Using the topology of large-scale structure in the WiggleZ Dark Energy Survey as a cosmological standard ruler

MNRAS 437, 2488–2506 (2014) doi:10.1093/mnras/stt2062 Advance Access publication 2013 November 19 Using the topology of large-scale structure in the WiggleZ Dark Energy Survey as a cosmological standard ruler Chris Blake,1‹ J. Berian James2,3 and Gregory B. Poole4 1 Centre for Astrophysics & Supercomputing, Swinburne University of Technology, PO Box 218, Hawthorn, VIC 3122, Australia Department, University of California, Berkeley, CA 94720-3411, USA 3 Dark Cosmology Centre, University of Copenhagen, Juliane Maries Vej 30, DK-2100 Copenhagen Ø, Denmark 4 School of Physics, University of Melbourne, Parkville, VIC 3010, Australia 2 Astronomy ABSTRACT We present new and accurate measurements of the cosmic distance–redshift relation, spanning 0.2 < z < 1, using the topology of large-scale structure as a cosmological standard ruler. Our results derive from an analysis of the Minkowski functionals of the density field traced by the WiggleZ Dark Energy Survey. The Minkowski functionals are a set of statistics which completely describe the topological nature of each isodensity surface within the field, as a function of the density value. Given the shape of the underlying matter power spectrum, measured by fluctuations in the cosmic microwave background radiation, the expected amplitudes of the Minkowski functionals are specified as an excursion set of a Gaussian random field, with minimal non-Gaussian corrections for the smoothing scales ≥10 h−1 Mpc considered in this analysis. The measured amplitudes then determine the cosmic distance DV (z), which we obtain with 3–7 per cent accuracies in six independent redshift slices, with the standard ruler originating in the known curvature of the model power spectrum at the smoothing scale. We introduce a new method for correcting the topological statistics for the sparse-sampling of the density field by the galaxy tracers, and validate our overall methodology using mock catalogues from N-body simulations. Our distance measurements are consistent with standard models which describe the cosmic expansion history, and with previous analyses of baryon acoustic oscillations (BAOs) detected by the WiggleZ Survey, with the topological results yielding a higher distance precision by a factor of 2. However, the full redshift-space power-spectrum shape is required to recover the topological distances, in contrast to the preferred length scale imprinted by BAOs, which is determined by simpler physics. Key words: surveys – galaxies: statistics – distance scale – large-scale structure of Universe. 1 I N T RO D U C T I O N The large-scale structure of the Universe, mapped by large galaxy surveys, is one of the principal tools for testing the physical laws on cosmological scales, in particular the unknown nature of the ‘dark energy’ which appears to dominate today’s Universe. The pattern of the galaxy distribution is sensitive to the matter and energy constituents of the Universe, the cosmic expansion history, and the gravitational physics which amplifies the initial density seeds into today’s web of structure. However, it is also affected by processes for which there currently exists no complete model: the non-linear gravitational evolution of structure beyond perturbation  E-mail: theory, redshift-space distortions due to galaxy peculiar velocities, and galaxy bias, which describes the complex astrophysical manner in which the observed galaxy distribution traces the underlying mass. The major challenge for cosmological analyses of large-scale structure is to extract robust information about the underlying cosmological quantities in the presence of the poorly modelled nonlinear or astrophysical effects. For example, one of the most important methods for obtaining robust cosmological information from large-scale structure surveys is to use the baryon acoustic oscillations (BAOs) encoded in the clustering pattern as a standard ruler to map out the cosmic expansion history (Eisenstein, Hu & Tegmark 1998; Blake & Glazebrook 2003; Seo & Eisenstein 2003). This technique exploits a preferred length scale imprinted in the clustering of galaxies, a late-time signature of the sound waves which propagated in the  C 2013 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society Accepted 2013 October 23. Received 2013 October 18; in original form 2013 August 4 WiggleZ Survey: cosmic topology monotonic, non-linear galaxy bias. Moreover, they are only very weakly distorted by non-linear gravitational evolution and redshiftspace distortions (Matsubara 1994; Matsubara & Yokoyama 1996). In summary, the topology of the density field in comoving space is exactly conserved over time during linear evolution, and nonlinear corrections remain small for scales ≥10 h−1 Mpc. Indeed, we determine that the most important systematic modelling issue in our analysis is not non-linear evolution, but the ‘sparse-sampling’ distortions arising when the smoothing scale of the Gaussian filter is comparable to the mean inter-galaxy separation (James 2012). We also note that, even if the initial density statistics were significantly non-Gaussian, the topological statistics would nonetheless be conserved during linear evolution. The pattern of matter overdensities today reflects the distribution of ‘seeds’ from which they were formed. If this initial distribution constituted a Gaussian random field as assumed in this study, predicted by simple models of inflation, and supported by observations of the CMB, then the Minkowski functionals of the smoothed density field have simple analytic forms. In this case the dependence of the functionals on the isodensity threshold ν is a known function of ν, regardless of the power spectrum of the field, with an unknown overall normalization that only depends on the shape of the underlying power spectrum at the smoothing scale. If the shape of this power spectrum is known, then theory predicts each of the Minkowski functionals, independently of the normalization of the underlying power spectrum. A measurement of the Minkowski functional amplitudes is then sensitive to the cosmic distance–redshift relation in two ways, which allow a ‘standard-ruler’ technique to be applied (Park & Kim 2010; Zunckel, Gott & Lunnan 2011). First, the distance–redshift relation determines the physical length scales mapped by the survey, and hence the amplitudes of the Minkowski functionals in dimensional units. Secondly, the smoothing scale applied when filtering the density field in order to perform these measurements assumes a fiducial distance–redshift relation, and selects a scale in the underlying model power spectrum to which the measurements are sensitive. For a power-law power spectrum these two effects are precisely degenerate, yielding no sensitivity of the Minkowski functional amplitudes to the distance scale. However, if the underlying power spectrum possesses a curvature which is accurately known, for example u (...truncated)