Beyond the plane-parallel approximation for redshift surveys

Redshift space distortions privilege the location of the observer in cosmological redshift surveys, breaking the translational symmetry of the underlying theory. This violation of statistical homogeneity has consequences for the modeling of clustering observables, leading to what are frequently called `wide angle effects'. We study these effects analytically, computing their signature in the clustering of the multipoles in configuration and Fourier space. We take into account both physical wide angle contributions as well as the terms generated by the galaxy selection function. Similar considerations also affect the way power spectrum estimators are constructed. We quantify, in an analytical way the biases which enter and clarify the relation between what we measure and the underlying theoretical modeling. The presence of an angular window function is also discussed. Motivated by this analysis we present new estimators for the three dimensional Cartesian power spectrum and bispectrum multipoles written in terms of spherical Fourier-Bessel coefficients. We show how the latter have several interesting properties, allowing in particular a clear separation between angular and radial modes.Comment: 16 pages, 5 figure

The Zeldovich approximation and wide-angle redshift-space distortions

The contribution of line-of-sight peculiar velocities to the observed redshift of objects breaks the translational symmetry of the underlying theory, modifying the predicted 2-point functions. These `wide angle effects' have mostly been studied using linear perturbation theory in the context of the multipoles of the correlation function and power spectrum. In this work we present the first calculation of wide angle terms in the Zeldovich approximation, which is known to be more accurate than linear theory on scales probed by the next generation of galaxy surveys. We present the exact result for dark matter and perturbatively biased tracers as well as the small angle expansion of the configuration- and Fourier-space two-point functions and the connection to the multi-frequency angular power spectrum. We compare different definitions of the line-of-sight direction and discuss how to translate between them. We show that wide angle terms can reach tens of percent of the total signal in a measurement at low redshift in some approximations, and that a generic feature of wide angle effects is to slightly shift the Baryon Acoustic Oscillation scale.Comment: 13 pages, 7 figures, matches published versio

On the spatial distribution of neutral hydrogen in the Universe: bias and shot-noise of the HI Power Spectrum

The spatial distribution of neutral hydrogen (HI) in the Universe contains a wealth of cosmological information. The 21 cm emission line can be used to map the HI up to very high redshift and therefore reveal us something about the evolution of the large scale structures in the Universe. However little is known about the abundance and clustering properties of the HI over cosmic time. Motivated by this, we build an analytic framework where the relevant parameters that govern how the HI is distributed among dark matter halos can be fixed using observations. At the same time we provide tools to study the column density distribution function of the HI absorbers together with their clustering properties. Our formalism is the first one able to account for all observations at a single redshift, $z = 2.3$. The linear bias of the HI and the mean number density of HI sources, two main ingredients in the calculation of the signal-to-noise ratio of a cosmological survey, are then discussed in detail, also extrapolating the results to low and high redshift. We find that HI bias is relatively higher than the value reported in similar studies, but the shot noise level is always sub dominant, making the HI Power Spectrum always a high signal-to-noise measurements up to $z\simeq5$ in the limit of no instrumental noise and foreground contamination.Comment: 10 pages, 9 figure

Stochastic bias in multi-dimensional excursion set approaches

We describe a simple fully analytic model of the excursion set approach associated with two Gaussian random walks: the first walk represents the initial overdensity around a protohalo, and the second is a crude way of allowing for other factors which might influence halo formation. This model is richer than that based on a single walk, because it yields a distribution of heights at first crossing. We provide explicit expressions for the unconditional first crossing distribution which is usually used to model the halo mass function, the progenitor distributions, and the conditional distributions from which correlations with environment are usually estimated. These latter exhibit perhaps the simplest form of what is often called nonlocal bias, and which we prefer to call stochastic bias, since the new bias effects arise from `hidden-variables' other than density, but these may still be defined locally. We provide explicit expressions for these new bias factors. We also provide formulae for the distribution of heights at first crossing in the unconditional and conditional cases. In contrast to the first crossing distribution, these are exact, even for moving barriers, and for walks with correlated steps. The conditional distributions yield predictions for the distribution of halo concentrations at fixed mass and formation redshift. They also exhibit assembly bias like effects, even when the steps in the walks themselves are uncorrelated. Finally, we show how the predictions are modified if we add the requirement that halos form around peaks: these depend on whether the peaks constraint is applied to a combination of the overdensity and the other variable, or to the overdensity alone. Our results demonstrate the power of requiring models to reproduce not just halo counts but the distribution of overdensities at fixed protohalo mass as well.Comment: 9 pages, 5 figures, submitted to MNRA

Measuring dark matter-neutrino relative velocity on cosmological scales

We present a new method to measure neutrino masses using the dark matter-neutrino relative velocity. The relative motion between dark matter and neutrinos results in a parity-odd bispectrum which can be measured from cross-correlation of different cosmic fields. This new method is not affected by most systematics which are parity even and not limited by the knowledge of optical depth to the cosmic microwave background. We estimate the detectability of the relative velocity effect and find that the minimal sum of neutrino masses could be detected at high significance with upcoming surveys.Comment: 6 pages, 2 figures, 1 table, published versio

Local Primordial Non-Gaussianities and Super-Sample Variance

Fluctuations with wavelengths larger than the volume of a galaxy survey affect the measurement of the galaxy power spectrum within the survey itself. In the presence of local Primordial Non- Gaussianities (PNG), in addition to the super-sample matter density and tidal fluctuations, the large-scale gravitational potential also induces a modulation of the observed power spectrum. In this work we investigate this modulation by computing for the first time the response of the redshift-space galaxy power spectrum to the presence of a long wavelength gravitational potential, fully accounting for the stochastic contributions. For biased tracers new response functions arise due to couplings between the small-scale fluctuations in the density, velocity and gravitational fields, the latter through scale dependent bias operators, and the large-scale gravitational potential. We study the impact of the super-sample modes on the measurement of the amplitude of the primordial bispectrum of the local-shape, $f_{\rm NL}^{\rm loc}$, accounting for modulations of both the signal and the covariance of the galaxy power spectrum by the long modes. Considering DESI-like survey specifications, we show that in most cases super-sample modes cause little or no degradation of the constraints, and could actually reduce the errorbars on $f_{\rm NL}^{\rm loc}$ by (10 - 30)\%, if external information on the bias parameters is available.Comment: 15 pages, 4 figure

Massive neutrinos and the Large Scale Structure of the Universe

This thesis deals with the phenomenology of large scale structures in cosmolo- gies with massive neutrinos. Cosmology has the power to constraint the value of neutrino masses down to very high accuracy, but to achieve this target a careful description of the effect neutrinos could induce on cosmological observables is needed. With the help on numerical N-body simulations that include a massive neutrino component we provide results for clustering beyond the linear level of both cold dark matter and neutrinos, comparing the measurements with analytical predictions derived in higher order perturbative approaches and with existing fitting formulae. We also discuss the abundance in mass of tracers of the cold dark matter like halos, identifying the right variable, the variance of the cold dark matter field, that describe the counts measured in the simulations. We highlight the systematics effects introduced by a wrong parametrization of the halo mass function, that can bias the inferred cosmological parameters. We present results for the spatial distribution of halos, focusing on the relation with the underlying cold dark matter distribution. To this end we computed the power spectrum of halos in the simulations, finding that the same variable describing the halo mass function provides a consistent picture of spatial clustering of the halos. The analysis is repeated in redshift space and with higher order correlation functions, the bispectrum in our case, leading to the same conclusions and reinforcing our results

The Gaussian streaming model and Lagrangian effective field theory

We update the ingredients of the Gaussian streaming model (GSM) for the redshift-space clustering of biased tracers using the techniques of Lagrangian perturbation theory, effective field theory (EFT) and a generalized Lagrangian bias expansion. After relating the GSM to the cumulant expansion, we present new results for the real-space correlation function, mean pairwise velocity and pairwise velocity dispersion including counter terms from EFT and bias terms through third order in the linear density, its leading derivatives and its shear up to second order. We discuss the connection to the Gaussian peaks formalism. We compare the ingredients of the GSM to a suite of large N-body simulations, and show the performance of the theory on the low order multipoles of the redshift-space correlation function and power spectrum. We highlight the importance of a general biasing scheme, which we find to be as important as higher-order corrections due to non-linear evolution for the halos we consider on the scales of interest to us.Comment: 28 pages, 5 figures. Revised to match version accepted by journa

Halo bias in Lagrangian Space: Estimators and theoretical predictions

We present several methods to accurately estimate Lagrangian bias parameters and substantiate them using simulations. In particular, we focus on the quadratic terms, both the local and the non local ones, and show the first clear evidence for the latter in the simulations. Using Fourier space correlations, we also show for the first time, the scale dependence of the quadratic and non-local bias coefficients. For the linear bias, we fit for the scale dependence and demonstrate the validity of a consistency relation between linear bias parameters. Furthermore we employ real space estimators, using both cross-correlations and the Peak-Background Split argument. This is the first time the latter is used to measure anisotropic bias coefficients. We find good agreement for all the parameters among these different methods, and also good agreement for local bias with ESP$\tau$ theory predictions. We also try to exploit possible relations among the different bias parameters. Finally, we show how including higher order bias reduces the magnitude and scale dependence of stochasticity of the halo field.Comment: 13 pages, 12 figure

Intensity mapping with neutral hydrogen and the Hidden Valley simulations

This paper introduces the Hidden Valley simulations, a set of trillion-particle N-body simulations in gigaparsec volumes aimed at intensity mapping science. We present details of the simulations and their convergence, then specialize to the study of 21-cm fluctuations between redshifts 2 and 6. Neutral hydrogen is assigned to halos using three prescriptions, and we investigate the clustering in real and redshift-space at the 2-point level. In common with earlier work we find the bias of HI increases from near 2 at z = 2 to 4 at z = 6, becoming more scale dependent at high z. The level of scale-dependence and decorrelation with the matter field are as predicted by perturbation theory. Due to the low mass of the hosting halos, the impact of fingers of god is small on the range relevant for proposed 21-cm instruments. We show that baryon acoustic oscillations and redshift-space distortions could be well measured by such instruments. Taking advantage of the large simulation volume, we assess the impact of fluctuations in the ultraviolet background, which change HI clustering primarily at large scales.Comment: 36 pages, 21 figures. Simulations available at http://cyril.astro.berkeley.edu/HiddenValley/ Minor changes in HI normalization described in footnote of section