Cluster Power Spectrum Research Articles

The clustering of galaxy clusters in cosmological models with non-Gaussian initial conditions: predictions for future surveys

We predict the biasing and clustering properties of galaxy clusters that are expected to be observed in the catalogues produced by two forthcoming X-ray and Sunyaev-Zel'dovich effect surveys. We study a set of flat cosmological models where the primordial density probability distribution shows deviations from Gaussianity in agreement with current observational bounds form the background radiation. We consider both local and equilateral shapes for the primordial bispectrum in non-Gaussian models. The two catalogues investigated are those produced by the \emph{e}ROSITA wide survey and from a survey based on South Pole Telescope observations. It turns out that both the bias and observed power spectrum of galaxy clusters are severely affected in non-Gaussian models with local shape of the primordial bispectrum, especially at large scales. On the other hand, models with equilateral shape of the primordial bispectrum show only a mild effect at all scales, that is difficult to be detected with clustering observations. Between the two catalogues, the one performing better is the \emph{e}ROSITA one, since it contains only the largest masses, that are more sensitive to primordial non-Gaussianity.

Improved limit on the neutrino mass with CMB and redshift-dependent halo bias-mass relations from SDSS, DEEP2, and Lyman-break galaxies

We use measurements of luminosity-dependent galaxy bias at several different redshifts, SDSS at $z=0.05$, DEEP2 at $z=1$, and LBGs at $z=3.8$, combined with WMAP 5-year cosmic microwave background anisotropy data and SDSS Red Luminous Galaxy survey three-dimensional clustering power spectrum to put constraints on cosmological parameters. Fitting this combined dataset, we show that the luminosity-dependent bias data that probe the relation between halo bias and halo mass and its redshift evolution are very sensitive to sum of the neutrino masses: in particular, we obtain the upper limit of $\ensuremath{\sum}_{}^{}{m}_{\ensuremath{\nu}}<0.28\text{ }\text{ }\mathrm{eV}$ at the 95% confidence level for a $\ensuremath{\Lambda}\mathrm{CDM}+{m}_{\ensuremath{\nu}}$ model, with a ${\ensuremath{\sigma}}_{8}$ equal to ${\ensuremath{\sigma}}_{8}=0.759\ifmmode\pm\else\textpm\fi{}0.025$ ($1\ensuremath{\sigma}$). When we allow the dark energy equation-of-state parameter $w$ to vary, we find $w=\ensuremath{-}1.30\ifmmode\pm\else\textpm\fi{}0.19$ for a general $w\mathrm{CDM}+{m}_{\ensuremath{\nu}}$ model with the 95% confidence level upper limit on the neutrino masses at $\ensuremath{\sum}_{}^{}{m}_{\ensuremath{\nu}}<0.59\text{ }\text{ }\mathrm{eV}$. The constraint on the dark energy equation of state further improves to $w=\ensuremath{-}1.125\ifmmode\pm\else\textpm\fi{}0.092$ when using also ACBAR and supernovae Union data, in addition to above, with a prior on the Hubble constant from the Hubble Space Telescope.

Impact of point source clustering on cosmological parameters with CMB anisotropies

The faint radio point sources that are unresolved in cosmic microwave background (CMB) anisotropy maps are likely to be a biased tracer of the large-scale structure dark matter distribution. While the shot-noise contribution to the angular power spectrum of unresolved radio point sources is included either when optimally constructing the CMB angular power spectrum, as with WMAP data, or when extracting cosmological parameters, we suggest that clustering part of the point source power spectrum should also be included. This is especially necessary at high frequencies above 150 GHz, where the clustering of far-IR sources is expected to dominate the shot-noise level of the angular power spectrum at tens of arcminute angular scales of both radio and sub-mm sources. We make an estimate of source clustering of unresolved radio sources in both WMAP and ACBAR, and marginalize over the amplitude of source clustering in each CMB data set when model fitting for cosmological parameters. For the combination of WMAP 5-year data and ACBAR, we find that the spectral index changes from the value of $0.963\ifmmode\pm\else\textpm\fi{}0.014$ to $0.959\ifmmode\pm\else\textpm\fi{}0.014$ (at 68% C.L.) when the clustering power spectrum of point sources is included in model fits. While we find that the differences are marginal with and without source clustering in current data, it may be necessary to account for source clustering with future data sets such as Planck, especially to properly model fit anisotropies at arcminute angular scales. If clustering is not accounted and point sources are modeled with a shot noise only out to $l\ensuremath{\sim}2000$, the spectral index will be biased by about $1.5\ensuremath{\sigma}$.

Constraining neutrino masses with the integrated-Sachs-Wolfe-galaxy correlation function

Temperature anisotropies in the cosmic microwave background (CMB) are affected by the late integrated Sachs-Wolfe (lISW) effect caused by any time variation of the gravitational potential on linear scales. Dark energy is not the only source of lISW, since massive neutrinos induce a small decay of the potential on small scales during both matter and dark energy domination. In this work, we study the prospect of using the cross correlation between CMB and galaxy-density maps as a tool for constraining the neutrino mass. On the one hand massive neutrinos reduce the cross-correlation spectrum because free-streaming slows down structure formation; on the other hand, they enhance it through their change in the effective linear growth. We show that in the observable range of scales and redshifts, the first effect dominates, but the second one is not negligible. We carry out an error forecast analysis by fitting some mock data inspired by the Planck satellite, Dark Energy Survey (DES) and Large Synoptic Survey Telescope (LSST). The inclusion of the cross correlation data from Planck and LSST increases the sensitivity to the neutrino mass ${m}_{\ensuremath{\nu}}$ by 38% (and to the dark energy equation of state $w$ by 83%) with respect to Planck alone. The correlation between Planck and DES brings a far less significant improvement. This method is not potentially as good for detecting ${m}_{\ensuremath{\nu}}$ as the measurement of galaxy, cluster, or cosmic shear power spectra, but since it is independent and affected by different systematics, it remains potentially interesting if the total neutrino mass is of the order of 0.2 eV; if instead it is close to the lower bound from atmospheric oscillations, ${m}_{\ensuremath{\nu}}\ensuremath{\sim}0.05\text{ }\text{ }\mathrm{eV}$, we do not expect the ISW-galaxy correlation to be ever sensitive to ${m}_{\ensuremath{\nu}}$.

Multiple inflation and the WMAP “glitches”. II. Data analysis and cosmological parameter extraction

Detailed analyses of the WMAP data indicate possible oscillatory features in the primordial curvature perturbation, which moreover appears to be suppressed beyond the present Hubble radius. Such deviations from the usual inflationary expectation of an approximately Harrison-Zeldovich spectrum are expected in the supergravity-based 'multiple inflation' model wherein phase transitions during inflation induce sudden changes in the mass of the inflaton, thus interrupting its slow-roll. In a previous paper we calculated the resulting curvature perturbation and showed how the oscillations arise. Here we perform a Markov Chain Monte Carlo fitting exercise using the 3-year WMAP data to determine how the fitted cosmological parameters vary when such a primordial spectrum is used as an input, rather than the usually assumed power-law spectrum. The 'concordance' LCDM model is still a good fit when there is just a 'step' in the spectrum. However if there is a 'bump' in the spectrum (due e.g. to two phase transitions in rapid succession), the precision CMB data can be well-fitted by a flat Einstein-de Sitter cosmology without dark energy. This however requires the Hubble constant to be h ~ 0.44 which is lower than the locally measured value. To fit the SDSS data on the power spectrum of galaxy clustering requires a ~10% component of hot dark matter, as would naturally be provided by 3 species of neutrinos of mass ~0.5 eV. This CHDM model cannot however fit the position of the baryon acoustic peak in the LRG redshift two-point correlation function. It may be possible to overcome these difficulties in an inhomogeneous Lemaitre-Tolman-Bondi cosmological model with a local void, which can potentially also account for the SN Ia Hubble diagram without invoking cosmic acceleration.

Cosmology with galaxy correlations

In this review, I outline the use of galaxy correlations to constrain cosmological parameters. As with the cosmic microwave background (CMB), the density of dark and baryonic matter imprints important scales on the fluctuations of matter and thus the clustering of galaxies, e.g., the particle horizon at matter-radiation equality and the sound horizon at recombination. Precision measurements of these scales from the baryon acoustic oscillations (BAO) and the large scale shape of the power spectrum of galaxy clustering provide constraints on Ω m h 2. Recent measurements from the Sloan Digital Sky Survey (SDSS) and 2dF Galaxy Redshift Survey (2dFGRS) strongly suggest that Ω m < 0.3. This forms the basic evidence for a flat Universe dominated by a Cosmological Constant (Λ) today (when combined with results from the CMB and supernova surveys). Further evidence for this cosmological model is provided by the late-time Integrated Sachs–Wolfe (ISW) effect, which has now been detected using a variety of tracers of the large scale structure in the Universe out to redshifts of z > 1. The ISW effect also provides an opportunity to discriminate between Λ, dynamical dark energy models and the modification of gravity on large scales.

QSO lensing magnification: a comparison of 2QZ and Sloan Digital Sky Survey results

The lensing magnification of background QSOs by foreground galaxies and clusters is a powerful probe of the mass density of the Universe and the power spectrum of mass clustering. However, the observational results in this area have been controversial. In particular, the results of Myers et al. from the 2dF QSO survey suggested that a strong anticorrelation effect at g < 21 is seen for both galaxies and clusters which implied that galaxies are antibiased (b≈ 0.1) on small scales at a higher level than predicted by the standard cosmology whereas the results of Scranton et al. from the Sloan Digital Sky Survey (SDSS) suggested that the effect was much smaller (b≈ 1) and in line with standard expectations. We first cross-correlate the SDSS photo-z, g < 21, 1.0 < zp < 2.2 QSOs with g < 21 galaxies and clusters in the same areas. The anticorrelation found is somewhat less than the results of Myers et al. based on 2QZ QSOs. But contamination of the QSOs by low-redshift narrow emission-line galaxies and QSOs can cause underestimation of the anticorrelation lensing signal. Correcting for such low-redshift contamination at the levels indicated by our spectroscopic checks suggests that the effect is generally small for QSO cross-correlations with g < 21 galaxies but may be an issue for fainter galaxy samples. Thus when this correction is applied to the photo-z QSO sample of Scranton et al. the anticorrelation increases and the agreement with the 2QZ results of Myers et al. is improved. When we also take into account the fainter r < 21 galaxy limit of Scranton et al. as opposed to g < 21 for Myers et al., the two observational results appear to be in very good agreement. This therefore leaves open the question of why the theoretical interpretations are so different for these analyses. We note that the results of Guimaraes, Myers and Shanks based on mock catalogues from the Hubble Volume simulation strongly suggest that QSO lensing at the levels detected by both Myers et al. and now Scranton et al. is incompatible with a galaxy bias of b≈ 1 in the standard cosmological model. If the QSO lensing results are correct then the consequences for cosmology may be significant.

The clustering of luminous red galaxies in the Sloan Digital Sky Survey imaging data

We present the 3D real space clustering power spectrum of a sample of \~600,000 luminous red galaxies (LRGs) measured by the Sloan Digital Sky Survey (SDSS), using photometric redshifts. This sample of galaxies ranges from redshift z=0.2 to 0.6 over 3,528 deg^2 of the sky, probing a volume of 1.5 (Gpc/h)^3, making it the largest volume ever used for galaxy clustering measurements. We measure the angular clustering power spectrum in eight redshift slices and combine these into a high precision 3D real space power spectrum from k=0.005 (h/Mpc) to k=1 (h/Mpc). We detect power on gigaparsec scales, beyond the turnover in the matter power spectrum, on scales significantly larger than those accessible to current spectroscopic redshift surveys. We also find evidence for baryonic oscillations, both in the power spectrum, as well as in fits to the baryon density, at a 2.5 sigma confidence level. The statistical power of these data to constrain cosmology is ~1.7 times better than previous clustering analyses. Varying the matter density and baryon fraction, we find \Omega_M = 0.30 \pm 0.03, and \Omega_b/\Omega_M = 0.18 \pm 0.04, The detection of baryonic oscillations also allows us to measure the comoving distance to z=0.5; we find a best fit distance of 1.73 \pm 0.12 Gpc, corresponding to a 6.5% error on the distance. These results demonstrate the ability to make precise clustering measurements with photometric surveys (abridged).

Strong constraint on ever-presentΛ

We show that the causal-set approach to creating an ever-present cosmological ``constant'' in the expanding universe is strongly constrained by the isotropy of the microwave background. Fluctuations generated by stochastic lambda generation which are consistent with COBE and WMAP observations are far too small to dominate the expansion dynamics at $zl1000$ and so cannot explain the observed late-time acceleration of the universe. We also discuss other observational constraints from the power spectrum of galaxy clustering and show that the theoretical possibility of ever-present lambda arises only in $3+1$ dimensional space-times.

Astrophysical and cosmological information from large-scale submillimetre surveys of extragalactic sources

We present a quantitative analysis of the astrophysical and cosmological information that can be extracted from the many important wide-area, shallow surveys that will be carried out in the next few years. Our calculations combine the predictions of the physical model by Granato et al. for the formation and evolution of spheroidal galaxies with up-to-date phenomenological models for the evolution of starburst and normal late-type galaxies and of radio sources. We compute the expected number counts and the redshift distributions of these source populations separately and then focus on protospheroidal galaxies. For the latter objects, we predict the counts and redshift distributions of strongly lensed sources at 250, 350, 500 and 850 μm, the angular correlation function of sources detected in the surveys considered, and the angular power spectra due to clustering of sources below the detection limit in Herschel and Planck surveys. An optimal survey for selecting strongly lensed protospheroidal galaxies is described, and it is shown how they can be easily distinguished from the other source populations. We also discuss the detectability of the imprints of the one-halo and two-halo regimes on angular correlation functions and clustering power spectra, as well as the constraints on cosmological parameters that can be obtained from the determinations of these quantities. The novel data relevant to derive the first submillimetre estimates of the local luminosity functions of starburst and late-type galaxies, and the constraints on the properties of rare source populations, such as blazars, are also briefly described.

Angular Diameter Distance Measurement with Galaxy Clustering in the Multipole Space

The shape of the angular power spectrum of galaxies in the linear regime is defined by the horizon size at the matter-radiation equality. When calibrated by cosmic microwave background measurements, the shape of the clustering spectrum can be used as a standard ruler to estimate angular diameter distance as a function of redshift at which galaxy clustering is measured. We apply the proposed cosmological test of Cooray et al. (2001) to a recent set of luminous red galaxy angular clustering spectra from the Sloan Digital Sky Survey between redshifts of 0.2 and 0.6. Using the overall shape of the clustering power spectrum in the linear regime, w e measure comoving angular diameter distances to eight redshift bins by marginalizing over the bias factors that determine the overall amplitude of the clustering spectrum in each of the bins. The Hubble constant consistent with these distance estimates is 68.5^+6.7_-6.1 km s^-1 Mpc-1 at the 68% confidence level. We comment on the expected improvements with future surveys and the potential to measure dark energy parameters with this method.

Cosmological parameters from cosmic microwave background measurements and the final 2dF Galaxy Redshift Survey power spectrum

We derive constraints on cosmological parameters using the power spectrum of galaxy clustering measured from the final 2dF Galaxy Redshift Survey (2dFGRS) and a compilation of measurements of the temperature power spectrum and temperature–polarization cross-correlation of the cosmic microwave background radiation. We analyse a range of parameter sets and priors, allowing for massive neutrinos, curvature, tensors and general dark energy models. In all cases, the combination of data sets tightens the constraints, with the most dramatic improvements found for the density of dark matter and the energy density of dark energy. If we assume a flat universe, we find a matter density parameter of Ωm= 0.237 ± 0.020, a baryon density parameter of Ωb= 0.041 ± 0.002, a Hubble constant of H0= 74 ± 2 kms1 Mpc1, a linear theory matter fluctuation amplitude of σ8= 0.77 ± 0.05 and a scalar spectral index of ns= 0.954 ± 0.023 (all errors show the 68 per cent interval). Our estimate of ns is only marginally consistent with the scale-invariant value ns= 1; this spectrum is formally excluded at the 95 per cent confidence level. However, the detection of a tilt in the spectrum is sensitive to the choice of parameter space. If we allow the equation of state of the dark energy to float, we find wDE=−0.85+0.180.17, consistent with a cosmological constant. We also place new limits on the mass fraction of massive neutrinos: f< 0.105 at the 95 per cent level, corresponding to Σm< 1.2 eV.

Clustering of SZ clusters on a past light-cone: acoustic oscillations and constraints on dark energy

We study the clustering of SZ-selected galaxy clusters on a past light-cone, particularly paying attention to the possibility of constraining properties of dark energy. The prospects of detecting baryonic features in the cluster power spectrum for a wide and shallow survey like PLANCK, and for an SPT-like narrow and deep survey are discussed. It is demonstrated that these future blank sky SZ surveys will have the capability to improve over the recently announced detection of baryonic oscillations based on the SDSS Luminous Red Galaxy (LRG) sample. We carry out parameter estimation using a Fisher matrix approach taking into account the anisotropic nature of the power spectrum due to redshift space and cosmological distortions. The clustering signal which is not too sensitive to systematic uncertainties serves as a valuable piece of information that in combination with other sources of data helps in breaking degeneracies between the cosmological parameters.

The power of general relativity

We study the cosmological and weak-field properties of theories of gravity derived by extending general relativity by means of a Lagrangian proportional to ${R}^{1+\ensuremath{\delta}}$. This scale-free extension reduces to general relativity when $\ensuremath{\delta}\ensuremath{\rightarrow}0$. In order to constrain generalizations of general relativity of this power class, we analyze the behavior of the perfect-fluid Friedmann universes and isolate the physically relevant models of zero curvature. A stable matter-dominated period of evolution requires $\ensuremath{\delta}&gt;0$ or $\ensuremath{\delta}&lt;\ensuremath{-}1/4$. The stable attractors of the evolution are found. By considering the synthesis of light elements (helium-4, deuterium and lithium-7) we obtain the bound $\ensuremath{-}0.017&lt;\ensuremath{\delta}&lt;0.0012$. We evaluate the effect on the power spectrum of clustering via the shift in the epoch of matter-radiation equality. The horizon size at matter-radiation equality will be shifted by $\ensuremath{\sim}1%$ for a value of $\ensuremath{\delta}\ensuremath{\sim}0.0005$. We study the stable extensions of the Schwarzschild solution in these theories and calculate the timelike and null geodesics. No significant bounds arise from null geodesic effects but the perihelion precession observations lead to the strong bound $\ensuremath{\delta}=2.7\ifmmode\pm\else\textpm\fi{}4.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}19}$ assuming that Mercury follows a timelike geodesic. The combination of these observational constraints leads to the overall bound $0\ensuremath{\le}\ensuremath{\delta}&lt;7.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}19}$ on theories of this type.

Universal fitting formulae for baryon oscillation surveys

The next generation of galaxy surveys will attempt to measure the baryon oscillations in the clustering power spectrum with high accuracy. These oscillations encode a preferred scale which may be used as a standard ruler to constrain cosmological parameters and dark energy models. In this paper we present simple analytical fitting formulae for the accuracy with which the preferred scale may be determined in the tangential and radial directions by future spectroscopic and photometric galaxy redshift surveys. We express these accuracies as a function of survey parameters such as the central redshift, volume, galaxy number density and (where applicable) photometric redshift error. These fitting formulae should greatly increase the efficiency of optimizing future surveys, which requires analysis of a potentially vast number of survey configurations and cosmological models. The formulae are calibrated using a grid of Monte Carlo simulations, which are analysed by dividing out the overall shape of the power spectrum before fitting a simple decaying sinusoid to the oscillations. The fitting formulae reproduce the simulation results with a fractional scatter of 7 per cent (10 per cent) in the tangential (radial) directions over a wide range of input parameters. We also indicate how sparse-sampling strategies may enhance the effective survey area if the sampling scale is much smaller than the projected baryon oscillation scale.

Cosmology with photometric redshift surveys

We explore the utility of future photometric redshift imaging surveys for delineating the large-scale structure of the Universe, and assess the resulting constraints on the cosmological model. We perform two complementary types of analysis: (1) We quantify the statistical confidence and the accuracy with which such surveys will be able to detect and measure characteristic features in the clustering power spectrum such as the acoustic oscillations and the turnover, in a 'model-independent' fashion. We show for example that a 10,000 deg^2 imaging survey with depth r = 22.5 and photometric redshift accuracy dz/(1+z) = 0.03 will detect the acoustic oscillations with 99.9% confidence, measuring the associated preferred cosmological scale with 2% precision. Such a survey will also detect the turnover with 95% confidence, determining the corresponding scale with 20% accuracy. (2) By assuming a Lambda-CDM model power spectrum we calculate the confidence with which a non-zero baryon fraction can be deduced from such future galaxy surveys. We quantify 'wiggle detection' by calculating the number of standard deviations by which the baryon fraction is measured, after marginalizing over the shape parameter. This is typically a factor of four more significant (in terms of number of standard deviations) than the 'model-independent' result. We conclude that the precision with which the clustering pattern may be inferred from future photometric redshift surveys will be competitive with contemporaneous spectroscopic redshift surveys, assuming that systematic effects can be controlled. We also note that an analysis of Luminous Red Galaxies in the Sloan Digital Sky Survey may yield a marginal detection of acoustic oscillations in the imaging survey, in addition to that recently reported for the spectroscopic component.

Constraints on the dark energy equation of state from the imprint of baryons on the power spectrum of clusters

Abstract Acoustic oscillations in the baryon–photon fluid leave a signature in the matter power spectrum. The overall shape of the spectrum and the wavelength of the oscillations depend upon the sound horizon scale at recombination. Using the Λ cold dark matter Hubble Volume simulation, we show that the imprint of baryons is visible in the power spectrum of cluster-mass dark matter haloes, in spite of significant differences between the halo power spectrum and the prediction of linear perturbation theory. A measurement of the sound horizon scale can constrain the dark energy equation of state. We show that a survey of clusters at intermediate redshift (z∼ 1), like the Sunyaev–Zel'dovich survey proposed by the South Pole Telescope or a red sequence photometric survey with VISTA or the Dark Energy Survey, could potentially constrain the sound horizon scale to an accuracy of ∼2 per cent, in turn fixing the ratio of the pressure of the dark energy to its density (w) to better than ∼10 per cent. Our approach does not require knowledge of the cluster mass, unlike those that depend upon the abundance of clusters.

Measuring the Cosmic Evolution of Dark Energy with Baryonic Oscillations in the Galaxy Power Spectrum

We use Monte Carlo techniques to simulate the ability of future large high-redshift galaxy surveys to measure the temporal evolution of the dark energy equation-of-state w(z), using the baryonic acoustic oscillations in the clustering power spectrum as a 'standard ruler'. Our analysis only utilizes the oscillatory component of the power spectrum and not its overall shape, which is potentially susceptible to broadband tilts induced by a host of model-dependent systematic effects. Our results are therefore robust and conservative. We show that baryon oscillation constraints can be thought of, to high accuracy, as a direct probe of the distance - redshift and expansion rate - redshift relations where distances are measured in units of the sound horizon. Distance precisions of 1% are obtainable for a fiducial redshift survey covering 10,000 deg^2 and redshift range 0.5 < z < 3.5. If the dark energy is further characterized by w(z) = w_0 + w_1 z (with a cut-off in the evolving term at z = 2), we can then measure the parameters w_0 and w_1 with a precision exceeding current knowledge by a factor of ten: 1 sigma accuracies Delta w_0 ~ 0.03 and Delta w_1 ~ 0.06 are obtainable (assuming a flat universe and that the other cosmological parameters Omega_m} and h could be measured independently to a precision of +/- 0.01 by combinations of future CMB and other experiments). We quantify how this performance degrades with redshift/areal coverage and knowledge of Omega_m and h, and discuss realistic observational prospects for such large-scale spectroscopic redshift surveys, with a variety of diverse techniques. We also quantify how large photometric redshift imaging surveys could be utilized to produce measurements of (w_0,w_1) with the baryonic oscillation method which may be competitive in the short term.

Constraining the evolution of dark energy with a combination of galaxy cluster observables

We show that the abundance and redshift distribution ($dN/dz$) of galaxy clusters in future high-yield cluster surveys, combined with the spatial power spectrum [${P}_{c}(k)$] of the same clusters, can place significant constraints on the evolution of the dark energy equation of state, $w=w(a)$. We evaluate the expected errors on ${w}_{a}=\ensuremath{-}dw/da$ and other cosmological parameters using a Fisher matrix approach, and simultaneously including cluster structure evolution parameters in our analysis. We study three different types of forthcoming surveys that will identify clusters based on their x-ray emission (such as DUO, the Dark Universe Observatory), their Sunyaev-Zel'dovich (SZ) decrement (such as SPT, the South Pole Telescope), or their weak-lensing shear (such as LSST, the Large Synoptic Survey Telescope). We find that combining the cluster abundance and power spectrum significantly enhances constraints from either method alone. We show that the weak-lensing survey can deliver a constraint as tight as $\ensuremath{\Delta}{w}_{a}\ensuremath{\sim}0.1$ on the evolution of the dark energy equation of state, and that the x-ray and SZ surveys each yield $\ensuremath{\Delta}{w}_{a}\ensuremath{\sim}0.4$ separately, or $\ensuremath{\Delta}{w}_{a}\ensuremath{\sim}0.2$ when these two surveys are combined. For the x-ray and SZ surveys, constraints on dark energy parameters are improved by a factor of 2 by combining the cluster data with cosmic microwave background anisotropy measurements by Planck, but degrade by a factor of 2 if the survey is required to solve simultaneously for cosmological and cluster structure evolution parameters. The constraint on ${w}_{a}$ from the weak-lensing survey is improved by $\ensuremath{\sim}25%$ with the addition of Planck data.

Cosmology with the SKA

We argue that the Square Kilometer Array has the potential to make both redshift (HI) surveys and radio continuum surveys that will revolutionize cosmological studies, provided that it has sufficient instantaneous field-of-view that these surveys can cover a hemisphere ( f sky ∼ 0.5) in a timescale ∼1 yr. Adopting this assumption, we focus on two key experiments which will yield fundamental new measurements in cosmology, characterizing the properties of the mysterious dark energy which dominates the dynamics of today’s Universe. Experiment I will map out ∼10 9( f sky/0.5) HI galaxies to redshift z ≈ 1.5, providing the premier measurement of the clustering power spectrum of galaxies: accurately delineating the acoustic oscillations and the ‘turnover’. Experiment II will quantify the cosmic shear distortion of ∼10 10( f sky/0.5) radio continuum sources, determining a precise power spectrum of the dark matter, and its growth as a function of cosmic epoch. We contrast the performance of the SKA in precision cosmology with that of other facilities which will, probably or possibly, be available on a similar timescale. We conclude that data from the SKA will yield transformational science as the direct result of four key features: (i) the immense cosmic volumes probed, exceeding future optical redshift surveys by more than an order of magnitude; (ii) well-controlled systematic effects such as the narrow ‘ k-space window function’ for Experiment I and the accurately known ‘point-spread function’ (synthesized beam) for Experiment II; (iii) the ability to measure with high precision large-scale modes in the clustering power spectra, for which nuisance effects such as non-linear structure growth, peculiar velocities and ‘galaxy bias’ are minimised; and (iv) different degeneracies between key parameters to those which are inherent in the Cosmic Microwave Background.