We present updates on the cosmology inference using the effective field theory (EFT) likelihood presented previously in Schmidt et al., 2018, Elsner et al., 2019 [1,2]. Specifically, we add a cutoff to the initial conditions that serve as starting point for the matter forward model. We show that this cutoff, which was not employed in any previous related work, is important to regularize loop integrals that otherwise involve small-scale, non-perturbative modes. We then present results on the inferred value of the linear power spectrum normalization $σ_{8}$ from rest-frame halo catalogs using both second- and third-order bias expansions, imposing uniform priors on all bias parameters. Due to the perfect bias-$σ_{8}$ degeneracy at linear order, constraints on $σ_{8}$ rely entirely on nonlinear information. The results show the expected convergence behavior when lowering the cutoff in wavenumber, $Λ$. When including modes up to $k \leq Λ= 0.1\,h\,{\rm Mpc}^{-1}$ in the second-order case, $σ_{8}$ is recovered to within $\lesssim 6\,\%$ for a range of halo masses and redshifts. The systematic bias shrinks to $4\,\%$ or less for the third-order bias expansion on the same range of scales. Together with additional evidence we provide, this shows that the residual mismatch in $σ_{8}$ can be attributed to higher-order bias contributions. We conclude that the EFT likelihood is able to infer unbiased cosmological constraints, within expected theoretical systematic errors, from physical biased tracers on quasilinear scales
We derive, using functional methods and the bias expansion, the conditional likelihood for observing a specific tracer field given an underlying matter field. This likelihood is necessary for Bayesian-inference methods. If we neglect all stochastic terms apart from the ones appearing in the auto two-point function of tracers, we recover the result of Schmidt et al., 2018. We then rigorously derive the corrections to this result, such as those coming from a non-Gaussian stochasticity (which include the stochastic corrections to the tracer bispectrum) and higher-derivative terms. We discuss how …
The effective-field-theory (EFT) approach to the clustering of galaxies and other biased tracers allows for an isolation of the cosmological information that is protected by symmetries, in particular the equivalence principle, and thus is robust to the complicated dynamics of dark matter, gas, and stars on small scales. All existing implementations proceed by making predictions for the lowest-order $n$-point functions of biased tracers, as well as their covariance, and comparing with measurements. Recently, we presented an EFT-based expression for the conditional probability of the density fie…
The Effective Field Theory of Large-Scale Structure (EFTofLSS) provides a novel formalism that is able to accurately predict the clustering of large-scale structure (LSS) in the mildly non-linear regime. Here we provide the first computation of the power spectrum of biased tracers in redshift space at one loop order, and we make the associated code publicly available. We compare the multipoles $\ell=0,2$ of the redshift-space halo power spectrum, together with the real-space matter and halo power spectra, with data from numerical simulations at $z=0.67$. For the samples we compare to, which ha…
Multi-tracers, multi-surveys: a joint Fisher analysis of DESI+PFS
Center for Data-Driven Discovery, Kavli IPMU (WPI), UTIAS, The University of Tokyo（东京大学 数据驱动发现中心，Kavli IPMU (WPI)，UTIAS）；Institute For Interdisciplinary Research in Science and Education, ICISE（科学与教育跨学科研究所，ICISE）
The effective field theory likelihood for the density field of biased tracers allows for cosmology inference from the clustering of galaxies that consistently uses all available information at a given order in perturbation theory. This paper presents results and implementation details on the real-space (as opposed to Fourier-space) formulation of the likelihood, which allows for the incorporation of survey window functions. The implementation further uses a Lagrangian forward model for biased tracers which automatically accounts for all relevant contributions up to any desired order. Unbiased …
The physical scale corresponding to baryon acoustic oscillations (BAO), the size of the sound horizon at recombination, is precisely determined by CMB experiments. Measuring the apparent size of the BAO scale imprinted in the clustering of galaxies gives us a direct estimate of the angular-diameter distance and the Hubble parameter as a function of redshift. The BAO feature is damped by non-linear structure formation, which reduces the precision with which we can infer the BAO scale from standard galaxy clustering analysis methods. Many methods to undo this damping via the so-called BAO recons…
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 non-Gaussianities, finding that new bias coefficients are required. Then, restric…
We study the effect of the Einstein - de Sitter (EdS) approximation on the one-loop power spectrum of galaxies in redshift space in the Effective Field Theory of Large-Scale Structure. The dark matter density perturbations and velocity divergence are treated with exact time dependence. Splitting the density perturbation into its different temporal evolutions naturally gives rise to an irreducible basis of biases. While, as in the EdS approximation, at each time this basis spans a seven-dimensional space, this space is a slightly different one, and the difference is captured by a single calcula…
Conventional approaches to cosmology inference from galaxy redshift surveys are based on n-point functions, which are under rigorous perturbative control on sufficiently large scales. Here, we present an alternative approach, which employs a likelihood at the level of the galaxy density field. By integrating out small-scale modes based on effective-field theory arguments, we prove that this likelihood is under perturbative control if certain specific conditions are met. We further show that the information captured by this likelihood is equivalent to the combination of the next-to-leading orde…
We model the mass distribution of long gamma-ray burst (GRB) host galaxies given recent results suggesting that GRBs occur in low metallicity environments. By utilizing measurements of the redshift evolution of the mass-metallicity (M-Z) relationship for galaxies, along with a sharp host metallicity cut-off suggested by Modjaz and collaborators, we estimate an upper limit on the stellar mass of a galaxy that can efficiently produce a GRB as a function of redshift. By employing consistent abundance indicators, we find that sub-solar metallicity cut-offs effectively limit GRBs to low stellar mas…
We investigate the impact of each ingredient in the employed physical data model on the Bayesian forward inference of initial conditions from biased tracers at the field level. Specifically, we use dark matter halos in a given cosmological simulation volume as tracers of the underlying matter density field. We study the effect of tracer density, grid resolution, gravity model, bias model and likelihood on the inferred initial conditions. We find that the cross-correlation coefficient between true and inferred phases reacts weakly to all ingredients above, and is well predicted by the theoretic…
We study the EFT likelihood for biased tracers in redshift space, for which the bias expansion of the galaxy velocity field $\mathbf{v}_g$ plays a fundamental role. The equivalence principle forbids stochastic contributions to $\mathbf{v}_g$ to survive at small $k$. Therefore, at leading order in derivatives the form of the likelihood ${\cal P}[\tildeδ_g|δ,\!\mathbf{v}]$ to observe a redshift-space galaxy overdensity $\tildeδ_g(\tilde{\mathbf{x}})$ given a rest-frame matter and velocity fields $δ(\mathbf{x})$, $\mathbf{v}(\mathbf{x})$ is fixed by the rest-frame noise. If this noise is Gaussian…
We provide in depth MCMC comparisons of two different models for the halo redshift space power spectrum, namely a variant of the commonly applied Taruya-Nishimichi-Saito (TNS) model and an effective field theory of large scale structure (EFTofLSS) inspired model. Using many simulation realisations and Stage IV survey-like specifications for the covariance matrix, we check each model's range of validity by testing for bias in the recovery of the fiducial growth rate of structure formation. The robustness of the determined range of validity is then tested by performing additional MCMC analyses u…
In the EFT of biased tracers the noise field $\varepsilon_g$ is not exactly uncorrelated with the nonlinear matter field $δ$. Its correlation with $δ$ is effectively captured by adding stochasticities to each bias coefficient. We show that if these stochastic fields are Gaussian (the impact of their non-Gaussianity being subleading on quasi-linear scales anyway) it is possible to resum exactly their effect on the conditional likelihood ${\cal P}[δ_g|δ]$ to observe a galaxy field $δ_g$ given an underlying $δ$. This resummation allows to take them into account in EFT-based approaches to Bayesian…
We present a Bayesian reconstruction algorithm to generate unbiased samples of the underlying dark matter field from halo catalogues. Our new contribution consists of implementing a non-Poisson likelihood including a deterministic non-linear and scale-dependent bias. In particular we present the Hamiltonian equations of motions for the negative binomial (NB) probability distribution function. This permits us to efficiently sample the posterior distribution function of density fields given a sample of galaxies using the Hamiltonian Monte Carlo technique implemented in the Argo code. We have tes…
Cosmic voids are the major volume component in the matter distribution of the Universe. They posses great potential for constraining dark energy as well as for testing theories of gravity. Nevertheless, in spite of their growing popularity as cosmological probes, a gap of knowledge between cosmic void observations and theory still persists. In particular, the void size function models proposed in literature have been proven unsuccessful in reproducing the results obtained from cosmological simulations in which cosmic voids are detected from biased tracers of the density field, undermining the …
Since Kaiser introduced galaxies as a biased tracer of the underlying total mass field, the linear galaxies bias, b(z) appears ubiquitously both in theoretical calculations and in observational measurements related to galaxy surveys. However, the generic approaches to the galaxy density is a non-local and stochastic function of the underlying dark matter density and it becomes difficult to make the analytic form of b(z). Due to this fact, b(z) is known as a nuisance parameter and the effort has been made to measure bias free observable quantities. We provide the exact and analytic function of …
We develop two general methods to infer the gravitational potential of a system using steady-state tracers, i.e., tracers with a time-independent phase-space distribution. Combined with the phase-space continuity equation, the time independence implies a universal Orbital Probability Density Function (oPDF) $\mathrm{d} P(λ|{\rm orbit})\propto \mathrm{d} t$, where $λ$ is the coordinate of the particle along the orbit. The oPDF is equivalent to Jeans theorem, and is the key physical ingredient behind most dynamical modelling of steady-state tracers. In the case of a spherical potential, we devel…
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 Ga…
Cosmological simulations play an increasingly important role in analysing the observed large-scale structure of the Universe. Recently, they have been particularly important in building hybrid models that combine a perturbative bias expansion with displacement fields extracted from N-body simulations to describe the clustering of biased tracers. Here, we show that simulations that employ a technique referred to as "Fixing-and-pairing" (F&P) can dramatically improve the statistical precision of such hybrid models. Specifically, by numerical and analytic means, we show that F&P simulations provi…
Probabilistic reconstruction of Dark Matter fields from biased tracers using diffusion models
Harvard University（哈佛大学）；Harvard-Smithsonian Center for Astrophysics（哈佛-史密森天体物理中心）；The NSF AI Institute for Artificial Intelligence and Fundamental Interactions（NSF人工智能与基础相互作用研究所）；Massachusetts Institute of Technology（麻省理工学院）
A new generation of surveys will soon map large fractions of sky to ever greater depths and their science goals can be enhanced by exploiting cross correlations between them. In this paper we study cross correlations between the lensing of the CMB and biased tracers of large-scale structure at high $z$. We motivate the need for more sophisticated bias models for modeling increasingly biased tracers at these redshifts and propose the use of perturbation theories, specifically Convolution Lagrangian Effective Field Theory ({\sc CLEFT}). Since such signals reside at large scales and redshifts, th…
We study how the properties of cosmic voids depend on those of the tracer galaxy populations in which they are identified. We use a suite of halo occupation distribution (HOD) mocks in a simulation, identify voids in these populations using the ZOBOV void finder and measure their abundances, sizes, tracer densities, and dark matter content. To separate the effects of bias from those of sampling density, we do the same for voids traced by randomly down-sampled subsets of the simulation dark matter particles. At the same sampling density, galaxy bias reduces the total number of voids by ~50% and…
Galaxy Power Spectrum at Two-Loop Order: Implications for Weak Lensing Surveys and New Physics
Massachusetts Institute of Technology（麻省理工学院）；Center for Theoretical Physics – a Leinweber Institute, Massachusetts Institute of Technology（麻省理工学院理论物理中心（莱因韦伯研究所））
We use field-level forward models of galaxy clustering and the EFT likelihood formalism to study, for the first time for self-consistently simulated galaxies, the relations between the linear $b_1$ and second-order bias parameters $b_2$ and $b_{K^2}$. The forward models utilize all of the information available in the galaxy distribution up to a given order in perturbation theory, which allows us to infer these bias parameters with high signal-to-noise, even from relatively small volumes ($L_{\rm box} = 205{\rm Mpc}/h$). We consider galaxies from the IllustrisTNG simulations, and our main resul…
We implement a model for the two-point statistics of biased tracers that combines dark matter dynamics from $N$-body simulations with an analytic Lagrangian bias expansion. Using Aemulus, a suite of $N$-body simulations built for emulation of cosmological observables, we emulate the cosmology dependence of these nonlinear spectra from redshifts $z = 0$ to $z=2$. We quantify the accuracy of our emulation procedure, which is sub-per cent at $k=1\, h {\rm Mpc}^{-1}$ for the redshifts probed by upcoming surveys and improves at higher redshifts. We demonstrate its ability to describe the statistics…
Compensated isocurvature perturbations (CIPs) are modulations of the relative baryon and dark matter density that leave the total matter density constant. The best current constraints from the primary cosmic microwave background (CMB) are consistent with CIPs some two orders of magnitude larger in amplitude than adiabatic perturbations, suggesting that there may be a huge gap in our knowledge of the early Universe. However, it was recently suggested by Barreira~et.~al. that CIPs which are correlated with the primordial curvature perturbation, as arises in some versions of the curvaton model, l…
We use the VIPERS final data release to investigate the performance of colour-selected populations of galaxies as tracers of linear large-scale motions. We empirically select volume-limited samples of blue and red galaxies as to minimise the systematic error on the estimate of the growth rate $fσ_8$ from the anisotropy of the two-point correlation function. To this end, rather than rigidly splitting the sample into two colour classes we define the red/blue fractional contribution of each object through a weight based on the $(U-V)$ colour distribution. Using mock surveys that are designed to r…
We present a self-consistent Bayesian formalism to sample the primordial density fields compatible with a set of dark matter density tracers after cosmic evolution observed in redshift space. Previous works on density reconstruction did not self-consistently consider redshift space distortions or included an additional iterative distortion correction step. We present here the analytic solution of coherent flows within a Hamiltonian Monte Carlo posterior sampling of the primordial density field. We test our method within the Zel'dovich approximation, presenting also an analytic solution includi…
Cosmological Constraints from Bias-Robust Wavelet Scattering Statistics for Stage-IV Galaxy Surveys
School of Physics and Astronomy, Sun Yat-sen University（中山大学物理学院）；Tsung-Dao Lee Institute, Shanghai Jiao Tong University（上海交通大学李政道研究所）；Department of Astronomy, School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理学院天文学系）；State Key Laboratory of Dark Matter Physics, School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理学院暗物质物理全国重点实验室）；Key Laboratory for Particle Astrophysics and Cosmology (MOE)/Shanghai Key Laboratory for Particle Physics and Cosmology（粒子天体物理教育部重点实验室/上海粒子物理与天体物理重点实验室）；Department of Physics and Electronic Engineering, Tongren University（铜仁学院物理与电子工程学院）
We constrain the linear and quadratic bias parameters from the configuration dependence of the three-point correlation function (3PCF) in both redshift and projected space, utilizing measurements of spectroscopic galaxies in the Sloan Digital Sky Survey (SDSS) Main Galaxy Sample. We show that bright galaxies (M_r < -21.5) are biased tracers of mass, measured at a significance of 4.5 sigma in redshift space and 2.5 sigma in projected space by using a thorough error analysis in the quasi-linear regime (9-27 Mpc/h). Measurements on a fainter galaxy sample are consistent with an unbiased model. We…
