Field Theory Of Large Scale Structures Research Articles

A multitracer analysis for the eBOSS galaxy sample based on the effective field theory of large-scale structure

ABSTRACT We perform a multitracer full-shape analysis in Fourier space based on the effective field theory of large-scale structure (EFTofLSS) using the complete Sloan Digital Sky Survey IV (SDSS-IV) extended Baryon Oscillation Spectroscopic Survey (eBOSS) DR16 luminous red galaxy (LRG) and emission line galaxy (ELG) samples. We study in detail the impact of the volume projection effect and different prior choices when doing the full-shape analysis based on the EFTofLSS model. We show that adopting a combination of Jeffreys prior and Gaussian prior can mitigate the volume effect and avoid exploring unphysical regions in the parameter space at the same time, which is crucial when jointly analysing the eBOSS LRG and ELG samples. We validate our pipeline using 1000 eBOSS EZmocks. By performing a multitracer analysis on mocks with comparable footprints, we find that cosmological constraints can be improved by $\sim 10-35~{{\ \rm per\ cent}}$ depending on whether we assume zero stochastic terms in the cross power spectrum, which breaks the degeneracy and boosts the constraints on the standard deviation of matter density fluctuation σ8. Combining with the Big Bang Nucleosynthesis (BBN) prior and fixing the spectral tilt ns to Planck value, our multitracer full-shape analysis measures H0 = 70.0 ± 2.3 km s−1Mpc−1, $\Omega _m=0.317^{+0.017}_{-0.021}$, $\sigma _8=0.787_{-0.062}^{+0.055}$, and $S_8=0.809_{-0.078}^{+0.064}$, consistent with the Planck 2018 results. In particular, the constraint on σ8 is improved beyond that obtained from the single tracer analysis by 18 per cent, or by 27 per cent when assuming zero stochastic terms in the cross power spectrum.

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.

Efficiently evaluating loop integrals in the EFTofLSS using QFT integrals with massive propagators

We develop a new way to analytically calculate loop integrals in the Effective Field Theory of Large Scale-Structure. Previous available methods show severe limitations beyond the one-loop power spectrum due to analytical challenges and computational and memory costs. Our new method is based on fitting the linear power spectrum with cosmology-independent functions that resemble integer powers of quantum field theory massive propagators with complex masses. A remarkably small number of them is sufficient to reach enough accuracy. Similarly to former approaches, the cosmology dependence is encoded in the coordinate vector of the expansion of the linear power spectrum in our basis. We first produce cosmology-independent tensors where each entry is the loop integral evaluated on a given combination of basis vectors. For each cosmology, the evaluation of a loop integral amounts to contracting this tensor with the coordinate vector of the linear power spectrum. The 3-dimensional loop integrals for our basis functions can be evaluated using techniques familiar to particle physics, such as recursion relations and Feynman parametrization. We apply our formalism to evaluate the one-loop bispectrum of galaxies in redshift space. The final analytical expressions are quite simple and can be evaluated with little computational and memory cost. We show that the same expressions resolve the integration of all one-loop N-point function in the EFTofLSS. This method, which is originally presented here, has already been applied in the first one-loop bispectrum analysis of the BOSS data to constraint ΛCDM parameters and primordial non-Gaussianities [1, 2].

The effective field theory of large-scale structure and multi-tracer II: redshift space and realistic tracers

We extend the multi-tracer (MT) formalism of the effective field theory of large-scale structure to redshift space, comparing the results of MT to a single-tracer analysis when extracting cosmological parameters from simulations. We used a sub-halo abundance matching method to obtain more realistic multi-tracer galaxy catalogs constructed from N-body simulations. Considering different values for the sample shot noise and volume, we show that the MT error bars on A s, ω cdm, and h in a full-shape analysis are approximately 50% smaller relative to ST. We find that cosmological and bias coefficients from MT are less degenerate, indicating that the MT parameter basis is more orthogonal. We conclude that using MT combined with perturbation theory is a robust and competitive way to accommodate the information present in the mildly non-linear scales.

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.

The Effective Field Theory of Large-scale Structures of a Fuzzy Dark Matter Universe

Ultralight scalar fields and their noninteracting class, i.e., the so-called fuzzy dark matter (FDM), are dark matter candidates introduced to solve the small-scale problems of the standard cold dark matter. In this paper, we investigate whether the physics of FDM, particularly the quantum pressure that leads to the suppression of structure formation on small scales, could leave significant imprints on the large-scale statistics of matter fluctuations. For this purpose, we utilize the Effective Field Theory of Large Scale Structures (EFT of LSS), wherein small-scale physics is integrated and represented on large scales by only a set of free parameters. These parameters can be determined by fitting them into the cosmological simulations. By fitting the EFT predictions to the simulation data, we determine the value of the speed of sound as a quantitative measure of how UV physics affects large-scale perturbation. We use the Gadget-2 code to study the evolution of 5123 particles in a box with a side length 250 h −1 Mpc. We exploit the suppressed FDM initial power for the FDM universe and perform N-body simulation sufficient to produce accurate—enough for our purpose—results on large scales. In particular, we perform three FDM simulations with different masses and compare their sound speed with the standard cold dark matter (CDM) simulation. We found no difference between the FDM and CDM sound speeds beyond the confidence intervals. However, a consistently increasing trend can be seen in the sound speed for lower masses. This result suggests further investigations using higher-resolution simulations.

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 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.

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.

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 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 max = 0.30 h/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 max = 0.05 h/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.

Analysis of unified galaxy power spectrum multipole measurements

ABSTRACTWe present a series of full-shape analyses of galaxy power spectrum multipole measurements from the 6dFGS, BOSS, and eBOSS galaxy surveys. We use an emulated effective field theory of large-scale structure (EFTofLSS) model to conduct these analyses. We exploit the accelerated prediction speed of the neural-network-based emulator to explore various analysis setups for our cosmological inference pipeline. Via a set of mock full-shape analyses of synthetic power spectrum multipoles, designed to approximate measurements from the surveys above, we demonstrate that the use of alternative priors on nuisance parameters and restricted model complexity reduces many of the biases previously observed in marginalized cosmological constraints coming from EFTofLSS analyses. The alternative priors take the form of a Jeffreys prior; a non-informative prior that can mitigate against biases induced by marginalizing over poorly constrained nuisance parameters. When performing a joint analysis of all synthetic multipoles, we see an improvement in the level of agreement between the marginalized ln (1010As) constraints and the truth; from ∼2.0σ to ∼0.42σ. Using our pipeline to analyse the measured multipoles, we find an improvement in the level of agreement with cosmic microwave background (CMB) results; from ∼2.4σ to ∼0.5σ. Therefore, we conclude that the spectroscopic galaxy survey data sets listed above are consistent with constraints obtained from the CMB.

S8 Tension in the Context of Dark Matter–Baryon Scattering

We explore an interacting dark matter (IDM) model that allows for a fraction of dark matter (DM) to undergo velocity-independent scattering with baryons. In this scenario, structure on small scales is suppressed relative to the cold DM scenario. Using the effective field theory of large-scale structure, we perform the first systematic analysis of BOSS full-shape galaxy clustering data for the IDM scenario, and we find that this model ameliorates the S 8 tension between large-scale structure and Planck data. Adding the S 8 prior from the Dark Energy Survey (DES) to our analysis further leads to a mild ∼3σ preference for a nonvanishing DM–baryon scattering cross section, assuming ∼10% of DM is interacting and has a particle mass of 1 MeV. This result produces a modest ∼20% suppression of the linear power at k ≲ 1 h Mpc−1, consistent with other small-scale structure observations. Similar scale-dependent power suppression was previously shown to have the potential to resolve S 8 tension between cosmological data sets. The validity of the specific IDM model explored here will be critically tested with upcoming galaxy surveys at the interaction level needed to alleviate the S 8 tension.

Constraints on modified gravity from the BOSS galaxy survey

We develop a pipeline to set new constraints on scale-independent modified gravity, from the galaxy power spectrum in redshift space of BOSS DR12. The latter is modelled using the effective field theory of large-scale structure up to 1-loop order in perturbation theory.We test our pipeline on synthetic and simulated data, to assess systematic biases on the inferred cosmological parameters due to marginalization and theoretical errors, and we apply it to the normal branch of the DGP model with a ΛCDM background. When applied to synthetic data and cosmological simulations, we observe biased posteriors due to the strong degeneracy between the nDGP parameter Ωrc and the primordial amplitude of fluctuations As . Fixing the latter to the Planck central value, we obtain a posterior distribution with Ωrc ≲ 0.65 at 95% C.L., under the assumption of a flat prior on log10 Ωrc. This upper bound, however, depends strongly on the prior on Ωrc. To alleviate this effect, we provide an upper bound based on the Bayes factor between the nDGP model and ΛCDM model, which gives Ωrc ≲ 0.2 at 95% C.L..

Updated constraints from the effective field theory analysis of the BOSS power spectrum on early dark energy

Analyses of the full shape of BOSS DR12 power spectrum using the one-loop prediction from the Effective Field Theory of Large-Scale Structure (EFTBOSS) have led to new constraints on extensions to the $\Lambda$CDM model, such as Early Dark Energy (EDE) which has been suggested as a resolution to the "Hubble tension". In this paper, we re-assess the constraining power of the EFTBOSS on EDE in light of a correction to the normalization of BOSS window functions. Overall we find that constraints from EFTBOSS on EDE are weakened, and represent a small change compared to constraints from Planck and the conventional BAO/$f\sigma_8$ measurements. The combination of Planck data with EFTBOSS provides a bound on the maximal fractional contribution of EDE $f_{\rm EDE}<0.083$ at 95% C.L. (compared to $<0.054$ with the incorrect normalization, and $<0.088$ without full-shape data) and the Hubble tension is reduced to $2.1\sigma$. However, the more extreme model favored by an analysis with just data from the Atacama Cosmology Telescope is disfavored by the EFTBOSS data. We also show that the updated Pantheon+ Type Ia supernova analysis can slightly increase the constraints on EDE. Yet, the inclusion of the SN1a magnitude calibration by SH0ES strongly increases the preference for EDE to above $5\sigma$, yielding $f_{\rm EDE}\sim 0.12^{+0.03}_{-0.02}$ around the redshift $z_c=4365^{+3000}_{-1100}$. Our results demonstrate that EFTBOSS data (alone or combined with Planck data) do not exclude the EDE resolution of the Hubble tension.

Interacting dark energy from the joint analysis of the power spectrum and bispectrum multipoles with the EFTofLSS

ABSTRACT Interacting dark energy models have been suggested as alternatives to the standard cosmological model, ΛCDM. We focus on a phenomenologically interesting class of dark scattering models that is characterized by pure momentum exchange between dark energy and dark matter. This model extends the parameter space with respect to ΛCDM by two parameters, w and A, which define the dark energy equation of state and the strength of the coupling between dark energy and dark matter, respectively. In order to test non-standard cosmologies with Stage-IV galaxy clustering surveys, it is crucial to model mildly non-linear scales and perform precision versus accuracy tests. We use the Effective Field Theory of Large-Scale Structure; and we perform validation tests by means of an MCMC analysis using a large set of N-body simulations. We find that adding the bispectrum monopole to the power spectrum multipoles improves the constraints on the dark energy parameters by $\sim 30 {{\ \rm per\ cent}}$ for $k_{\mathrm{max}, B}^{l=0} = 0.11$ h Mpc−1, without introducing biases in the parameter estimation. We also find that the same improvement can be achieved with more moderate scale cuts and the use of bias relations, or with the addition of the bispectrum quadrupole. Finally, we study degeneracies between the dark energy parameters and the scalar amplitude As and discuss the corresponding projection effects, as well as degeneracies with other cosmological parameters.

Colliders and ghosts: Constraining inflation with the parity-odd galaxy four-point function

Could new physics break the mirror symmetry of the Universe? Utilizing recent measurements of the parity-odd four-point correlation function of BOSS galaxies, we probe the physics of inflation by placing constraints on the amplitude of a number of parity-violating models. Within canonical models of (single-field, slow-roll) inflation, no parity-asymmetry can occur; however, it has recently been shown that breaking of the standard assumptions can lead to parity violation within the Effective Field Theory of Inflation (EFTI). In particular, we consider the Ghost Condensate and Cosmological Collider scenarios -- the former for the leading and subleading operators in the EFTI and the latter for different values of mass and speed of an exchanged spin-$1$ particle -- for a total of $18$ models. Each instance yields a definite prediction for the inflationary trispectrum, which we convert to a late-time galaxy correlator prediction (through a highly non-trivial calculation) and constrain using the observed data. We find no evidence for inflationary parity-violation (with each of the $18$ models having significances below $2\sigma$), and place the first constraints on the relevant coupling strengths, at a level comparable with the theoretical perturbativity bounds. This is also the first time Cosmological Collider signatures have directly been searched for in observational data. We further show that possible secondary parity-violating signatures in galaxy clustering can be systematically described within the Effective Field Theory of Large-Scale Structure. We argue that these late-time contributions are subdominant compared to the primordial parity-odd signal for a vast region of parameter space. In summary, the results of this paper disfavor the notion that the recent hints of parity-violation observed in the distribution of galaxies are due to new physics.

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.

Constraining decaying dark matter with BOSS data and the effective field theory of large-scale structures

We update cosmological constraints on two decaying dark matter models in light of BOSS-DR12 data analyzed under the effective field theory of large-scale structures (EFTofLSS) formalism, together with Planck, Pantheon and other BOSS measurements of the baryonic acoustic oscillation (BAO). In the first model, a fraction ${f}_{\mathrm{dcdm}}$ of cold dark matter (CDM) decays into dark radiation (DR) with a lifetime $\ensuremath{\tau}$. In the second model (recently suggested as a potential resolution to the ${S}_{8}$ tension), all the CDM decays with a lifetime $\ensuremath{\tau}$ into DR and a massive warm dark matter (WDM) particle, with a fraction $ϵ$ of the CDM rest mass energy transferred to the DR. Using numerical codes from the recent literature, we perform the first calculation of the mildly nonlinear (matter and galaxy) power spectra with the EFTofLSS for these two models. In the case of DR products, we obtain the constraints ${f}_{\mathrm{dcdm}}\ensuremath{\lesssim}0.022$ (95% C.L.) for lifetimes shorter than the age of the Universe, and $\ensuremath{\tau}/{f}_{\mathrm{dcdm}}\ensuremath{\gtrsim}250\text{ }\text{ }\mathrm{Gyr}$ in the long-lived regime assuming ${f}_{\mathrm{dcdm}}\ensuremath{\rightarrow}1$. We show that Planck data contributes the most to these constraints, with EFTofBOSS providing a marginal improvement over conventional BAO and redshift space distortions ($f{\ensuremath{\sigma}}_{8}$) data. In the case of DR and WDM decay products, we find that EFTofBOSS data significantly improves the constraints at 68% C.L. on the CDM lifetime with a ${S}_{8}$ prior from KiDS-1000. We show that, in order to fit EFTofBOSS data while lowering ${S}_{8}$ to match KiDS-1000, the best-fit model has a longer lifetime $\ensuremath{\tau}=120\text{ }\text{ }\mathrm{Gyr}$, with a larger kick velocity ${v}_{\mathrm{kick}}/c\ensuremath{\simeq}ϵ\ensuremath{\simeq}1.2%$, than that without EFTofBOSS ($\ensuremath{\tau}=43\text{ }\text{ }\mathrm{Gyr}$, $ϵ=0.6%$). We anticipate that future surveys will provide exquisite constraints on such models.

The effective field theory of large-scale structure and multi-tracer

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 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 them and with their error being typically half of the single-tracer case. Finally, we studied the impacts caused in parameter extraction when including a correlation between the stochastic field of distinct tracers. We also include a study with galaxies showing that multi-tracer still lead to substantial gains in the cosmological parameters.