We develop a simple formalism of biased tracers that we dub $\mathit{Monkey\ bias}$. In this formalism, a biased tracer field is constructed directly in terms of the linear matter fluctuation field and the set of derivative operators acting on it. Such bias expansion is first organized based on the general structure of non-linear dynamical equations for the biased tracers. Further physical conditions, like the equivalence principle, are imposed on tree-level correlators utilising the consistency relations. We obtain the bias expansion up to the third-order in linear matter fluctuation in the generalized $Λ$CDM background, which reproduces the previous results in the limit of the EdS universe. This algorithmic construction of our bias operator basis is well suited for extensions towards higher-order bias fields. Moreover, this formalism reveals that biased tracer dynamics in generalized $Λ$CDM background is not entirely degenerate with the rest of bias parameters, thus opening a possibility of testing the background cosmology through the observations of biased tracers.
Most of the upcoming cosmological information will come from analyzing the clustering of the Large Scale Structures (LSS) of the universe through LSS or CMB observations. It is therefore essential to be able to understand their behavior with exquisite precision. The Effective Field Theory of Large Scale Structures (EFTofLSS) provides a consistent framework to make predictions for LSS observables in the mildly non-linear regime. In this paper we focus on biased tracers. We argue that in calculations at a given order in the dark matter perturbations, highly biased tracers will underperform becau…
We study the impact of the nonlinear growth of the large-scale structure (LSS) on the removal of the gravitational lensing effect (delensing) in cosmic microwave background (CMB) $B$ modes. The importance of the nonlinear growth of the LSS in the gravitational lensing analysis of CMB has been recently recognized by several works, while its impact on delensing is not yet explored. The delensing using mass-tracers such as galaxies and cosmic infrared background (CIB) could be also affected by the nonlinear growth. We find that the nonlinear growth of the LSS leads to $\sim 0.3\%$ corrections to …
Recent progress in high sensitivity Cosmic Microwave Background (CMB) polarization experiments opens up a window on large scale structure (LSS), as CMB polarization fluctuations on small angular scales can arise from a combination of LSS and ionization fluctuations in the late universe. Gravitational lensing effects can be extracted from CMB datasets with quadratic estimators but reconstructions of electron density fluctuations (EDFs) with quadratic estimators are found to be significantly biased by the much larger lensing effects in the secondary CMB fluctuations. In this paper we establish a…
From South to North: Leveraging Ground-Based LATs for Full-Sky CMB Delensing and Constraints on $r$
Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences（高能物理研究所粒子天体物理重点实验室）；University of Chinese Academy of Sciences（中国科学院大学）
Detecting the neutrino mass via the cross-correlation between matter tracers and the ISWRS effect?
Università degli Studi di Roma Tor Vergata（罗马第二大学）；INFN, Sezione di Roma 2（意大利国家核物理研究所罗马第二分部）；Astronomical Observatory of the Autonomous Region of the Aosta Valley (OAVdA)（瓦莱达奥斯塔大区天文台）；INAF – Istituto di Astrofisica Spaziale e Fisica cosmica di Milano (IASF-MI)（意大利国家天体物理研究所米兰空间天体物理与宇宙物理研究所）
Cross-Correlating the Universe: The Gravitational Wave Background and Large-Scale Structure
Università degli Studi di Padova（帕多瓦大学）；INFN, Sezione di Padova（意大利国家核物理研究所帕多瓦分部）；INAF - Osservatorio Astronomico di Padova（意大利国家天体物理研究所帕多瓦天文台）；University of Connecticut（康涅狄格大学）；Yale University（耶鲁大学）
It has been recognized that the observables of large-scale structure (LSS) is susceptible to long-wavelength density and tidal fluctuations whose wavelengths exceed the accessible scale of a finite-volume observation, referred to as the super-sample modes. The super-sample modes modulate the growth and expansion rate of local structures, thus affecting the cosmological information encoded in the statistics of galaxy clustering data. In this paper, based on the Lagrangian perturbation theory, we develop a new formalism to systematically compute the response of a biased tracer of LSS, which is e…
Probing the Bias of Large-Scale Structure with Unlocalized Fast Radio Bursts
School of Physics and Astronomy, Beijing Normal University（北京师范大学物理与天文学院）；Institute for Frontiers in Astronomy and Astrophysics, Beijing Normal University（北京师范大学前沿天体物理研究所）
A specific value for the cosmological constant, Λ, can account for late-time cosmic acceleration. However, motivated by the so-called cosmological constant problem(s), several alternative mechanisms have been explored. To date, a host of well-studied dynamical dark energy and modified gravity models exists. Going beyond ΛCDM often comes with additional degrees of freedom (dofs). For these to pass existing observational tests, an efficient screening mechanism must be in place. The linear and quasi-linear regimes of structure formation are ideal probes of such dofs and can capture the onset of s…
Plenty of crucial information about our Universe is encoded in the cosmic large-scale structure (LSS). However, the extractions of these information are usually hindered by the nonlinearities of the LSS, which can be largely alleviated by various techniques known as the reconstruction. In realistic applications, the efficiencies of these methods are always degraded by many limiting factors, a quite important one being the shot noise induced by the finite number density of biased matter tracers (i.e., luminous galaxies or dark matter halos) in observations. In this work, we explore the gains of…
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…
The Consistency Relations for the Large Scale Structure provide a link between the amplitude of Baryonic Acoustic Oscillations in the squeezed bispectrum (BS) and in the power spectrum (PS). This relation depends on the large scale bias of the considered tracer, $b_α$, and on the growth rate of structures, $f$. Remarkably, originating from basic symmetry principles, this relation is exact and independent on the underlying cosmological model. By analysing data from large volume simulations, both for dark matter and for haloes, we illustrate how BS and PS measurements can be used to extract $b_α…
We derive exact analytic solutions for density and velocity fields to all orders in Eulerian standard perturbation theory for $Λ$CDM cosmology. In particular, we show that density and velocity field kernels can be written in a separable form in time and momenta at each perturbative order. The kernel solutions are built from an analytic basis of momentum operators and their time-dependent coefficients, which solve a set of recursive differential equations. We also provide an exact closed perturbative solution for such coefficients, expanding around the (quasi-)EdS approximation. We find that th…
Recent development in the reconstruction of the large-scale structure (LSS) has seen significant improvement in restoring the linear baryonic acoustic oscillation (BAO) from at least the non-linear matter field. This outstanding performance is achieved by iteratively solving the Monge-Ampere equation of the mass conservation. However, this technique also relies on several assumptions that are not valid in reality, namely the longitudinal displacement, the absence of shell-crossing and homogeneous initial condition. In particular, the conservation equation of the tracers comprises the biasing i…
The Lagrangian peaks of a 1D cosmological random field representing dark matter are used as a proxy for a catalogue of biased tracers in order to investigate the small-scale exclusion in the two-halo term. The two-point correlation function of peaks of a given height is numerically estimated and analytical approximations that are valid inside the exclusion zone are derived. The resulting power spectrum of these tracers is investigated and shows clear deviations from Poisson noise at low frequencies. On large scales, the convergence of a perturbative bias expansion is discussed. Finally, we go …
The Effective Field Theory of Large-Scale Structure (EFTofLSS) provides a consistent perturbative framework for describing the statistical distribution of cosmological large-scale structure. In a previous EFTofLSS calculation that involved the one-loop power spectra and tree-level bispectra, it was shown that the $k$-reach of the prediction for biased tracers is comparable for all investigated masses if suitable higher-derivative biases, which are less suppressed for more massive tracers, are added. However, it is possible that the non-linear biases grow faster with tracer mass than the linear…
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…
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 extend the scale-dependent Gaussian Streaming Model (GSM) to produce analytical predictions for the anisotropic redshift-space correlation function for biased tracers in modified gravity models. Employing the Convolution Lagrangian Perturbation Theory (CLPT) re-summation scheme, with a local Lagrangian bias schema provided by the peak-background split formalism, we predict the necessary ingredients that enter the GSM, the real-space halo pairwise velocity and the pairwise velocity dispersion. We further consider effective field theory contributions to the pairwise velocity dispersion in ord…
We compare analytic predictions for real and Fourier space two-point statistics for biased tracers from a variety of Lagrangian Perturbation Theory approaches against those from state of the art N-body simulations in $f(R)$ Hu-Sawicki and the nDGP braneworld modified gravity theories. We show that the novel physics of gravitational collapse in scalar tensor theories with the chameleon or the Vainshtein screening mechanism can be effectively factored in with bias parameters analytically predicted using the Peak-Background Split formalism when updated to include the environmental sensitivity of …
Cosmic Microwave Background (CMB) is a powerful probe to study the early universe and various cosmological models. Weak gravitational lensing affects the CMB by changing its power spectrum, but meanwhile, it also carries information about the distribution of lensing mass and hence, the large scale structure (LSS) of the universe. When studies of the CMB is combined with the tracers of LSS, one can constrain cosmological models, models of LSS development and astrophysical parameters simultaneously. The main focus of this project is to study the cross-correlations between CMB lensing and the gal…
In this paper we test the perturbative halo bias model at the field level. The advantage of this approach is that any analysis can be done without sample variance if the same initial conditions are used in simulations and perturbation theory calculations. We write the bias expansion in terms of modified bias operators in Eulerian space, designed such that the large bulk flows are automatically resummed and not treated perturbatively. Using these operators, the bias model accurately matches the Eulerian density of halos in N-body simulations. The mean-square model error is close to the Poisson …
The dark matter halos that host galaxies and clusters form out of initial high-density patches, providing a biased tracer of the linear matter density field. In the simplest local bias approximation, the halo field is treated as a perturbative series in the average overdensity of the Lagrangian patch. In more realistic models, however, additional quantities will affect the clustering of halo-patches, and this expansion becomes a function of several stochastic variables. In this paper, we present a general multivariate expansion scheme that can parametrize the clustering of any biased Lagrangia…
Gravitationally collapsed objects are known to be biased tracers of an underlying density contrast. Using symmetry arguments, generalised biasing schemes have recently been developed to relate the halo density contrast $δ_h$ with the underlying density contrast $δ$, divergence of velocity $θ$ and their higher-order derivatives. This is done by constructing invariants such as $s, t, ψ,η$. We show how the generating function formalism in Eulerian standard perturbation theory (SPT) can be used to show that many of the additional terms based on extended Galilean and Lifshitz symmetry actually do n…
We study the performance of the perturbative bias expansion when combined with the multi-tracer technique, and their impact on the extraction of cosmological parameters. We consider two populations of tracers of large-scale structure and perform a series of Markov chain Monte Carlo analysis for those two tracers separately. The constraints in $ω_{\rm cdm}$ and $h$ using multi-tracer are less biased and approximately $60\%$ better than those obtained for a single tracer. The multi-tracer approach also provides stronger constraints on the bias expansion parameters, breaking degeneracies between …
Biased tracers, Hybrid Effective Field Theory and Modified Gravity
CBPF - Brazilian Center for Research in Physics（巴西物理研究中心）；Institute for Computational Cosmology, Department of Physics, Durham University（杜伦大学）；Institute of Cosmology and Gravitation, University of Portsmouth（朴茨茅斯大学）；Kavli IPMU (WPI), UTIAS, The University of Tokyo（东京大学）；Yukawa Institute for Theoretical Physics, Kyoto University（京都大学）
We study the ability of perturbative models with effective field theory contributions and infra-red resummation to model the redshift space clustering of biased tracers in models where the linear power spectrum has "features" -- either imprinted during inflation or induced by non-standard expansion histories. We show that both Eulerian and Lagrangian perturbation theory are capable of reproducing the Fourier space two-point functions of halos up to the non-linear scale from a suite of $4096^3$ particle N-body simulations. This is the first demonstration that perturbative models can accurately …
Associating the formation sites of haloes with the maxima of the smoothed linear density field, we present non-perturbative predictions for the Lagrangian and evolved halo correlation functions that are valid at all separations. In Lagrangian space, we find significant deviations from the perturbative bias calculation at small scales, in particular, a pronounced exclusion region where $ξ=-1$ for maxima of unequal height. Our predictions are in good agreement with the Lagrangian clustering of dark matter proto-haloes reconstructed from N-body simulations. Our predictions for the mean infall and…
We present the one-loop perturbation theory for the power spectrum of the marked density field of matter and biased tracers in real- and redshift-space. The statistic has been shown to yield impressive constraints on cosmological parameters; to exploit this, we require an accurate and computationally inexpensive theoretical model. Comparison with $N$-body simulations demonstrates that linear theory fails on all scales, but inclusion of one-loop Effective Field Theory terms gives a substantial improvement, with $\sim 5\%$ accuracy at $z = 1$. The expansion is less convergent in redshift-space (…
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…
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…
The integrated Sachs-Wolfe (ISW) effect and its non-linear extension Rees-Sciama (RS) effect provide us the information of the time evolution of gravitational potential. The cross-correlation between the cosmic microwave background (CMB) and the large scale structure (LSS) is known as a promising way to extract the ISW (RS) effect. It is known that the RS effect shows the unique behavior by changing the anti-correlated cross correlation between the CMB and the mass tracer into the positively correlated cross correlation compared to the linear ISW effect. We show that the dependence of this fli…
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 bo…
The interpretation of redshift surveys requires modeling the relationship between large-scale fluctuations in the observed number density of tracers, $δ_\mathrm{h}$, and the underlying matter density, $δ$. Bias models often express $δ_\mathrm{h}$ as a truncated series of integro-differential operators acting on $δ$, each weighted by a bias parameter. Due to the presence of `composite operators' (obtained by multiplying fields evaluated at the same spatial location), the linear bias parameter measured from clustering statistics does not coincide with that appearing in the bias expansion. This i…
