On the interpretation of clustering from the angular APM Galaxy Survey

We analyze the uncertainties in the amplitudes of the spatial correlation functions estimated from angular correlations in a sample from the APM Galaxy Survey, with $b_J=17-20$. We model the uncertainties in the selection function and in the evolution of clustering. In particular we estimate $\sigma_8^{APM}$, the rms galaxy number fluctuations in spheres of radius at 8 \Mpc, from the measured angular variance in the APM. The uncertainty in $\sigma_8^{APM}$ has three main contributions: 8\% from sampling and selection function uncertainties, 7\% from the uncertainty in the evolution of clustering and 3\% from the uncertainty in the value of $\Omega_0$. Including all these contributions, we find $\sigma_8^{APM}$ is in the range $0.78-1.08$. If the galaxy clustering in the APM evolves as expected from gravitational clustering of matter fluctuations, then $\sigma_8^{APM}=0.95 \pm 0.07$ ($1.00 \pm 0.08$) for $\Omega_0 \simeq 1$ ($\Omega_0 \simeq 0$), close to the values for nearby optical samples. On the other hand, if we assume that clustering evolution is fixed in comoving coordinates $\sigma_8^{APM}=0.83 \pm 0.05$ ($0.87 \pm 0.06$), closer to the results for nearby IRAS samples. The final uncertainty in the range of values for the hierarchical amplitudes S_J\equiv \xibar_J/\xibar_2^{J-1} is typically twice the estimated sampling errors, with the highest values for the case of less clustering evolution. We compare our estimates with other results and discuss the implications for models of structure formation.Comment: 11 pages plus 12 figures, uuencoded compress postscrip

Modeling the angular correlation function and its full covariance in Photometric Galaxy Surveys

Near future cosmology will see the advent of wide area photometric galaxy surveys, like the Dark Energy Survey (DES), that extent to high redshifts (z ~ 1 - 2) but with poor radial distance resolution. In such cases splitting the data into redshift bins and using the angular correlation function $w(\theta)$, or the $C_{\ell}$ power spectrum, will become the standard approach to extract cosmological information or to study the nature of dark energy through the Baryon Acoustic Oscillations (BAO) probe. In this work we present a detailed model for $w(\theta)$ at large scales as a function of redshift and bin width, including all relevant effects, namely nonlinear gravitational clustering, bias, redshift space distortions and photo-z uncertainties. We also present a model for the full covariance matrix characterizing the angular correlation measurements, that takes into account the same effects as for $w(\theta)$ and also the possibility of a shot-noise component and partial sky coverage. Provided with a large volume N-body simulation from the MICE collaboration we built several ensembles of mock redshift bins with a sky coverage and depth typical of forthcoming photometric surveys. The model for the angular correlation and the one for the covariance matrix agree remarkably well with the mock measurements in all configurations. The prospects for a full shape analysis of $w(\theta)$ at BAO scales in forthcoming photometric surveys such as DES are thus very encouraging.Comment: 23 pages, 21 figures Revised version accepted by MNRAS. Description of mocks re-structured. Mocks including redshift distortions and Photo-z publicly available at http://www.ice.cat/mic

What determines large scale galaxy clustering: halo mass or local density?

Using dark matter simulations we show how halo bias is determined by local density and not by halo mass. This is not totally surprising, as according to the peak-background split model, local density is the property that constraints bias at large scales. Massive haloes have a high clustering because they reside in high density regions. Small haloes can be found in a wide range of environments which determine their clustering amplitudes differently. This contradicts the assumption of standard Halo Occupation Distribution (HOD) models that the bias and occupation of haloes is determined solely by their mass. We show that the bias of central galaxies from semi-analytic models of galaxy formation as a function of luminosity and colour is not correctly predicted by the standard HOD model. Using local density instead of halo mass the HOD model correctly predicts galaxy bias. These results indicate the need to include information about local density and not only mass in order to correctly apply HOD analysis in these galaxy samples. This new model can be readily applied to observations and has the advantage that the galaxy density can be directly observed, in contrast with the dark matter halo mass.Comment: 11 pages, 9 figure

The Real and Redshift Space Density Distribution Function for Large-Scale Structure in the Spherical Collapse Approximation

We use the spherical collapse (SC) approximation to derive expressions for the smoothed redshift-space probability distribution function (PDF), as well as the $p$-order hierarchical amplitudes $S_p$, in both real and redshift space. We compare our results with numerical simulations, focusing on the $\Omega=1$ standard CDM model, where redshift distortions are strongest. We find good agreement between the SC predictions and the numerical PDF in real space even for \sigma_L \simgt 1, where $\sigma_L$ is the linearly-evolved rms fluctuation on the smoothing scale. In redshift space, reasonable agreement is possible only for \sigma_L \simlt 0.4. Numerical simulations also yield a simple empirical relation between the real-space PDF and redshift-space PDF: we find that for \sigma \simlt 1, the redshift space PDF, P[\delta_z], is, to a good approximation, a simple rescaling of the real space PDF, P[\delta], i.e., P[\delta/\sigma] d[\delta/\sigma] = P[\delta_z/\sigma_z] d[\delta_z/\sigma_z], where $\sigma$ and \sigma_z are the real-space and redshift-space rms fluctuations, respectively. This result applies well beyond the validity of linear perturbation theory, and it is a good fit for both the standard CDM model and the Lambda-CDM model. It breaks down for SCDM at $\sigma \approx 1$, but provides a good fit to the \Lambda-CDM models for $\sigma$ as large as 0.8.Comment: 9 pages, latex, 12 figures added (26 total), minor changes to conclusions, to appear in MNRA

Inverting the Angular Correlation Function

The two point angular correlation function is an excellent measure of structure in the universe. To extract from it the three dimensional power spectrum, one must invert Limber's Equation. Here we perform this inversion using a Bayesian prior constraining the smoothness of the power spectrum. Among other virtues, this technique allows for the possibility that the estimates of the angular correlation function are correlated from bin to bin. The output of this technique are estimators for the binned power spectrum and a full covariance matrix. Angular correlations mix small and large scales but after the inversion, small scale data can be trivially eliminated, thereby allowing for realistic constraints on theories of large scale structure. We analyze the APM catalogue as an example, comparing our results with previous results. As a byproduct of these tests, we find -- in rough agreement with previous work -- that APM places stringent constraints on Cold Dark Matter inspired models, with the shape parameter constrained to be $0.25\pm 0.04$ (using data with wavenumber $k \le 0.1 h{\rm Mpc}^{-1}$). This range of allowed values use the full power spectrum covariance matrix, but assumes negligible covariance in the off-diagonal angular correlation error matrix, which is estimated with a large angular resolution of 0.5degrees (in the range 0.5 and 20 degrees).Comment: 7 pages, 11 figures, replace to match accepted version, MNRAS in pres

A measurement of the scale of homogeneity in the Early Universe

We present the first measurement of the homogeneity index, $\mathcal{H}$, a fractal or Hausdorff dimension of the early Universe from the Planck CMB temperature variations $\delta T$ in the sky. This characterization of the isotropy scale is model-free and purely geometrical, independent of the amplitude of $\delta T$. We find evidence of homogeneity ($\mathcal{H}=0$) for scales larger than $\theta_{\mathcal{H}} = 65.9 \pm 9.2 \deg$ on the CMB sky. This finding is at odds with the $\Lambda$CDM prediction, which assumes a scale invariant infinite universe. Such anomaly is consistent with the well known low quadrupule amplitude in the angular $\delta T$ spectrum, but quantified in a direct and model independent way. We estimate the significance of our finding for $\mathcal{H}=0$ using a principal component analysis from the sampling variations of the observed sky. This analysis is validated with an independent theoretical prediction of the covariance matrix based purely on data. Assuming translation invariance (and flat geometry $k=0$) we can convert the isotropy scale $\theta_\mathcal{H}$ into a (comoving) homogeneity scale of $\chi_\mathcal{H} \simeq 3.3 c/H_0$, which is very close to the trapped surface generated by the observed cosmological constant $\Lambda$.Comment: 20 pages, 9 figure

Nuevos retos para la cosmología observacional

"Como muestra, presentaré uno de los más ambiciosos proyectos observacionales que se están preparando para los próximos años: El Cartografiado de la «energía oscura» (The Dark Energy Survey). La preparación y objetivos de este proyecto ilustran el estado actual de las observaciones en 5 de sus aspectos claves: la radiación cósmica de fondo, los c úmulos de galaxias, las lentes gravitacionales, la estructura a gran escala y la medición de supernovas lejanas."Factoria FM