Forecasting the dark energy measurement with baryon acoustic oscillations: prospects for the LAMOST surveys

The Large Area Multi-Object Fibre Spectroscopic Telescope (LAMOST) is a dedicated spectroscopic survey telescope being built in China, with an effective aperture of 4 m and equipped with 4000 fibres. Using the LAMOST telescope, one could make redshift survey of the large-scale structure (LSS). The baryon acoustic oscillation features in the LSS power spectrum provide standard rulers for measuring dark energy and other cosmological parameters. In this paper, we investigate the measurement precision achievable for a few possible surveys: (1) a magnitude-limited survey of all galaxies, (2) a survey of colour-selected luminous red galaxies (LRG) and (3) a magnitude-limited, high-density survey of   z < 2  quasars. For each survey, we use the halo model to estimate the bias of the sample, and calculate the effective volume. We then use the Fisher matrix method to forecast the error on the dark energy equation of state and other cosmological parameters for different survey parameters. In a few cases, we also use the Markov Chain Monte Carlo method to make the same forecast as a comparison. The fibre time required for each of these surveys is also estimated. These results would be useful in designing the surveys for LAMOST.     

Constraints on perfect fluid and scalar field dark energy models from future redshift surveys

We discuss the constraints that future photometric and spectroscopic redshift surveys can put on dark energy through the baryon oscillations of the power spectrum. We model the dark energy either with a perfect fluid or a scalar field and take into account the information contained in the linear growth function. We show that the growth function helps to break the degeneracy in the dark energy parameters and reduce the errors on   w ₀, w ₁  roughly by 30 per cent, making more appealing multicolour surveys based on photometric redshifts. We find that a 200-deg² spectroscopic survey reaching   z ≈ 3  can constrain   w ₀, w ₁  to within  Δ w ₀= 0.21, Δ w ₁= 0.26  , to  Δ w ₀= 0.39, Δ w ₁= 0.54  using photometric redshifts with an absolute uncertainty of 0.02, and to  Δ w ₀= 0.43, Δ w ₁= 0.66  with an uncertainty of 0.04. In the scalar field case, we show that the slope n of the inverse power-law potential for dark energy can be constrained to  Δ n = 0.26  (spectroscopic redshifts) or  Δ n = 0.40  (photometric redshifts), i.e. better than with future ground-based supernovae surveys or cosmic microwave background data.     

The 2dF Galaxy Redshift Survey: the power spectrum and the matter content of the Universe

The 2dF Galaxy Redshift Survey has now measured in excess of 160 000 galaxy redshifts. This paper presents the power spectrum of the galaxy distribution, calculated using a direct Fourier transform based technique. We argue that, within the k -space region     , the shape of this spectrum should be close to that of the linear density perturbations convolved with the window function of the survey. This window function and its convolving effect on the power spectrum estimate are analysed in detail. By convolving model spectra, we are able to fit the power-spectrum data and provide a measure of the matter content of the Universe. Our results show that models containing baryon oscillations are mildly preferred over featureless power spectra. Analysis of the data yields 68 per cent confidence limits on the total matter density times the Hubble parameter     , and the baryon fraction     , assuming scale-invariant primordial fluctuations.     

Markov chain reconstruction of the 2dF Galaxy Redshift Survey real-space power spectrum

The real-space power spectrum of L _* galaxies measured from the 2dF Galaxy Redshift Survey (2dFGRS) is presented. Markov chain Monte Carlo (MCMC) sampling was used to fit radial and angular modes resulting from a spherical harmonics decomposition of the 2dFGRS overdensity field (described in a previous paper) with 16 real-space power spectrum values and linear redshift-space distortion parameter  β( L _*, 0)  . The recovered marginalized band powers are compared to previous estimates of galaxy power spectra. Additionally, we provide a simple model for the 17-dimensional likelihood hypersurface in order to allow the likelihood to be quickly estimated given a set of model band powers and β( L _*, 0). The likelihood surface is not well approximated by a multivariate Gaussian distribution with model-independent covariances. Instead, a model is presented in which the distribution of each band power has a Gaussian distribution in a combination of the band power and its logarithm. The relative contribution of each component was determined by fitting the MCMC output. Using these distributions, we demonstrate how the likelihood of a given cosmological model can be quickly and accurately estimated, and we use a simple set of models to compare estimated likelihoods with likelihoods calculated using the full spherical harmonics procedure. All of the data are made publicly available (from http://www.roe.ac.uk/~wjp/ ), enabling the spherical harmonics decomposition of the 2dFGRS of Percival et al. to be easily used as a cosmological constraint.     

The galaxy power spectrum: precision cosmology from large-scale structure?

Published galaxy power spectra from the two-degree field galaxy redshift survey (2dFGRS) and Sloan Digital Sky Survey (SDSS) are not in good agreement. We revisit this issue by analysing both the 2dFGRS and SDSS Data Release 5 (DR5) catalogues using essentially identical techniques. We confirm that the 2dFGRS exhibits relatively more large-scale power than the SDSS, or, equivalently, SDSS has more small-scale power. We demonstrate that this difference is due to the r -band selected SDSS catalogue being dominated by more strongly clustered red galaxies, which have a stronger scale-dependent bias. The power spectra of galaxies of the same rest-frame colours from the two surveys match well. If not accounted for, the difference between the SDSS and 2dFGRS power spectra causes a bias in the obtained constraints on cosmological parameters which is larger than the uncertainty with which they are determined. We also found that the correction developed by Cole et al. to model the distortion in the shape of the power spectrum due to non-linear evolution and scale-dependent bias is not able to reconcile the constraints obtained from the 2dFGRS and SDSS power spectra. Intriguingly, the model is able to describe the differences between the 2dFGRS and the much more strongly clustered Luminous Red Galaxy (LRG) sample, which exhibits greater non-linearities. This shows that more work is needed to understand the relation between the galaxy power spectrum and the linear perturbation theory prediction for the power spectrum of matter fluctuations. It is therefore important to accurately model these effects to get precise estimates of cosmological parameters from these power spectra and from future galaxy surveys like Pan-STARRS, or the Dark Energy Survey, which will use selection criteria similar to the one of SDSS.     

Methods for rapidly processing angular masks of next-generation galaxy surveys

As galaxy surveys become larger and more complex, keeping track of the completeness, magnitude limit and other survey parameters as a function of direction on the sky becomes an increasingly challenging computational task. For example, typical angular masks of the Sloan Digital Sky Survey contain about   N = 300 000  distinct spherical polygons. Managing masks with such large numbers of polygons becomes intractably slow, particularly for tasks that run in time     with a naive algorithm, such as finding which polygons overlap each other. Here we present a 'divide-and-conquer' solution to this challenge: we first split the angular mask into pre-defined regions called 'pixels', such that each polygon is in only one pixel, and then perform further computations, such as checking for overlap, on the polygons within each pixel separately. This reduces     tasks to     , and also reduces the important task of determining in which polygon(s) a point on the sky lies from     to     , resulting in significant computational speedup. Additionally, we present a method to efficiently convert any angular mask to and from the popular healpix format. This method can be generically applied to convert to and from any desired spherical pixelization. We have implemented these techniques in a new version of the mangle software package, which is freely available at http://space.mit.edu/home/tegmark/mangle/ , along with complete documentation and example applications. These new methods should prove quite useful to the astronomical community, and since mangle is a generic tool for managing angular masks on a sphere, it has the potential to benefit terrestrial mapmaking applications as well.