of the Universe and the growth of cosmic structures. The estimation of the expected performance of the experiment, in terms of predicted constraints on cosmological parameters, has so far relied on various individual methodologies and numerical implementations, which were developed for different observational probes and for the combination thereof. In this paper we present validated forecasts, which combine both theoretical and observational ingredients for different cosmological probes. This work is presented to provide the community with reliable numerical codes and methods for Euclid cosmological forecasts. Methods. We describe in detail the methods adopted for Fisher matrix forecasts, which were applied to galaxy clustering, weak lensing, and the combination thereof. We estimated the required accuracy for Euclid forecasts and outline a methodology for their development. We then compare and improve different numerical implementations, reaching uncertainties on the errors of cosmological parameters that are less than the required precision in all cases. Furthermore, we provide details on the validated implementations, some of which are made publicly available, in different programming languages, together with a reference training-set of input and output matrices for a set of specific models. These can be used by the reader to validate their own implementations if required. Results. We present new cosmological forecasts for Euclid. We find that results depend on the specific cosmological model and remaining freedom in each setting, for example flat or non-flat spatial cosmologies, or different cuts at non-linear scales. The numerical implementations are now reliable for these settings. We present the results for an optimistic and a pessimistic choice for these types of settings. We demonstrate that the impact of cross-correlations is particularly relevant for models beyond a cosmological constant and may allow us to increase the dark energy figure of merit by at least a factor of three.

Prospects of strongly lensed repeating fast radio bursts: Complementary constraints on dark energy evolution

Fast radio bursts (FRBs) are highly dispersed and probably extragalactic radio flashes with millisecond-duration. Recently, the Canadian Hydrogen Intensity Mapping Experiment (using the CHIME/FRB instrument) has reported detections of 13 FRBs during a pre-commissioning phase. It is more exciting that one of the 13 FRBs is a second source of repeaters which suggests that CHIME/FRB and other wide-field sensitive radio telescopes will find a substantial population of repeating FRBs. We have proposed strongly lensed repeating FRBs as a precision cosmological probe, e.g. constraining the Hubble constant and model-independently estimating the cosmic curvature. Here, we study complementary constraints on the equation of state of dark energy from strongly lensed FRBs to currently available popular probes. It is found that, in the framework of Chevalier-Polarski-Linder parametrization, adding time delay measurement of 30 strongly lensed FRB systems to cosmic microwave background radiation and type Ia supernovae can improve the dark energy figure of merit by a factor 2. In the precision cosmology era, this improvement is of great significance for studying the nature of dark energy.

Complementary constraints on dark energy equation of state from strongly lensed gravitational wave

It has been shown that time delay of strong gravitational lensing is not only an effective cosmological probe to constrain the Hubble constant, the matter density and the curvature of the universe but also useful for breaking the degeneracy of the dark energy equation of state and thus provide complementarity with other popular probes, such as type Ia supernovae, baryon acoustic oscillations, and cosmic microwave background radiation. Interestingly, compared to traditional strong lensing systems where quasars act as sources, strongly lensed gravitational waves (GWs) from compact binary coalescence and their electromagnetic (EM) counterparts systems have been recently proposed to be more powerful for studying cosmology since GWs and their EM counterparts are transients. Short durations of GWs and their EM counterparts are very advantageous to time delay measurement and lens profile modeling. Here, in the framework of Chevalier-Polarski-Linder (CPL) parametrization, we investigate improvement of constraining power on dark energy equation of state due to including time delay measurements of strong lensed GW systems. It is suggested that, on the basis of the third generation ground-based detector, e.g. Einstein Telescope, adding time delay of only 30 strong lensed GW systems to type Ia supernovae and cosmic microwave background radiation can improve the dark energy figure of merit by a factor 2. For the traditional standard siren method where the uncertainties of luminosity distances of GWs are $\sim10\%$, a few $\times~10^4$ events are expected to present similar constraints. In the precision cosmology era, this progress is of great significance for studying the nature of dark energy.

The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: tomographic BAO analysis of DR12 combined sample in configuration space

We perform a tomographic baryon acoustic oscillations analysis using the two-point galaxy correlation function measured from the combined sample of BOSS DR12, which covers the redshift range of $0.2<z<0.75$. Splitting the sample into multiple overlapping redshift slices to extract the redshift information of galaxy clustering, we obtain a measurement of $D_A(z)/r_d$ and $H(z)r_d$ at nine effective redshifts with the full covariance matrix calibrated using MultiDark-Patchy mock catalogues. Using the reconstructed galaxy catalogues, we obtain the precision of $1.3\%-2.2\%$ for $D_A(z)/r_d$ and $2.1\%-6.0\%$ for $H(z)r_d$. To quantify the gain from the tomographic information, we compare the constraints on the cosmological parameters using our 9-bin BAO measurements, the consensus 3-bin BAO and RSD measurements at three effective redshifts in \citet{Alam2016}, and the non-tomographic (1-bin) BAO measurement at a single effective redshift. Comparing the 9-bin with 1-bin constraint result, it can improve the dark energy Figure of Merit by a factor of 1.24 for the Chevallier-Polarski-Linder parametrisation for equation of state parameter $w_{\rm DE}$. The errors of $w_0$ and $w_a$ from 9-bin constraints are slightly improved when compared to the 3-bin constraint result.

Parameter constraints from weak-lensing tomography of galaxy shapes and cosmic microwave background fluctuations

Recently, it has been shown that cross-correlating cosmic microwave background (CMB) lensing and three-dimensional (3D) cosmic shear allows to considerably tighten cosmological parameter constraints. We investigate whether similar improvement can be achieved in a conventional tomographic setup. We present Fisher parameter forecasts for a Euclid-like galaxy survey in combination with different ongoing and forthcoming CMB experiments. In contrast to a fully 3D analysis, we find only marginal improvement. Assuming Planck-like CMB data, we show that including the full covariance of the combined CMB and cosmic shear data improves the dark energy figure of merit (FOM) by only 3 per cent. The marginalized error on the sum of neutrino masses is reduced at the same level. For a next generation CMB satellite mission such as Prism, the predicted improvement of the dark energy FOM amounts to approximately 25 per cent. Furthermore, we show that the small improvement is contrasted by an increased bias in the dark energy parameters when the intrinsic alignment of galaxies is not correctly accounted for in the full covariance matrix.

Doubling strong lensing as a cosmological probe

Strong gravitational lensing provides a geometric probe of cosmology in a unique manner through distance ratios involving the source and lens. This is well known for the time delay distance derived from measured delays between lightcurves of the images of variable sources such as quasars. Recently, double source plane lens systems involving two constant sources lensed by the same foreground lens have been proposed as another probe, involving a different ratio of distances measured from the image positions and fairly insensitive to the lens modeling. Here we demonstrate that these two different sets of strong lensing distance ratios have strong complementarity in cosmological leverage. Unlike other probes, the double source distance ratio is actually more sensitive to the dark energy equation of state parameters $w_0$ and $w_a$ than to the matter density $\Omega_m$, for low redshift lenses. Adding double source distance ratio measurements can improve the dark energy figure of merit by 40% for a sample of fewer than 100 low redshift systems, or even better for the optimal redshift distribution we derive.

SKA weak lensing– II. Simulated performance and survey design considerations

We construct a pipeline for simulating weak lensing cosmology surveys with the Square Kilometre Array (SKA), taking as inputs telescope sensitivity curves; correlated source flux, size and redshift distributions; a simple ionospheric model; source redshift and ellipticity measurement errors. We then use this simulation pipeline to optimise a 2-year weak lensing survey performed with the first deployment of the SKA (SKA1). Our assessments are based on the total signal-to-noise of the recovered shear power spectra, a metric that we find to correlate very well with a standard dark energy figure of merit. We first consider the choice of frequency band, trading off increases in number counts at lower frequencies against poorer resolution; our analysis strongly prefers the higher frequency Band 2 (950-1760 MHz) channel of the SKA-MID telescope to the lower frequency Band 1 (350-1050 MHz). Best results would be obtained by allowing the centre of Band 2 to shift towards lower frequency, around 1.1 GHz. We then move on to consider survey size, finding that an area of 5,000 square degrees is optimal for most SKA1 instrumental configurations. Finally, we forecast the performance of a weak lensing survey with the second deployment of the SKA. The increased survey size (3$\pi$\,steradian) and sensitivity improves both the signal-to-noise and the dark energy metrics by two orders of magnitude.

Describing variations of the Fisher-matrix across parameter space

Forecasts in cosmology, both with Monte-Carlo Markov-chain methods and with the Fisher matrix formalism, depend on the choice of the fiducial model because both the signal strength of any observable as well as the model nonlinearities linking observables to cosmological parameters vary in the general case. In this paper we propose a method for extrapolating Fisher-forecasts across the space of cosmological parameters by constructing a suitable ba- sis. We demonstrate the validity of our method with constraints on a standard dark energy model extrapolated from a {\Lambda}CDM-model, as can be expected from 2-bin weak lensing to- mography with a Euclid-like survey, in the parameter pairs $(\Omega_\text{m},\sigma_8)$, $(\Omega_\text{m}, w_0)$ and $(w_0, w_\text{a})$. Our numerical results include very accurate extrapolations across a wide range of cosmo- logical parameters in terms of shape, size and orientation of the parameter likelihood, and a decomposition of the change of the likelihood contours into modes, which are straightforward to interpret in a geometrical way. We find that in particular the variation of the dark energy figure of merit is well captured by our formalism.

The extended Baryon Oscillation Spectroscopic Survey: a cosmological forecast

We present a science forecast for the eBOSS survey, part of the SDSS-IV project, which is a spectroscopic survey using multiple tracers of large-scale structure, including luminous red galaxies (LRGs), emission line galaxies (ELGs) and quasars (both as a direct probe of structure and through the Ly-$\alpha$ forest). Focusing on discrete tracers, we forecast the expected accuracy of the baryonic acoustic oscillation (BAO), the redshift-space distortion (RSD) measurements, the $f_{\rm NL}$ parameter quantifying the primordial non-Gaussianity, the dark energy and modified gravity parameters. We also use the line-of-sight clustering in the Ly-$\alpha$ forest to constrain the total neutrino mass. We find that eBOSS LRGs ($0.6<z<1.0$) (combined with the BOSS LRGs at $z>0.6$), ELGs ($0.6<z<1.2$) and Clustering Quasars (CQs) ($0.6<z<2.2$) can achieve a precision of 1%, 2.2% and 1.6% precisions, respectively, for spherically averaged BAO distance measurements. Using the same samples, the constraint on $f\sigma_8$ is expected to be 2.5%, 3.3% and 2.8% respectively. For primordial non-Gaussianity, eBOSS alone can reach an accuracy of $\sigma(f_{\rm NL})\sim10-15$, depending on the external measurement of the galaxy bias and our ability to model large-scale systematic errors. eBOSS can at most improve the dark energy Figure of Merit (FoM) by a factor of $3$ for the Chevallier-Polarski-Linder (CPL) parametrisation, and can well constrain three eigenmodes for the general equation-of-state parameter (Abridged).

Optimizing spectroscopic and photometric galaxy surveys: same-sky benefits for dark energy and modified gravity

The combination of multiple cosmological probes can produce measurements of cosmological parameters much more stringent than those possible with any individual probe. We examine the combination of two highly correlated probes of late-time structure growth: (i) weak gravitational lensing from a survey with photometric redshifts and (ii) galaxy clustering and redshift space distortions from a survey with spectroscopic redshifts. We choose generic survey designs so that our results are applicable to a range of current and future photometric redshift (e.g. KiDS, DES, HSC, Euclid) and spectroscopic redshift (e.g. DESI, 4MOST, Sumire) surveys. Combining the surveys greatly improves their power to measure both dark energy and modified gravity. An independent, non-overlapping combination sees a dark energy figure of merit more than 4 times larger than that produced by either survey alone. The powerful synergies between the surveys are strongest for modified gravity, where their constraints are orthogonal, producing a non-overlapping joint figure of merit nearly 2 orders of magnitude larger than either alone. Our projected angular power spectrum formalism makes it easy to model the cross-correlation observable when the surveys overlap on the sky, producing a joint data vector and full covariance matrix. We calculate a same-sky improvement factor, from the inclusion of these cross-correlations, relative to non-overlapping surveys. We find nearly a factor of 4 for dark energy and more than a factor of 2 for modified gravity. The exact forecast figures of merit and same-sky benefits can be radically affected by a range of forecasts assumption, which we explore methodically in a sensitivity analysis. We show that that our fiducial assumptions produce robust results which give a good average picture of the science return from combining photometric and spectroscopic surveys.

Cosmological performance of SKA H i galaxy surveys

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.