arXiv subjects

Fabian Schmidt

Publications and source records attributed to Fabian Schmidt.

At least 55 records · Page 3Linked to original sources

arXiv2023

Galaxy bias renormalization group

The effective field theory of large-scale structure allows for a consistent perturbative bias expansion of the rest-frame galaxy density field. In this work, we present a systematic approach to renormalize galaxy bias and stochastic parameters using a finite cutoff scale $Λ$. We derive the differential equations of the Wilson-Polchinski renormalization group that describe the evolution of the finite-scale bias parameters with $Λ$, analogous to the $β$-function running in QFT. We further provide the connection between the finite-cutoff scheme and the renormalization procedure for $n$-point functions that has been used as standard in the literature so far; some inconsistencies in the treatment of renormalized bias in current EFT analyses are pointed out as well. The fixed-cutoff scheme allows us to predict, in a principled way, the finite part of loop contributions which is due to perturbative modes and which, in the standard renormalization approach, is absorbed into counterterms. We expect that this will allow for the robust extraction of (a yet-to-be-determined amount of) additional cosmological information from galaxy clustering, both when using field-level techniques and $n$-point functions.

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arXiv2023

Consistency tests of field level inference with the EFT likelihood

Analyzing the clustering of galaxies at the field level in principle promises access to all the cosmological information available. Given this incentive, in this paper we investigate the performance of field-based forward modeling approach to galaxy clustering using the effective field theory (EFT) framework of large-scale structure (LSS). We do so by applying this formalism to a set of consistency and convergence tests on synthetic datasets. We explore the high-dimensional joint posterior of LSS initial conditions by combining Hamiltonian Monte Carlo sampling for the field of initial conditions, and slice sampling for cosmology and model parameters. We adopt the Lagrangian perturbation theory forward model from [1], up to second order, for the forward model of biased tracers. We specifically include model mis-specifications in our synthetic datasets within the EFT framework. We achieve this by generating synthetic data at a higher cutoff scale $Λ_0$, which controls which Fourier modes enter the EFT likelihood evaluation, than the cutoff $Λ$ used in the inference. In the presence of model mis-specifications, we find that the EFT framework still allows for robust, unbiased joint inference of a) cosmological parameters - specifically, the scaling amplitude of the initial conditions - b) the initial conditions themselves, and c) the bias and noise parameters. In addition, we show that in the purely linear case, where the posterior is analytically tractable, our samplers fully explore the posterior surface. We also demonstrate convergence in the cases of nonlinear forward models. Our findings serve as a confirmation of the EFT field-based forward model framework developed in [2-7], and as another step towards field-level cosmological analyses of real galaxy surveys.

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arXiv2023

Non-linear Eulerian Hydrodynamics of Dark Energy: Riemann problem and Finite Volume Schemes

Upcoming large-scale-structure surveys can shed new light on the properties of dark energy. In particular, if dark energy is a dynamical component, it must have spatial perturbations. Their behaviour is regulated by the speed of sound parameter, which is currently unconstrained. In this work we present the numerical methods that will allow to perform cosmological simulations of inhomogeneous dark energy scenarios where the speed of sound is small and non-vanishing. We treat the dark energy component as an effective fluid and build upon established numerical methods for hydrodynamics to construct a numerical solution of the effective continuity and Euler equations. In particular, we develop conservative finite volume schemes that rely on the solution of the Riemann problem, which we provide here in both exact and approximate forms for the case of a dark energy fluid.

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arXiv2023

Halo assembly bias from a deep learning model of halo formation

We build a deep learning framework that connects the local formation process of dark matter halos to the halo bias. We train a convolutional neural network (CNN) to predict the final mass and concentration of dark matter halos from the initial conditions. The CNN is then used as a surrogate model to derive the response of the halos' mass and concentration to long-wavelength perturbations in the initial conditions, and consequently the halo bias parameters following the "response bias" definition. The CNN correctly predicts how the local properties of dark matter halos respond to changes in the large-scale environment, despite no explicit knowledge of halo bias being provided during training. We show that the CNN recovers the known trends for the linear and second-order density bias parameters $b_1$ and $b_2$, as well as for the local primordial non-Gaussianity linear bias parameter $b_ϕ$. The expected secondary assembly bias dependence on halo concentration is also recovered by the CNN: at fixed mass, halo concentration has only a mild impact on $b_1$, but a strong impact on $b_ϕ$. Our framework opens a new window for discovering which physical aspects of the halo's Lagrangian patch determine assembly bias, which in turn can inform physical models of halo formation and bias.

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arXiv2023

Effective Field Theory of Intrinsic Alignments at One Loop Order: a Comparison to Dark Matter Simulations

We test the regime of validity of the effective field theory (EFT) of intrinsic alignments (IA) at the one-loop level by comparing with 3D halo shape statistics in N-body simulations. This model is based on the effective field theory of large-scale structure (EFT of LSS) and thus a theoretically well-motivated extension of the familiar non-linear alignment (NLA) model and the tidal-alignment-tidal-torquing (TATT) model. It contains a total of $8$ free bias parameters. Specifically, we measure the dark matter halo shape-shape multipoles $P_{EE}^{(0)}(k), P_{EE}^{(2)}(k), P_{BB}^{(0)}(k), P_{BB}^{(2)}(k)$ as well as the matter-shape multipoles $P_{δE}^{(0)}(k), P_{δE}^{(2)}(k)$ from the simulations and perform a joint fit to determine the largest wavenumber $k_{\text{max}}$ up to which the theory predictions from the EFT of IA are consistent with the measurements. We find that the EFT of IA is able to describe intrinsic alignments of dark matter halos up to $k_\text{max}=0.30\,h/\text{Mpc}$ at $z=0$. This demonstrates a clear improvement over other existing alignment models like NLA and TATT, which are only accurate up to $k_\text{max}=0.05\,h/\text{Mpc}$ . We examine the posterior distributions of the higher-order bias parameters, and show that their inclusion is necessary to describe intrinsic alignments in the quasi-linear regime. Further, the EFT of IA is able to accurately describe the auto-spectrum of intrinsic alignment B-modes, in contrast to the other alignment models considered.

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arXiv2023

Assembly bias in the local PNG halo bias and its implication for $f_{\rm NL}$ constraints

We use $N$-body simulations to study halo assembly bias (i.e., the dependence of halo clustering on properties beyond total mass) in the density and primordial non-Gaussianity (PNG) linear bias parameters $b_1$ and $b_ϕ$, respectively. We consider concentration, spin and sphericity as secondary halo properties, for which we find a clear detection of assembly bias for $b_1$ and $b_ϕ$. At fixed total mass, halo spin and sphericity impact $b_1$ and $b_ϕ$ in a similar manner, roughly preserving the shape of the linear $b_ϕ(b_1)$ relation satisfied by the global halo population. Halo concentration, however, drives $b_1$ and $b_ϕ$ in opposite directions. This induces significant changes to the $b_ϕ(b_1)$ relation, with higher concentration halos having higher amplitude of $b_ϕ(b_1)$. For $z=0.5$ and $b_1 \approx 2$ in particular, the population comprising either all halos, those with the $33\%$ lowest or those with the $33\%$ highest concentrations have a PNG bias of $b_ϕ\approx 3$, $b_ϕ\approx -1$ and $b_ϕ\approx 9$, respectively. Varying the halo concentration can make $b_ϕ$ very small and even change its sign. These results have important ramifications for galaxy clustering constraints of the local PNG parameter $f_{\rm NL}$ that assume fixed forms for the $b_ϕ(b_1)$ relation. We illustrate the significant impact of halo assembly bias in actual data using the BOSS DR12 galaxy power spectrum: assuming that BOSS galaxies are representative of all halos, the $33\%$ lowest or the $33\%$ highest concentration halos yields $σ_{f_{\rm NL}} = 44, 165, 19$, respectively. Our results suggest taking host halo concentration into account in galaxy selection strategies to maximize the signal-to-noise on $f_{\rm NL}$. They also motivate more simulation-based efforts to study the $b_ϕ(b_1)$ relation of halos and galaxies.

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arXiv2022

BAO scale inference from biased tracers using the EFT likelihood

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 reconstruction have so far been proposed; however, they all rely on backward modeling. In this paper, we present the first results of BAO inference from rest-frame halo catalogs using forward modeling combined with the EFT likelihood, in the case where the initial phases of the density field are fixed. We show that the remaining systematic bias is less than 2% when we consider cutoff values of $Λ\leq 0.25 \,h\,{\rm Mpc}^{-1}$ for all halo samples considered, and below 1% and consistent with zero for all but the most highly biased samples. We also demonstrate that, when compared to the standard power spectrum likelihood approach under the same assumption of fixed phases, the 1$σ$ errors associated to the field level inference of the BAO scale are 1.1 to 3.3 times smaller, depending on the value of the cutoff and the halo sample. Our analysis therefore unveils another promising feature of using field-level inference for high-precision cosmology.

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arXiv2022

Field-level inference of galaxy intrinsic alignment from the SDSS-III BOSS survey

As a large-scale overdensity collapses, it affects the orientation and shape of galaxies that form, by exerting tidal shear along their axes. Therefore, the shapes of elliptical galaxies align with the tidal field of cosmic structures. This intrinsic alignment provides insights into galaxy formation and the primordial universe, complements late-time cosmological probes and constitutes a significant systematic effect for weak gravitational lensing observations. In the present study, we provide constraints on the linear alignment model using a fully Bayesian field-level approach, using galaxy shape measurements from the SDSS-III BOSS LOWZ sample and three-dimensional tidal fields constrained with the LOWZ and CMASS galaxy samples of the SDSS-III BOSS survey. We find 4$σ$ evidence of intrinsic alignment, with an amplitude of $A_I=2.9 \pm 0.7$ at 20$h^{-1}\;\mathrm{Mpc}$.

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arXiv2022

Stellar streams and dark substructure: the diffusion regime

The cold dark matter picture predicts an abundance of substructure within the Galactic halo. However, most substructures host no stars and can only be detected indirectly. Stellar streams present a promising probe of this dark substructure. These streams arise from tidally stripped star clusters or dwarf galaxies, and their low dynamical temperature and negligible self-gravity give them a sharp memory of gravitational perturbations caused by passing dark substructures. For this reason, perturbed stellar streams have been the subject of substantial study. While previous studies have been largely numerical, we show here that in the diffusion regime -- where stream stars are subjected to many small velocity kicks -- stream perturbations can be understood on a fully analytic level. In particular, we derive how the (three-dimensional) power spectrum of the substructure density field determines the power spectrum of the (one-dimensional) density of a stellar stream. Our analytic description supplies a clear picture of the behaviour of stream perturbations in response to a perturbing environment, which may include contributions from both dark and luminous substructure. In particular, stream perturbations grow in amplitude initially, settle into a steady state, and ultimately decay. By directly relating stellar stream perturbations to the surrounding matter distribution, this analytic framework represents a versatile new tool for probing the nature of dark matter through astrophysical observations.

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arXiv2022

Bayesian field-level inference of primordial non-Gaussianity using next-generation galaxy surveys

Detecting and measuring a non-Gaussian signature of primordial origin in the density field is a major science goal of next-generation galaxy surveys. The signal will permit us to determine primordial physics processes and constrain models of cosmic inflation. While traditional approaches utilise a limited set of statistical summaries of the galaxy distribution to constrain primordial non-Gaussianity, we present a field-level approach by Bayesian forward-modelling the entire three-dimensional galaxy survey. Our method naturally and fully self-consistently exploits the entirety of the large-scale structure, e.g., higher-order statistics, peculiar velocity fields, and scale-dependent galaxy bias, to extract information on the local non-Gaussianity parameter, $\fnl$. We demonstrate the performance of our approach through various tests with mock galaxy data emulating relevant features of the \sdssiii{}-like survey, and additional tests with a \textit{Stage IV} mock data set. These tests reveal that the method infers unbiased values of $\fnl$ by accurately handling survey geometries, noise, and unknown galaxy biases. We demonstrate that our method can achieve constraints of $σ_{\fnl} \approx 8.78$ for \sdssiii{}-like data, an improvement of a factor $\sim 2.5$ over currently published constraints. Tests with next-generation mock data show that significant further improvements are feasible with sufficiently high resolution. Furthermore, the results demonstrate that our method can consistently marginalise all nuisance parameters of the data model. The method further provides an inference of the three-dimensional primordial density field, providing opportunities to explore additional signatures of primordial physics.

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arXiv2022

Covariant Decomposition of The Non-Linear Galaxy Number Counts and Their Monopole

We present a fully non-linear and relativistically covariant expression for the observed galaxy density contrast. Building on a null tetrad tailored to the cosmological observer's past light cone, we find a decomposition of the non-linear galaxy over-density into manifestly gauge-invariant quantities, each of which has a clear physical interpretation as a cosmological observable. This ensures that the monopole of the galaxy over-density field (the mean galaxy density as a function of observed redshift) is properly accounted for. We anticipate that this decomposition will be useful for future work on non-linearities in galaxy number counts, for example, deriving the relativistic expression for the galaxy bispectrum. We then specialise our results to conformal Newtonian gauge, with a Hubble parameter either defined globally or measured locally, illustrating the significance of the different contributions to the observed monopole of the galaxy density.

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arXiv2021

Assembly bias in quadratic bias parameters of dark matter halos from forward modeling

We use the forward modeling approach to galaxy clustering combined with the likelihood from the effective-field theory of large-scale structure to measure assembly bias, i.e. the dependence of halo bias on properties beyond the total mass, in the linear ($b_1$) and second order bias parameters ($b_2$ and $b_{K^2}$) of dark matter halos in $N$-body simulations. This is the first time that assembly bias in the tidal bias parameter $b_{K^2}$ is measured. We focus on three standard halo properties: the concentration $c$, spin $λ$, and sphericity $s$, for which we find an assembly bias signal in $b_{K^2}$ that is opposite to that in $b_1$. Specifically, at fixed mass, halos that get more (less) positively biased in $b_1$, get less (more) negatively biased in $b_{K^2}$. We also investigate the impact of assembly bias on the $b_2(b_1)$ and $b_{K^2}(b_1)$ relations, and find that while the $b_2(b_1)$ relation stays roughly unchanged, assembly bias strongly impacts the $b_{K^2}(b_1)$ relation. This impact likely extends also to the corresponding relation for galaxies, which motivates future studies to design better priors on $b_{K^2}(b_1)$ for use in cosmological constraints from galaxy clustering data.

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arXiv2021

An $n$-th order Lagrangian Forward Model for Large-Scale Structure

A forward model of matter and biased tracers at arbitrary order in Lagrangian perturbation theory (LPT) is presented. The forward model contains the complete LPT displacement field at any given order in perturbations, as well as all relevant bias operators at that order and leading order in derivatives. The construction is done for any expansion history and does not rely on the Einstein-de Sitter approximation. A large subset of higher-derivative bias operators is also included. As validation test, we compare the $n$LPT-predicted matter density field and that from N-body simulations using the same initial conditions. For simulations using a cutoff in the initial conditions, we find subpercent agreement up to scales of $k\sim 0.2 h\,{\rm Mpc}^{-1}$. We also find subpercent agreement with full simulations without cutoff, both for the power spectrum and nonlinear $σ_8$-inference, when allowing for the effective sound speed. The application to biased tracers (halos) has already been presented in a recent paper (arXiv:2009.14176).

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arXiv2021

Galaxy bias from forward models: linear and second-order bias of IllustrisTNG galaxies

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 result is that the $b_2(b_1)$ and $b_{K^2}(b_1)$ relations obtained from gravity-only simulations for total mass selected objects are broadly preserved for simulated galaxies selected by stellar mass, star formation rate, color and black hole accretion rate. We also find good agreement between the bias relations of the simulated galaxies and a number of recent estimates for observed galaxy samples. The consistency under different galaxy selection criteria suggests that theoretical priors on these bias relations may be used to improve cosmological constraints based on observed galaxy samples. We do identify some small differences between the bias relations in the hydrodynamical and gravity-only simulations, which we show can be linked to the environmental dependence of the relation between galaxy properties and mass. We also show that the EFT likelihood recovers the value of $σ_8$ to percent-level from various galaxy samples (including splits by color and star formation rate) and after marginalizing over 8 bias parameters. This demonstration using simulated galaxies adds to previous works based on halos as tracers, and strengthens further the potential of forward models to infer cosmology from galaxy data.

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arXiv2021

Neutrino mass constraints beyond linear order: cosmology dependence and systematic biases

We demonstrate the impact on forecasted neutrino mass constraints of extending galaxy clustering and CMB lensing predictions from linear to next-to-leading-order power spectra. The redshift-space 1-loop power spectrum model we adopt requires an additional four free bias parameters, a velocity bias parameter and two new stochastic parameters. These additional nuisance parameters appreciably weaken the constraints on $M_ν$. CMB lensing plays a significant role in helping to alleviate these degeneracies and tighten the final constraints. The constraint on the optical depth to reionisation $τ$ has a strong effect on the constraint on $M_ν$, but only when CMB lensing is included in the analysis to keep the degeneracies with the nuisance parameters under control. We also extract constraints when 1) using the BAO signature only as a distance probe, and 2) isolating the scale-dependence of the power spectrum, which, as shown in previous work, provides a cosmology-independent probe of $M_ν$. All constraints except the latter remain strongly sensitive to the assumption of a flat $Λ$CDM universe. We perform an analysis of the magnitude of the shift introduced in the inferred $M_ν$ value when neglecting nonlinear corrections, and show that, for a Euclid-like survey, this shift becomes roughly equal to the 1$σ$ constraint itself even with a conservative cut-off scale of $k_{max} = 0.1~h~{\rm Mpc}^{-1}$. We also perform a calculation of the appropriate expected bias in neutrino mass caused by not including the next, 2-loop order and expect a shift of only about 20% of the 1$σ$ error for $k_{max}=0.2~h~{\rm Mpc}^{-1}$ in a Euclid-like survey.

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arXiv2021

Sigma-Eight at the Percent Level: The EFT Likelihood in Real Space

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 inference of $σ_8$ is demonstrated at the 2% level for cutoff values $Λ\leq 0.14h\,{\rm Mpc}^{-1}$ for halo samples over a range of masses and redshifts. The inferred value shows the expected convergence to the ground truth in the low-cutoff limit. Apart from the possibility of including observational effects, this represents further substantial improvement over previous results based on the EFT likelihood.

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arXiv2021

Galaxy imaging surveys as spin-sensitive detector for cosmological colliders

Galaxy imaging surveys provide us with information on both the galaxy distribution and their shapes. In this paper, we systematically investigate the sensitivity of galaxy shapes to new physics in the initial conditions. For this purpose, we decompose the galaxy shape function into spin components, and compute the contributions to each spin component from both intrinsic alignment and weak lensing. We then consider the angular-dependent primordial non-Gaussianity, which is generated by a non-zero integer spin particle when active during inflation, and show that a galaxy imaging survey essentially functions as a spin-sensitive detector of such particles in the early universe. We also perform a forecast of the PNG generated from a higher spin particle, considering a Rubin Observatory LSST-like galaxy survey.

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arXiv2021

Impacts of the physical data model on the forward inference of initial conditions from biased tracers

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 theoretical expectation derived from a Gaussian model on a broad range of scales. The bias in the amplitude of the inferred initial conditions, on the other hand, depends strongly on the bias model and the likelihood. We conclude that the bias model and likelihood hold the key to an unbiased cosmological inference. Together they must keep the systematics -- which arise from the sub-grid physics that are marginalized over -- under control in order to obtain an unbiased inference.

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