L-PICOLA: A parallel code for fast dark matter simulation

Robust measurements based on current large-scale structure surveys require precise knowledge of statistical and systematic errors. This can be obtained from large numbers of realistic mock galaxy catalogues that mimic the observed distribution of galaxies within the survey volume. To this end we present a fast, distributed-memory, planar-parallel code, L-PICOLA, which can be used to generate and evolve a set of initial conditions into a dark matter field much faster than a full non-linear N-Body simulation. Additionally, L-PICOLA has the ability to include primordial non-Gaussianity in the simulation and simulate the past lightcone at run-time, with optional replication of the simulation volume. Through comparisons to fully non-linear N-Body simulations we find that our code can reproduce the $z=0$ power spectrum and reduced bispectrum of dark matter to within 2% and 5% respectively on all scales of interest to measurements of Baryon Acoustic Oscillations and Redshift Space Distortions, but 3 orders of magnitude faster. The accuracy, speed and scalability of this code, alongside the additional features we have implemented, make it extremely useful for both current and next generation large-scale structure surveys. L-PICOLA is publicly available at https://cullanhowlett.github.io/l-picolaComment: 22 Pages, 20 Figures. Accepted for publication in Astronomy and Computin

Maximal compression of the redshift space galaxy power spectrum and bispectrum

We explore two methods of compressing the redshift space galaxy power spectrum and bispectrum with respect to a chosen set of cosmological parameters. Both methods involve reducing the dimension of the original data-vector ( e.g. 1000 elements ) to the number of cosmological parameters considered ( e.g. seven ) using the Karhunen-Lo\`eve algorithm. In the first case, we run MCMC sampling on the compressed data-vector in order to recover the one-dimensional (1D) and two-dimensional (2D) posterior distributions. The second option, approximately 2000 times faster, works by orthogonalising the parameter space through diagonalisation of the Fisher information matrix before the compression, obtaining the posterior distributions without the need of MCMC sampling. Using these methods for future spectroscopic redshift surveys like DESI, EUCLID and PFS would drastically reduce the number of simulations needed to compute accurate covariance matrices with minimal loss of constraining power. We consider a redshift bin of a DESI-like experiment. Using the power spectrum combined with the bispectrum as a data-vector, both compression methods on average recover the 68% credible regions to within 0.7% and 2% of those resulting from standard MCMC sampling respectively. These confidence intervals are also smaller than the ones obtained using only the power spectrum by (81%, 80%, 82%) respectively for the bias parameter b_1, the growth rate f and the scalar amplitude parameter A_s.Comment: 27 pages, 8 figures, 1 table, Accepted 2018 January 28. Received 2018 January 25; in original form 2017 September 11. Added clarifications in the text on the bias modelling and compression limits following referee's comments. Removed tetraspectrum term from the pk-bk cross covariance + correction in the appendi

The Clustering of the SDSS DR7 Main Galaxy Sample I: A 4 per cent Distance Measure at z=0.15

We create a sample of spectroscopically identified galaxies with $z < 0.2$ from the Sloan Digital Sky Survey (SDSS) Data Release 7, covering 6813 deg$^2$. Galaxies are chosen to sample the highest mass haloes, with an effective bias of 1.5, allowing us to construct 1000 mock galaxy catalogs (described in Paper II), which we use to estimate statistical errors and test our methods. We use an estimate of the gravitational potential to "reconstruct" the linear density fluctuations, enhancing the Baryon Acoustic Oscillation (BAO) signal in the measured correlation function and power spectrum. Fitting to these measurements, we determine $D_{V}(z_{\rm eff}=0.15) = (664\pm25)(r_d/r_{d,{\rm fid}})$ Mpc; this is a better than 4 per cent distance measurement. This "fills the gap" in BAO distance ladder between previously measured local and higher redshift measurements, and affords significant improvement in constraining the properties of dark energy. Combining our measurement with other BAO measurements from BOSS and 6dFGS galaxy samples provides a 15 per cent improvement in the determination of the equation of state of dark energy and the value of the Hubble parameter at $z=0$ ($H_0$). Our measurement is fully consistent with the Planck results and the $\Lambda$CDM concordance cosmology, but increases the tension between Planck$+$BAO $H_0$ determinations and direct $H_0$ measurements.Comment: Accepted by MNRAS, distance likelihood is available in source file

Large-scale Bias and Efficient Generation of Initial Conditions for Non-Local Primordial Non-Gaussianity

We study the scale-dependence of halo bias in generic (non-local) primordial non-Gaussian (PNG) initial conditions of the type motivated by inflation, parametrized by an arbitrary quadratic kernel. We first show how to generate non-local PNG initial conditions with minimal overhead compared to local PNG models for a general class of primordial bispectra that can be written as linear combinations of separable templates. We run cosmological simulations for the local, and non-local equilateral and orthogonal models and present results on the scale-dependence of halo bias. We also derive a general formula for the Fourier-space bias using the peak-background split (PBS) in the context of the excursion set approach to halos and discuss the difference and similarities with the known corresponding result from local bias models. Our PBS bias formula generalizes previous results in the literature to include non-Markovian effects and non-universality of the mass function and are in better agreement with measurements in numerical simulations than previous results for a variety of halo masses, redshifts and halo definitions. We also derive for the first time quadratic bias results for arbitrary non-local PNG, and show that non-linear bias loops give small corrections at large-scales. The resulting well-behaved perturbation theory paves the way to constrain non-local PNG from measurements of the power spectrum and bispectrum in galaxy redshift surveys.Comment: 43 pages, 10 figures. v2: references added. 2LPT parallel code for generating non-local PNG initial conditions available at http://cosmo.nyu.edu/roman/2LP

GEOMAX: beyond linear compression for 3pt galaxy clustering statistics

We present the GEOMAX algorithm and its Python implementation for a two-step compression of bispectrum measurements. The first step groups bispectra by the geometric properties of their arguments; the second step then maximises the Fisher information with respect to a chosen set of model parameters in each group. The algorithm only requires the derivatives of the data vector with respect to the parameters and a small number of mock data, producing an effective, non-linear compression. By applying GEOMAX to bispectrum monopole measurements from BOSS DR12 CMASS redshift-space galaxy clustering data, we reduce the $68\%$ credible intervals for the inferred parameters $\left(b_1,b_2,f,\sigma_8\right)$ by $\left(50.4\%,56.1\%,33.2\%,38.3\%\right)$ with respect to standard MCMC on the full data vector. We run the analysis and comparison between compression methods over one hundred galaxy mocks to test the statistical significance of the improvements. On average GEOMAX performs $\sim15\%$ better than geometrical or maximal linear compression alone and is consistent with being lossless. Given its flexibility, the GEOMAX approach has the potential to optimally exploit three-point statistics of various cosmological probes like weak lensing or line-intensity maps from current and future cosmological data-sets such as DESI, Euclid, PFS and SKA.Comment: 17 pages, 9 figures, accepted version by MNRA

The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: mock galaxy catalogues for the low-redshift sample

We present one thousand mock galaxy catalogues for the analysis of the Low Redshift Sample (LOWZ, effective redshift z ~ 10.32) of the Baryon Oscillation Spectroscopic Survey Data Releases 10 and 11. These mocks have been created following the PTHalos method of Manera13 et al. (2013) revised to include new developments. The main improvement is the introduction of a redshift dependence in the Halo Occupation Distribution in order to account for the change of the galaxy number density with redshift. These mock catalogues are used in the analyses of the LOWZ galaxy clustering by the BOSS collaboration.Comment: 10 pages, 8 figure

COLA with scale-dependent growth: applications to screened modified gravity models

We present a general parallelized and easy-to-use code to perform numerical simulations of structure formation using the COLA (COmoving Lagrangian Acceleration) method for cosmological models that exhibit scale-dependent growth at the level of first and second order Lagrangian perturbation theory. For modified gravity theories we also include screening using a fast approximate method that covers all the main examples of screening mechanisms in the literature. We test the code by comparing it to full simulations of two popular modified gravity models, namely f(R) gravity and nDGP, and find good agreement in the modified gravity boost-factors relative to ΛCDM even when using a fairly small number of COLA time steps