Understanding the relation between underlying matter distribution and biased tracers such as galaxies or dark matter halos is essential to extract cosmological information from ongoing or future galaxy redshift surveys. At sufficiently large scales such as the Baryon Acoustic Oscillation (BAO) scale, a standard approach for the bias problem on the basis of the perturbation theory (PT) is to assume the 'local bias' model in which the density field of biased tracers is deterministically expanded in terms of matter density field at the same position. The higher-order bias parameters are then determined by combining the power spectrum with higher-order statistics such as the bispectrum.As is pointed out by recent studies, however, nonlinear gravitational evolution naturally induces nonlocal bias terms even if initially starting only with purely local bias. As a matter of fact, previous works showed that the second-order nonlocal bias term, which corresponds to the gravitational tidal field, is important to explain the characteristic scale-dependence of the bispectrum. In this paper we extend the nonlocal bias term up to third order, and investigate whether the PT-based model including nonlocal bias terms can simultaneously explain the power spectrum and the bispectrum of simulated halos in N -body simulations. The bias renormalization procedure ensures that only one additional term is necessary to be introduced to the power spectrum as a next-to-leading order correction, even if third-order nonlocal bias terms are taken into account. We show that the power spectrum, including density and momentum, and the bispectrum between halo and matter in Nbody simulations can be simultaneously well explained by the model including up to third-order nonlocal bias terms at k < ∼ 0.1h/Mpc. Also, the results are in a good agreement with theoretical predictions of a simple coevolution picture, although the agreement is not perfect. These trend can be found for a wide range of halo mass, 0.7 < ∼ M halo [10 13 M⊙/h] < ∼ 20 at various redshifts, 0 ≤ z ≤ 1. These demonstrations clearly show a failure of the local bias model even at such large scales, and we conclude that nonlocal bias terms should be consistently included in order to accurately model statistics of halos.

With the completion of the Planck mission, in order to continue to gather cosmological information it has become crucial to understand the Large Scale Structures (LSS) of the universe to percent accuracy. The Effective Field Theory of LSS (EFTofLSS) is a novel theoretical framework that aims to develop an analytic understanding of LSS at long distances, where inhomogeneities are small. We further develop the description of biased tracers in the EFTofLSS to account for the effect of baryonic physics and primordial nonGaussianities, finding that new bias coefficients are required. Then, restricting to dark matter with Gaussian initial conditions, we describe the prediction of the EFTofLSS for the one-loop halo-halo and halo-matter two-point functions, and for the tree-level halo-halo-halo, matter-halo-halo and matter-matter-halo threepoint functions. Several new bias coefficients are needed in the EFTofLSS, even though their contribution at a given order can be degenerate and the same parameters contribute to multiple observables. We develop a method to reduce the number of biases to an irreducible basis, and find that, at the order at which we work, seven bias parameters are enough to describe this extremely rich set of statistics. We then compare with the output of an N -body simulation where the normalization parameter of the linear power spectrum is set to σ 8 = 0.9. For the lowest mass bin, we find percent level agreement up to k 0.3 h Mpc −1 for the one-loop two-point functions, and up to k 0.15 h Mpc −1 for the tree-level three-point functions, with the k-reach decreasing with higher mass bins. This is consistent with the theoretical estimates, and suggests that the cosmological information in LSS amenable to analytical control is much more than previously believed.

Abstract. 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.

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Abstract. We have continued the development of Lagrangian, cosmological perturbation theory for the low-order correlators of the matter density field. We provide a new route to understanding how the effective field theory (EFT) of large-scale structure can be formulated in the Lagrandian framework and a new resummation scheme, comparing our results to earlier work and to a series of high-resolution N-body simulations in both Fourier and configuration space. The 'new' terms arising from EFT serve to tame the dependence of perturbation theory on small-scale physics and improve agreement with simulations (though with an additional free parameter). We find that all of our models fare well on scales larger than about two to three times the non-linear scale, but fail as the non-linear scale is approached. This is slightly less reach than has been seen previously. At low redshift the Lagrangian model fares as well as EFT in its Eulerian formulation, but at higher z the Eulerian EFT fits the data to smaller scales than resummed, Lagrangian EFT. All the perturbative models fare better than linear theory.

Abstract.We develop an analytic model for galaxy intrinsic alignments (IA) based on the theory of tidal alignment. We calculate all relevant nonlinear corrections at one-loop order, including effects from nonlinear density evolution, galaxy biasing, and source density weighting. Contributions from density weighting are found to be particularly important and lead to bias dependence of the IA amplitude, even on large scales. This effect may be responsible for much of the luminosity dependence in IA observations. The increase in IA amplitude for more highly biased galaxies reflects their locations in regions with large tidal fields. We also consider the impact of smoothing the tidal field on halo scales. We compare the performance of this consistent nonlinear model in describing the observed alignment of luminous red galaxies with the linear model as well as the frequently used "nonlinear alignment model," finding a significant improvement on small and intermediate scales. We also show that the cross-correlation between density and IA (the "GI" term) can be effectively separated into source alignment and source clustering, and we accurately model the observed alignment down to the one-halo regime using the tidal field from the fully nonlinear halo-matter cross correlation. Inside the one-halo regime, the average alignment of galaxies with density tracers no longer follows the tidal alignment prediction, likely reflecting nonlinear processes that must be considered when modeling IA on these scales. Finally, we discuss tidal alignment in the context of cosmic shear measurements.

We explore the relationship between the nonlinear matter power spectrum and the various Lagrangian and Standard Perturbation Theories (LPT and SPT). We first look at it in the context of one dimensional (1-d) dynamics, where 1LPT is exact at the perturbative level and one can exactly resum the SPT series into the 1LPT power spectrum. Shell crossings lead to non-perturbative effects, and the PT ignorance can be quantified in terms of their ratio, which is also the transfer function squared in the absence of stochasticity. At the order of PT we work, this parametrization is equivalent to the results of effective field theory (EFT), and can thus be expanded in terms of the same parameters. We find that its radius of convergence is larger than the SPT loop expansion. The same EFT parametrization applies to all SPT loop terms and if stochasticity can be ignored, to all N-point correlators. In 3d, the LPT structure is considerably more complicated, and we find that LPT models with parametrization motivated by the EFT exhibit running with k and that SPT is generally a better choice. Since these transfer function expansions contain free parameters that change with cosmological model their usefulness for broadband power is unclear. For this reason we test the predictions of these models on baryonic acoustic oscillations (BAO) and other primordial oscillations, including string monodromy models, for which we ran a series of simulations with and without oscillations. Most models are successful in predicting oscillations beyond their corresponding PT versions, confirming the basic validity of the model. We show that if primordial oscillations are localized to a scale q, the wiggles in power spectrum are approximately suppressed as exp[−k 2 Σ 2 (q)/2], where Σ(q) is rms displacement of particles separated by q, which saturates on large scales, and decreases as q is reduced. No oscillatory features survive past k ∼ 0.5h/Mpc at z = 0.

The peculiar velocities of biased tracers of the cosmic density field contain important information about the growth of large scale structure and generate anisotropy in the observed clustering of galaxies. Using N-body data, we show that velocity expansions for halo redshift-space power spectra are converged at the percent-level at perturbative scales for most line-of-sight angles μ when the first three pairwise velocity moments are included, and that the third moment is well-approximated by a counterterm-like contribution. We compute these pairwise-velocity statistics in Fourier space using both Eulerian and Lagrangian one-loop perturbation theory using a cubic bias scheme and a complete set of counterterms and stochastic contributions. We compare the models and show that our models fit both real-space velocity statistics and redshift-space power spectra for both halos and a mock sample of galaxies at sub-percent level on perturbative scales using consistent sets of parameters, making them appealing choices for the upcoming era of spectroscopic, peculiar-velocity and kSZ surveys.