Theory Of Large-scale Structure Research Articles

Spherical bispectrum: a novel visualization scheme for facilitating comparisons

Recent developments of Perturbation Theory (PT), specifically the Effective Field Theory of Large Scale Structure (EFTofLSS) and its equivalents, have proven powerful in analyzing galaxy clustering statistics such as the galaxy power spectrum and bispectrum. To further this pursuit, we have devised a novel spherical-bispectrum visualization scheme that collapses configuration dependencies to highlight the scale dependence of the bispectrum. The resulting one-dimensional curves facilitate the comparison between different bispectra, for example, from simulation and PT calculation. Using the new scheme, we present a quantitative analysis of the accuracy of PT modeling by comparing PT's analytical prediction to the result from a suite of Quijote simulations. Specifically, we determine k NL, the wavenunmber below which the analytical prediction matches well with the N-body result by inspectingboth leading order (LO) and next-to-leading order (NLO) power spectrum and bispectrum at redshifts z = 0, 0.5, 1, 2, 3. We also quantify the binning effect in Fourier space and show that an appropriate correction must be applied to the analytic predictions in order to compare them with the discrete Fourier transform results obtained from N-body-simulation or real data.

Interferometric H i intensity mapping: perturbation theory predictions and foreground removal effects

ABSTRACT We provide perturbation theory predictions for the H i intensity mapping power spectrum multipoles using the Effective Field Theory of Large Scale Structure, which should allow us to exploit mildly non-linear scales. Assuming survey specifications typical of proposed interferometric H i intensity mapping experiments like Canadian Hydrogen Observatory and Radio transient Detector and PUMA, and realistic ranges of validity for the perturbation theory modelling, we run mock full shape Markov chain Monte Carlo (MCMC) analyses at z = 0.5, and compare with Stage-IV optical galaxy surveys. We include the impact of 21cm foreground removal using simulations-based prescriptions, and quantify the effects on the precision and accuracy of the parameter estimation. We vary 11 parameters in total: three cosmological parameters, seven bias and counter terms parameters, and the H i brightness temperature. Amongst them, the four parameters of interest are: the cold dark matter density, ωc, the Hubble parameter, h, the primordial amplitude of the power spectrum, As, and the linear H i bias, b1. For the best-case scenario, we obtain unbiased constraints on all parameters with $\lt 3{{\ \rm per\ cent}}$ errors at $68{{\ \rm per\ cent}}$ confidence level. When we include the foreground removal effects, the parameter estimation becomes strongly biased for ωc, h, and b1, while As is less biased (<2σ). We find that scale cuts $k_{\rm min} \ge 0.03 \ h\,\mathrm{Mpc}^{-1}$ are required to return accurate estimates for ωc and h, at the price of a decrease in the precision, while b1 remains strongly biased. We comment on the implications of these results for real data analyses.

Full-shape galaxy power spectra and the curvature tension

ABSTRACT With recent evidence for a possible ‘curvature tension’ among early and late universe cosmological probes, Effective Field Theories of Large Scale Structure (EFTofLSS) have emerged as a promising new framework to generate constraints on Ωk that are independent of both CMB measurements, and some of the assumptions of flatness that enter into other large-scale structure analyses. In this work we use EFTofLSS to simultaneously constrain measurements from the 6dFGS, BOSS, and eBOSS catalogues, representing the most expansive full-shape investigation of curvature to date. Using the Bayesian evidence ratio our full-shape data assigns betting odds of 2:1 in favour of curvature, indicating present measurements remain broadly compatible with both flat and curved cosmological models. When our full-shape sample is combined with Planck 2018 CMB measurements, we break the geometric degeneracy and recover a joint fit on Ωk of $-0.0037^{+0.0025}_{-0.0026}$. Using the suspiciousness statistic we find evidence for a moderate tension between Planck 2018 and our suite of full-shape measurements, at a significance of $1.86 ^{+0.13}_{-0.11} \sigma$ (p ∼ 0.06 ± 0.02). These results demonstrate the usefulness of full-shape clustering measurements as a CMB independent probe of curvature in the ongoing curvature tension debate.

New early dark energy is compatible with current LSS data

Recently a full-shape analysis of large-scale structure (LSS) data was employed to provide new constraints on a class of Early Dark Energy (EDE) models. In this note, we derive similar constraints on New Early Dark Energy (NEDE) using the publicly available PyBird code, which makes use of the effective field theory of LSS. We study the NEDE base model with the fraction of NEDE and the trigger field mass as two additional parameters allowed to vary freely while making simplifying assumptions about the decaying fluid sector. Including the full-shape analysis of LSS together with measurements of the cosmic microwave background (CMB), baryonic acoustic oscillations (BAO) and supernovae (SN) data, we report $ H_0= 71.2 \pm 1.0~\textrm{km}\, \textrm{s}^{-1}\, \textrm{Mpc}^{-1}$ ($68 \%$ C.L.) together with a $\simeq 4 \, \sigma$ evidence for a non-vanishing fraction of NEDE. This is an insignificant change to the value previously found without full-shape LSS data, $ H_0= 71.4 \pm 1.0~\textrm{km}\, \textrm{s}^{-1}\, \textrm{Mpc}^{-1} $ ($68 \%$ C.L.). As a result, while the NEDE fit cannot be improved upon the inclusion of additional LSS data, it is also not adversely affected by it, making it compatible with current constraints from LSS data. In fact, we find evidence that the effective field theory of LSS acts in favor of NEDE.

Precise calibration of the one-loop trispectrum in the effective field theory of large scale structure

The Large-Scale Structure (LSS) of the universe has the potential to provide decisive answers to the remaining open questions in cosmology. Early attempts at modelling it analytically focused on using perturbation theory. However, small-scale effects introduced by gravitational collapse cannot be described perturbatively and this failure of perturbation theory is reflected even on the largest scales. The Effective Field Theory of Large Scale Structure (EFTofLSS) has emerged as a consistent method for describing LSS on large scales by introducing counterterms that account for the effects of small-scale dynamics. So far studies of the EFT have mostly focused on the two and three point functions with little attention devoted to the four point function or trispectrum. The trispectrum probes cubic interactions arising from non-linear clustering, biasing, and primordial non-Gaussianities, and constitutes a key element of the covariance matrix of the power spectrum. In this paper, we present explicit calibrations of the EFT counterterms for the one-loop trispectrum. Specifically, we find clear evidence for non-zero EFT corrections. We define two one-parameter ans\"{a}tze for the counterterm of the one-loop propagator and show that they provide a good correction to the residual at scales below k~0.07 h/Mpc. We then take the amplitudes of the linear and quadratic counterkernels calculated in our previous paper on the bispectrum and use them in the remaining counterterms, establishing consistency of the counterterms in the two, three and four point function. We also show that the commonly used EdS approximation for the growth of the density fields leads to errors that are of the same magnitude as loop corrections to the trispectrum on large scales.

Precise calibration of the one-loop bispectrum in the effective field theory of large scale structure

The large-scale structure (LSS) provides a three-dimensional cosmological probe containing significantly more information than the CMB, but its small-scale non-linearities render standard perturbation theory unreliable beyond tree-level. The authors study the bispectrum of the LSS, an important cosmological observable for non-Gaussianity, in the effective field theory approach up to 1-loop order, while taking the full $\mathrm{\ensuremath{\Lambda}}$CDM time-dependence into account, and show that this is essential for the next loop-level.

Constraining early dark energy with large-scale structure

An axion-like field comprising $\sim 10\%$ of the energy density of the universe near matter-radiation equality is a candidate to resolve the Hubble tension; this is the "early dark energy" (EDE) model. However, as shown in Hill et al. (2020), the model fails to simultaneously resolve the Hubble tension and maintain a good fit to both cosmic microwave background (CMB) and large-scale structure (LSS) data. Here, we use redshift-space galaxy clustering data to sharpen constraints on the EDE model. We perform the first EDE analysis using the full-shape power spectrum likelihood from the Baryon Oscillation Spectroscopic Survey (BOSS), based on the effective field theory (EFT) of LSS. The inclusion of this likelihood in the EDE analysis yields a $25\%$ tighter error bar on $H_0$ compared to primary CMB data alone, yielding $H_0 = 68.54^{+0.52}_{-0.95}$ km/s/Mpc ($68\%$ CL). In addition, we constrain the maximum fractional energy density contribution of the EDE to $f_{\rm EDE} < 0.072$ ($95\%$ CL). We explicitly demonstrate that the EFT BOSS likelihood yields much stronger constraints on EDE than the standard BOSS likelihood. Including further information from photometric LSS surveys,the constraints narrow by an additional $20\%$, yielding $H_0 = 68.73^{+0.42}_{-0.69}$ km/s/Mpc ($68\%$ CL) and $f_{\rm EDE}<0.053$ ($95\%$ CL). These bounds are obtained without including local-universe $H_0$ data, which is in strong tension with the CMB and LSS, even in the EDE model. We also refute claims that MCMC analyses of EDE that omit SH0ES from the combined dataset yield misleading posteriors. Finally, we demonstrate that upcoming Euclid/DESI-like spectroscopic galaxy surveys can greatly improve the EDE constraints. We conclude that current data preclude the EDE model as a resolution of the Hubble tension, and that future LSS surveys can close the remaining parameter space of this model.

Effective halo model: Creating a physical and accurate model of the matter power spectrum and cluster counts

We introduce a physically motivated model of the matter power spectrum, based on the halo model and perturbation theory. This model achieves 1% accuracy on all $k$-scales between $k=0.02h\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}$ to $k=1h\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}$. Our key ansatz is that the number density of halos depends on the nonlinear density contrast filtered on some unknown scale $R$. Using the effective field theory of large scale structure to evaluate the two-halo term, we obtain a model for the power spectrum with only two fitting parameters: $R$ and the effective ``sound speed,'' which encapsulates small-scale physics. This is tested with two suites of cosmological simulations across a broad range of cosmologies and found to be highly accurate. Due to its physical motivation, the statistics can be easily extended beyond the power spectrum; we additionally derive the one-loop covariance matrices of cluster counts and their combination with the matter power spectrum. This yields a significantly better fit to simulations than previous models, and includes a new model for supersample effects, which is rigorously tested with separate universe simulations. At low redshift, we find a significant ($\ensuremath{\sim}10%$) exclusion covariance from accounting for the finite size of halos which has not previously been modeled. Such power spectrum and covariance models will enable joint analysis of upcoming large-scale structure surveys, gravitational lensing surveys, and cosmic microwave background maps on scales down to the nonlinear scale. We provide a publicly released python code.

Nonlinear contributions to angular power spectra

Future galaxy clustering surveys will probe small scales where non-linearities become important. Since the number of modes accessible on intermediate to small scales is very high, having a precise model at these scales is important especially in the context of discriminating alternative cosmological models from the standard one. In the mildly non-linear regime, such models typically differ from each other, and galaxy clustering data will become very precise on these scales in the near future. As the observable quantity is the angular power spectrum in redshift space, it is important to study the effects of non-linear density and redshift space distortion (RSD) in the angular power spectrum. We compute non-linear contributions to the angular power spectrum using a flat-sky approximation that we introduce in this work, and compare the results of different perturbative approaches with $N$-body simulations. We find that the TNS perturbative approach is significantly closer to the $N$-body result than Eulerian or Lagrangian 1-loop approximations, effective field theory of large scale structure or a halofit-inspired model. However, none of these prescriptions is accurate enough to model the angular power spectrum well into the non-linear regime. In addition, for narrow redshift bins, $\Delta z \lesssim 0.01$, the angular power spectrum acquires non-linear contributions on all scales, right down to $\ell=2$, and is hence not a reliable tool at this time. To overcome this problem, we need to model non-linear RSD terms, for example as TNS does, but for a matter power spectrum that remains reasonably accurate well into the deeply non-linear regime, such as halofit.

The effective field theory of large scale structure at three loops

We study the power spectrum of dark matter density fluctuations in the framework of the Effective Field Theory of Large Scale Structures (EFTofLSS) up to three loop orders. We show that the extra coefficients in the EFT are sufficient to match numerical simulations with percent accuracy when a generic renormalization prescription is implemented (allowing for running of the individual counter-terms). We show that the level of accuracy increases with respect to the two loop results, up to k ≃ 0.4 h Mpc−1 at redshift z=0, although the overall improvement is somewhat marginal. At the same time, we argue there is evidence that the behavior of the loop expansion in the EFTofLSS is typical of an asymptotic series, already on the brink of its maximum predictive power (at z=0). Hence, the inclusion of higher orders will likely deteriorate the matching to data, even at moderate values of k. Part of the reason for this behavior is due to large contributions to the (renormalized) power spectrum at three loop order from mildly non-linear scales, even after the UV counter-terms are included. In conclusion, the EFTofLSS to three loop orders provides the best approximation to the (deterministic part of the) power spectrum in the weakly non-linear regime at z=0, and higher loops are not expected to improve our level of accuracy.

Assessing non-linear models for galaxy clustering III: theoretical accuracy for stage IV surveys

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 using higher order multipoles, a larger survey volume and a more highly biased tracer catalogue. We find that under all tests, the TNS model's range of validity remains robust and is found to be much higher than previous estimates. The EFTofLSS model fails to capture the spectra for highly biased tracers as well as becoming biased at lower wavenumbers when considering a very large survey volume. Further, we find that the marginalised constraints on f for all analyses are stronger when using the TNS model.

Solving the Vlasov equation in two spatial dimensions with the Schrödinger method

We demonstrate that the Vlasov equation describing collisionless self-gravitating matter may be solved with the so-called Schr\"odinger method (ScM). With the ScM, one solves the Schr\"odinger-Poisson system of equations for a complex wave function in d dimensions, rather than the Vlasov equation for a 2d-dimensional phase space density. The ScM also allows calculating the d-dimensional cumulants directly through quasi-local manipulations of the wave function, avoiding the complexity of 2d-dimensional phase space. We perform for the first time a quantitive comparison of the ScM and a conventional Vlasov solver in d=2 dimensions. Our numerical tests were carried out using two types of cold cosmological initial conditions: the classic collapse of a sine wave and those of a gaussian random field as commonly used in cosmological cold dark matter N-body simulations. We compare the first three cumulants, that is, the density, velocity and velocity dispersion, to those obtained by solving the Vlasov equation using the publicly available code ColDICE. We find excellent qualitative and quantitative agreement between these codes, demonstrating the feasibility and advantages of the ScM as an alternative to N-body simulations. We discuss, the emergence of effective vorticity in the ScM through the winding number around the points where the wave function vanishes. As an application we evaluate the background pressure induced by the non-linearity of large scale structure formation, thereby estimating the magnitude of cosmological backreaction. We find that it is negligibly small and has time dependence and magnitude compatible with expectations from the effective field theory of large scale structure.

Efficient exploration of cosmology dependence in the EFT of LSS

The most effective use of data from current and upcoming large scale structure (LSS) and CMB observations requires the ability to predict the clustering of LSS with very high precision. The Effective Field Theory of Large Scale Structure (EFTofLSS) provides an instrument for performing analytical computations of LSS observables with the required precision in the mildly nonlinear regime. In this paper, we develop efficient implementations of these computations that allow for an exploration of their dependence on cosmological parameters. They are based on two ideas. First, once an observable has been computed with high precision for a reference cosmology, for a new cosmology the same can be easily obtained with comparable precision just by adding the difference in that observable, evaluated with much less precision. Second, most cosmologies of interest are sufficiently close to the Planck best-fit cosmology that observables can be obtained from a Taylor expansion around the reference cosmology. These ideas are implemented for the matter power spectrum at two loops and are released as public codes. When applied to cosmologies that are within 3σ of the Planck best-fit model, the first method evaluates the power spectrum in a few minutes on a laptop, with results that have 1% or better precision, while with the Taylor expansion the same quantity is instantly generated with similar precision. The ideas and codes we present may easily be extended for other applications or higher-precision results.

Principal shapes and squeezed limits in the effective field theory of large scale structure

We apply an orthogonalization procedure on the effective field theory of large scale structure (EFT of LSS) shapes, relevant for the angle-averaged bispectrum and non-Gaussian covariance of the matter power spectrum at one loop. Assuming natural-sized EFT parameters, this identifies a linear combination of EFT shapes—referred to as the principal shape—that gives the dominant contribution for the whole kinematic plane, with subdominant combinations suppressed by a few orders of magnitude. For the covariance, our orthogonal transformation is in excellent agreement with a principal component analysis applied to available data. Additionally we find that, for both observables, the coefficients of the principal shapes are well approximated by the EFT coefficients appearing in the squeezed limit, and are thus measurable from power spectrum response functions. Employing data from N-body simulations for the growth-only response, we measure the single EFT coefficient describing the angle-averaged bispectrum with \U0001d4aa(10%) precision. These methods of shape orthogonalization and measurement of coefficients from response functions are valuable tools for developing the EFT of LSS framework, and can be applied to more general observables.

Non-Gaussian covariance of the matter power spectrum in the effective field theory of large scale structure

We compute the non-Gaussian contribution to the covariance of the matter power spectrum at one-loop order in standard perturbation theory (SPT), using the framework of the effective field theory (EFT) of large scale structure (LSS). The complete one-loop contributions are evaluated for the first time, including the leading EFT corrections that involve seven independent operators, of which four appear in the power spectrum and bispectrum. We compare the non-Gaussian part of the one-loop covariance computed with both SPT and EFT of LSS to two separate simulations. In one simulation, we find that the one-loop prediction from SPT reproduces the simulation well to ${k}_{i}+{k}_{j}\ensuremath{\sim}0.25\text{ }\text{ }\mathrm{h}/\mathrm{Mpc}$, while in the other simulation we find a substantial improvement of EFT of LSS (with one free parameter) over SPT, more than doubling the range of $k$ where the theory accurately reproduces the simulation. The disagreement between these two simulations points to unaccounted for systematics, highlighting the need for improved numerical and analytic understanding of the covariance.

The trispectrum in the Effective Field Theory of Large Scale Structure

We compute the connected four point correlation function (the trispectrum in Fourier space) of cosmological density perturbations at one-loop order in Standard Perturbation Theory (SPT) and the Effective Field Theory of Large Scale Structure (EFT of LSS). This paper is a companion to our earlier work on the non-Gaussian covariance of the matter power spectrum, which corresponds to a particular wavenumber configuration of the trispectrum. In the present calculation, we highlight and clarify some of the subtle aspects of the EFT framework that arise at third order in perturbation theory for general wavenumber configurations of the trispectrum. We consistently incorporate vorticity and non-locality in time into the EFT counterterms and lay out a complete basis of building blocks for the stress tensor. We show predictions for the one-loop SPT trispectrum and the EFT contributions, focusing on configurations which have particular relevance for using LSS to constrain primordial non-Gaussianity.

Systematic renormalization of the effective theory of Large Scale Structure

A perturbative description of Large Scale Structure is a cornerstone of our understanding of the observed distribution of matter in the universe. Renormalization is an essential and defining step to make this description physical and predictive. Here we introduce a systematic renormalization procedure, which neatly associates counterterms to the UV-sensitive diagrams order by order, as it is commonly done in quantum field theory. As a concrete example, we renormalize the one-loop power spectrum and bispectrum of both density and velocity. In addition, we present a series of results that are valid to all orders in perturbation theory. First, we show that while systematic renormalization requires temporally non-local counterterms, in practice one can use an equivalent basis made of local operators. We give an explicit prescription to generate all counterterms allowed by the symmetries. Second, we present a formal proof of the well-known general argument that the contribution of short distance perturbations to large scale density contrast δ and momentum density π(k) scale as k2 and k, respectively. Third, we demonstrate that the common practice of introducing counterterms only in the Euler equation when one is interested in correlators of δ is indeed valid to all orders.

Effective field theory of large scale structure at two loops: The apparent scale dependence of the speed of sound

We study the Effective Field Theory of Large Scale Structure for cosmic density and momentum fields. We show that the finite part of the two-loop calculation and its counterterms introduce an apparent scale dependence for the leading order parameter $c_\text{s}^2$ of the EFT starting at k=0.1 h/Mpc. These terms limit the range over which one can trust the one-loop EFT calculation at the 1 % level to k<0.1 h/Mpc at redshift z=0. We construct a well motivated one parameter ansatz to fix the relative size of the one- and two-loop counterterms using their high-k sensitivity. Although this one parameter model is a very restrictive choice for the counterterms, it explains the apparent scale dependence of $c_\text{s}^2$ seen in simulations. It is also able to capture the scale dependence of the density power spectrum up to k$\approx$ 0.3 h/Mpc at the 1 % level at redshift $z=0$. Considering a simple scheme for the resummation of large scale motions, we find that the two loop calculation reduces the need for this IR-resummation at k<0.2 h/Mpc. Finally, we extend our calculation to momentum statistics and show that the same one parameter model can also describe density-momentum and momentum-momentum statistics.

The bispectrum in the Effective Field Theory of Large Scale Structure

We study the bispectrum in the Effective Field Theory of Large Scale Structure, consistently accounting for the effects of short-scale dynamics. We begin by proving that, as long as the theory is perturbative, it can be formulated to arbitrary order using only operators that are local in time. We then derive all the new operators required to cancel the UV-divergences and obtain a physically meaningful prediction for the one-loop bispectrum. In addition to new, subleading stochastic noises and the viscosity term needed for the one-loop power spectrum, we find three new effective operators. The three new parameters can be constrained by comparing with N-body simulations. The best fit is precisely what is suggested by the structure of UV-divergences, hence justifying a formula for the EFTofLSS bispectrum whose only fitting parameter is already fixed by the power spectrum. This result predicts the bispectrum of N-body simulations up to kmax≈0.22 h Mpc−1 at 0z=, an improvement by nearly a factor of two as compared to one-loop standard perturbation theory.

Coarse-grained cosmological perturbation theory: Stirring up the dust model

We study the effect of coarse graining the dynamics of a pressureless self-gravitating fluid (coarse-grained dust) in the context of cosmological perturbation theory, in both the Eulerian and Lagrangian frameworks. We obtain recursion relations for the Eulerian perturbation kernels of the coarse-grained dust model by relating them to those of the standard pressureless fluid model. The effect of the coarse graining is illustrated by means of power and cross spectra for the density and velocity, which are computed up to one-loop order. In particular, the large-scale vorticity power spectrum that arises naturally from a mass-weighted velocity is derived from first principles. We find qualitatively good agreement for the magnitude, shape, and spectral index of the vorticity power spectrum with recent measurements from $N$-body simulations and results from the effective field theory of large-scale structure. To lay the ground for applications in the context of Lagrangian perturbation theory, we finally describe how the kernels obtained in Eulerian space can be mapped to Lagrangian ones.