Effective Field Theory Of Large-Scale Structure Research Articles

The BOSS bispectrum analysis at one loop from the Effective Field Theory of Large-Scale Structure

We analyze the BOSS power spectrum monopole and quadrupole, and the bispectrum monopole and quadrupole data, using the predictions from the Effective Field Theory of Large-Scale Structure (EFTofLSS). Specifically, we use the one loop prediction for the power spectrum and the bispectrum monopole, and the tree level for the bispectrum quadrupole. After validating our pipeline against numerical simulations as well as checking for several internal consistencies, we apply it to the observational data. We find that analyzing the bispectrum monopole to higher wavenumbers thanks to the one-loop prediction, as well as the addition of the tree-level quadrupole, significantly reduces the error bars with respect to our original analysis of the power spectrum at one loop and bispectrum monopole at tree level. After fixing the spectral tilt to Planck preferred value and using a Big Bang Nucleosynthesis prior, we measure σ 8 = 0.794 ± 0.037, h = 0.692 ± 0.011, and Ω m = 0.311 ± 0.010 to about 4.7%, 1.6%, and 3.2%, at 68% CL, respectively.This represents an error bar reduction with respect to the power spectrum-only analysis of about 30%, 18%, and 13% respectively. Remarkably, the results are compatible with the ones obtained with a power-spectrum-only analysis, showing the power of the EFTofLSS in simultaneously predicting several observables. We find no tension with Planck.

Cosmological constraints on early dark energy from the full shape analysis of eBOSS DR16

ABSTRACT We evaluate the effectiveness of early dark energy (EDE) in addressing the Hubble tension using the luminous red galaxy (LRG), quasar (QSO), and emission line galaxy (ELG) samples from the completed eBOSS survey. We perform cosmological parameter measurements based on full shape analysis of the power spectrum employing the effective field theory of large-scale structure (EFTofLSS). EDE is known to strongly suffer from volume projection effects, complicating cosmological constraints’ interpretation. To quantify the volume projection effects within an EDE full shape analysis, we explore the impact of different prior choices on the nuisance parameters of EFTofLSS through an extensive mock study. We compare classical Gaussian priors to the non-informative Jeffreys prior, known to mitigate volume projection effects in ΛCDM. Our full shape analysis combines eBOSS and BOSS data with Planck, external Baryon Acoustic Oscillation (BAO), PantheonPlus, and SH0ES supernova data. EDE reduces the tension from 5.2σ to 3σ compared to ΛCDM, yielding $H_0=71.73_{-0.86}^{+0.82}$ km s−1 Mpc−1 with $f_\mathrm{EDE} = 0.1179_{-0.022}^{+0.025}$ (Gaussian priors) and $H_0=72.03_{-0.87}^{+0.82}$ km s−1 Mpc−1 with $f_\mathrm{EDE} = 0.1399_{-0.022}^{+0.023}$ (Jeffreys prior). Although the Hubble tension is mitigated compared to ΛCDM, the inclusion of eBOSS data amplifies the tension within EDE from 2σ to 3σ, in contrast to the full shape analysis of BOSS data with Planck, external BAO, PantheonPlus, and SH0ES. This highlights the significance of incorporating additional large-scale structure data in discussions concerning models aiming to resolve the Hubble tension.

Limits on clustering and smooth quintessence from the EFTofLSS

We apply the Effective Field Theory of Large-Scale Structure (EFTofLSS) to analyze cosmological models with clustering quintessence, which allows us to consistently describe the parameter region in which the quintessence equation of state w < -1. First, we extend the description of biased tracers in redshift space to the presence of clustering quintessence, and compute the one-loop power spectrum. We solve the EFTofLSS equations using the exact time dependence, which is relevant to obtain unbiased constraints. Then, fitting the full shape of BOSS pre-reconstructed power spectrum measurements, the BOSS post-reconstruction BAO measurements, BAO measurements from 6DF/MGS and eBOSS, the Supernovae from Pantheon, and a prior from BBN, we bound the clustering quintessence equation of state parameter w = -1.011-0.048 +0.053 at 68% C.L. Further combining with Planck, we obtain w = -1.028-0.030 +0.037 at 68% C.L. We also obtain constraints on smooth quintessence, in the physical regime w ≥ -1: combining all datasets, we get -1 ≤ w < -0.979 at 68% C.L. These results strongly support a cosmological constant.

Taming redshift-space distortion effects in the EFTofLSS and its application to data

Former analyses of the BOSS data using the Effective Field Theory of Large-Scale Structure (EFTofLSS) have measured that the largest counterterms are the redshift-space distortion ones. This allows us to adjust the power-counting rules of the theory, and to explicitly identify that the leading next-order terms have a specific dependence on the cosine of the angle between the line-of-sight and the wavenumber of the observable, μ. Such a specific μ-dependence allows us to construct a linear combination of the data multipoles, P̸, where these contributions are effectively projected out, so that EFTofLSS predictions for P̸ have a much smaller theoretical error and so a much higher k-reach. The remaining data are organized in wedges in μ space, have a μ-dependent k-reach because they are not equally affected by the leading next-order contributions, and therefore can have a higher k-reach than the multipoles. Furthermore, by explicitly including the highest next-order terms, we define a `one-loop+' procedure, where the wedges have even higher k-reach. We study the effectiveness of these two procedures on several sets of simulations and on the BOSS data. The resulting analysis has identical computational cost as the multipole-based one, but leads to an improvement on the determination of some of the cosmological parameters that ranges from 10% to 100%, depending on the survey properties.

Testing the assumptions of the Effective Field Theory of Large-Scale Structure

The Effective Field Theory of Large-Scale Structure (EFTofLSS) attempts to amend some of the shortcomings of the traditional perturbative methods used in cosmology. It models the evolution of long-wavelength perturbations above a cutoff scale without the need for a detailed description of the short-wavelength ones. Short-scale physics is encoded in the coefficients of a series of operators composed of the long-wavelength fields, and ordered in a systematic expansion. As applied in the literature, the EFTofLSS corrects a summary statistic (such as the power spectrum) calculated from standard perturbation theory by matching it to N-body simulations or observations. This `bottom-up' construction is remarkably successful in extending the range of validity of perturbation theory. In this work, we compare this framework to a `top-down' approach, which estimates the EFT coefficients from the stress tensor of an N-body simulation, and propagates the corrections to the summary statistic. We consider simple initial conditions, viz. two sinusoidal, plane-parallel density perturbations with substantially different frequencies and amplitudes. We find that the leading EFT correction to the power spectrum in the top-down model is in excellent agreement with that inferred from the bottom-up approach which, by construction, provides an exact match to the numerical data. This result is robust to changes in the wavelength separation between the two linear perturbations. However, in our setup, the leading EFT coefficient does not always grow linearly with the cosmic expansion factor as assumed in the literature based on perturbative considerations. Instead, it decreases after orbit crossing takes place.

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.

Matryoshka II: accelerating effective field theory analyses of the galaxy power spectrum

ABSTRACT In this paper, we present an extension to the matryoshka suite of neural-network-based emulators. The new editions have been developed to accelerate effective field theory of large-scale structure (EFTofLSS) analyses of galaxy power spectrum multipoles in redshift space. They are collectively referred to as the EFTEMU. We test the EFTEMU at the power spectrum level and achieve a prediction accuracy of better than 1 per cent with BOSS-like bias parameters and counterterms on scales 0.001 ≤ k ≤ 0.19 h Mpc−1. We also run a series of mock full-shape analyses to test the performance of the EFTEMU when carrying out parameter inference. Through these mock analyses, we verify that the EFTEMU recovers the true cosmology within 1σ at several redshifts (z = [0.38, 0.51, 0.61]), and with several noise levels (the most stringent of which is Gaussian covariance associated with a volume of 50003 Mpc3 h−3). We compare the mock inference results from the EFTEMU to those obtained with a fully analytic EFTofLSS model and again find no significant bias, whilst speeding up the inference by three orders of magnitude. The EFTEMU is publicly available as part of the matryoshkaPython package.

BOSS full-shape analysis from the EFTofLSS with exact time dependence

We re-analyze the full shape of BOSS galaxy two-point function from the Effective-Field Theory of Large-Scale Structure at the one loop within ΛCDM with massive neutrinos using a big bang nucleosynthesis (BBN) prior, removing the Einstein-de Sitter (EdS) approximation in the time dependence of the loop, and, properly accounting for the redshift selection over the BOSS samples instead of assuming an effective redshift. We constrain, at 68%-confidence level (CL), the present-day matter fraction to Ωm = 0.322 ± 0.018, the Hubble constant to H 0 = 69.1 ± 0.14 (km/s)/Mpc, the log-amplitude of the primordial spectrum to ln (1010 A s) = 2.97 ± 0.25, the spectral tilt to n s = 0.938 ± 0.082, and bound the total neutrino mass to < 1.1 at 95%-CL. We find no significant shift in the posteriors of the cosmological parameters due to the EdS approximation, but a marginal difference in ln (1010 A s) due to the effective redshift approximation of about 0.4σ, where σ is the 68%-confidence interval. Regarding the EdS approximation, we check that the same conclusion holds on simulations of volume like DESI in ΛCDM and wCDM, with a BBN prior. In contrast, for an approximate, effective redshift, to be assumed, we advocate systematic assessments on redshift selection for ongoing and future large-volume surveys.

Baryonic effects in the Effective Field Theory of Large-Scale Structure and an analytic recipe for lensing in CMB-S4

Upcoming Large-Scale Structure surveys will likely become the next leading sources of cosmological information, making it crucial to have a precise understanding of the influence of baryons on cosmological observables. The Effective Field Theory of Large-Scale Structure (EFTofLSS) provides a consistent way to predict the clustering of dark matter and baryons on large scales, where their leading corrections in perturbation theory are given by a simple and calculable functional form even after the onset of baryonic processes. In this paper, we extend the two-fluid-like system up to two-loop order in perturbation theory. Along the way, we show that a new linear counterterm proportional to the relative velocity of the fluids could generically be present, but we show that its effects are expected to be small in our universe. Regardless, we show how to consistently perform perturbation theory in the presence of this new term. We find that the EFTofLSS at two-loop order can accurately account for the details of baryonic processes on large scales. We compare our results to a hydrodynamical N-body simulation at many redshifts and find that the counterterms associated with the leading corrections to dark matter and baryons start to differ between redshifts z ≈ 3 and z ≈ 2, signaling the onset of star-formation physics. We then use these fits to compute the lensing power spectrum, show that the understanding of baryonic processes will be important for analyzing CMB-S4 data, and show that the two-loop EFTofLSS accurately captures these effects for ℓ ≲ 2000. Our results are also potentially of interest for current and future weak lensing surveys.

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 (b1) and second order bias parameters (b2 and bK 2) of dark matter halos in N-body simulations. This is the first time that assembly bias in the tidal bias parameter bK 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 bK 2 that is opposite to that in b1. Specifically, at fixed mass, halos that get more (less) positively biased in b1, get less (more) negatively biased in bK 2. We also investigate the impact of assembly bias on the b2(b1) and bK 2(b1) relations, and find that while the b2(b1) relation stays roughly unchanged, assembly bias strongly impacts the bK 2(b1) relation. This impact likely extends also to the corresponding relation for galaxies, which motivates future studies to design better priors on bK 2(b1) for use in cosmological constraints from galaxy clustering data.

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.

Assessing non-linear models for galaxy clustering – II. Model validation and forecasts for Stage IV surveys

ABSTRACT Accurate modelling of non-linear scales in galaxy clustering will be crucial for data analysis of Stage IV galaxy surveys. A selection of competing non-linear models must be made based on validation studies. We provide a comprehensive set of forecasts of two different models for the halo redshift space power spectrum, namely the commonly applied TNS model and an effective field theory of large-scale structure (EFTofLSS) inspired model. Using simulation data and a least-χ2 analysis, we determine ranges of validity for the models. We then conduct an exploratory Fisher analysis using the full anisotropic power spectrum to investigate parameter degeneracies. We proceed to perform an MCMC analysis utilizing the monopole, quadrupole, and hexadecapole spectra, with a restricted range of scales for the latter in order to avoid biasing our growth rate, f, constraint. We find that the TNS model with a Lorentzian damping and standard Eulerian perturbative modelling outperforms other variants of the TNS model. Our MCMC analysis finds that the EFTofLSS-based model may provide tighter marginalized constraints on f at z = 0.5 and z = 1 than the TNS model, despite having additional nuisance parameters. However this depends on the range of scales used as well as the fiducial values and priors on the EFT nuisance parameters. Finally, we extend previous work to provide a consistent comparison between the Fisher matrix and MCMC forecasts using the multipole expansion formalism, and find good agreement between them.

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.

Tree-level bispectrum in the effective field theory of large-scale structure extended to massive neutrinos

We compute the tree-level bispectrum of dark matter in the presence of massive neutrinos in the mildly non-linear regime in the context of the effective field theory of large-scale structure (EFTofLSS) . For neutrinos, whose typical free streaming wavenumber (kfs) is longer than the non-linear scale (kNL), we solve a Boltzmann equation coupled to the effective fluid equation for dark matter. We solve perturbatively the coupled system by expanding in powers of the neutrino density fraction (fν) and the ratio of the wavenumber of interest over the non-linear scale (k/kNL) and add suitable counterterms to remove the dependence from short distance physics. For equilateral configurations, we find that the total-matter tree-level bispectrum is approximately 16fν times the dark matter one on short scales (k > kfs). The largest contribution stems from the back-reaction of massive neutrinos on the dark matter growth factor. On large scales (k < kfs) the contribution of neutrinos to the bispectrum is smaller by up to two orders of magnitude.

Towards precision constraints on gravity with the Effective Field Theory of Large-Scale Structure

We compare analytical computations with numerical simulations for dark-matter clustering, in general relativity and in the normal branch of DGP gravity (nDGP). Our analytical frameword is the Effective Field Theory of Large-Scale Structure (EFTofLSS), which we use to compute the one-loop dark-matter power spectrum, including the resummation of infrared bulk displacement effects. We compare this to a set of 20 COLA simulations at redshifts z = 0, z = 0.5, and z = 1, and fit the free parameter of the EFTofLSS, called the speed of sound, in both ΛCDM and nDGP at each redshift. At one-loop at z = 0, the reach of the EFTofLSS is kreach ≈ 0.14 Mpc−1 for both ΛCDM and nDGP. Along the way, we compare two different infrared resummation schemes and two different treatments of the time dependence of the perturbative expansion, concluding that they agree to approximately 1% over the scales of interest. Finally, we use the ratio of the COLA power spectra to make a precision measurement of the difference between the speeds of sound in ΛCDM and nDGP, and verify that this is proportional to the modification of the linear coupling constant of the Poisson equation.

On the bispectra of very massive tracers in the Effective Field Theory of Large-Scale Structure

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 bias, implying that loop contributions could be the leading correction to the bispectra. To check this, we include the one-loop contributions in a fit to numerical data in the limit of strongly enhanced higher-order biases. We show that the resulting one-loop power spectra and higher-derivative plus leading one-loop bispectra fit the two- and three-point functions respectively up to k≃ 0.19 h Mpc−1 and k≃ 0.14 h Mpc−1 at the percent level. We find that the higher-order bias coefficients are not strongly enhanced, and we argue that the gain in perturbative reach due to the leading one-loop contributions to the bispectra is relatively small. Thus, we conclude that higher-derivative biases provide the leading correction to the bispectra for tracers of a very wide range of masses.

IR-safe and UV-safe integrands in the EFTofLSS with exact time dependence

Because large-scale structure surveys may very well be the next leading sources of cosmological information, it is important to have a precise understanding of the cosmological observables; for this reason, the Effective Field Theory of Large-Scale Structure (EFTofLSS) was developed. So far, most results in the EFTofLSS have used the so-called Einstein-de Sitter approximation, an approximation of the time dependence which is known to be accurate to better than one percent. However, in order to reach even higher accuracy, the full time dependence must be used. The computation with exact time dependence is sensitive to both infrared (IR) and ultraviolet (UV) effects in the loop integrands, and while these effects must cancel because of diffeomorphism invariance, they make numerical computation much less efficient. We provide a formulation of the one-loop, equal-time exact-time-dependence power spectrum of density perturbations which is manifestly free of these spurious IR and UV divergences at the level of the integrand. We extend our results to the total matter mode with clustering quintessence, show that IR and UV divergences cancel, and provide the associated IR- and UV-safe integrand. This also establishes that the consistency conditions are satisfied in this system. We then use our one-loop result to do an improved precision comparison of the two-loop dark-matter power spectrum with the Dark Sky N-body simulation.

An effective description of dark matter and dark energy in the mildly non-linear regime

In the next few years, we are going to probe the low-redshift universe with unprecedented accuracy. Among the various fruits that this will bear, it will greatly improve our knowledge of the dynamics of dark energy, though for this there is a strong theoretical preference for a cosmological constant. We assume that dark energy is described by the so-called Effective Field Theory of Dark Energy, which assumes that dark energy is the Goldstone boson of time translations. Such a formalism makes it easy to ensure that our signatures are consistent with well-established principles of physics. Since most of the information resides at high wavenumbers, it is important to be able to make predictions at the highest wavenumber that is possible. The Effective Field Theory of Large-Scale Structure (EFTofLSS) is a theoretical framework that has allowed us to make accurate predictions in the mildly non-linear regime. In this paper, we derive the non-linear equations that extend the EFTofLSS to include the effect of dark energy both on the matter fields and on the biased tracers. For the specific case of clustering quintessence, we then perturbatively solve to cubic order the resulting non-linear equations and construct the one-loop power spectrum of the total density contrast.

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.