The reach of next-to-leading-order perturbation theory for the matter bispectrum

Alkhanishvili, Davit; Porciani, Cristiano; Sefusatti, Emiliano; Biagetti, Matteo; Lazanu, Andrei; Oddo, Andrea; Yankelevich, Victoria

doi:10.1093/mnras/stac567

Cited by 22 publications

(19 citation statements)

References 105 publications

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“…Our algorithm completely eliminates the need (still present in [45]) for an ansatz to be put forward at every perturbative step to identify the solution. This is a striking improvement, especially relevant as the community has been increasingly recognising the importance of tackling higher orders in PT [46][47][48][49][50][51][52][53][54][55]. Moreover, we derive explicit perturbative solutions for time-dependent coefficients.…”

Section: Introductionmentioning

confidence: 95%

Perturbation theory of LSS in the $Λ$CDM Universe: exact time evolution and the two-loop power spectrum

Fasiello¹,

Fujita²,

Vlah³

2022

Preprint

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We derive exact analytic solutions for density and velocity fields to all orders in Eulerian perturbation theory for ΛCDM 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 the perturbative solution rapidly converges towards the numerically obtained solutions and its leading order result suffices for any practical requirements. To illustrate our findings, we compute the exact two-loop dark matter density and velocity power spectra in ΛCDM cosmology. We show that the difference between the exact ΛCDM and the (quasi-)EdS approximated result can reach the level of several percent. This deviation can be partially mitigated by exploiting the degeneracy with the EFT counterterms. As an additional benefit of our algorithm for the solutions of time-dependent coefficients, the computational complexity of power spectra loops in ΛCDM is reduced to the same level of the EdS case. In performing the two-loop computation, we devise an explicit method to implement the so-called IR cancellations, as well as the cancellations arising as a consequence of mass and momentum conservation.

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Section: Introductionmentioning

confidence: 95%

Perturbation theory of LSS in the $Λ$CDM Universe: exact time evolution and the two-loop power spectrum

Fasiello¹,

Fujita²,

Vlah³

2022

Preprint

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“…Note that the same argument applies to the stochastic bias parameter in the general bias method. For a comparison of the range of validity of a few different methods at 𝑧 = 1, see Alkhanishvili et al (2022) Here we see significant redshift evolution, with the first point inconsistent with 5% going from ∼ 0.2 ℎ/Mpc at 𝑧 = 0 to ∼ 0.375 ℎ/Mpc at 𝑧 = 3. Right: The error for the three LO+NLO models sees a similar redshift evolution, going from diverging at ∼ 0.2 ℎ/Mpc at 𝑧 = 0 to ∼ 0.5 ℎ/Mpc at 𝑧 = 3.…”

Section: Discussionmentioning

confidence: 79%

Perturbation Theory vs Simulation: Quasi-linear Scale, Binning Effect, and Visualization of Bispectrum

Tomlinson¹,

Jeong²

2022

Preprint

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Recently, Perturbation Theory (PT), specifically the Effective Field Theory of Large Scale Structure (EFTofLSS) and its equivalents, have proven powerful in analyzing observational data. To further this pursuit, we present a quantitative analysis for the accuracy of PT modeling by comparing its 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, for both 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. Finally, we have devised a novel spherical-Bispectrum visualization scheme fully capturing the scale and configuration dependences. The new scheme facilitates bispectrum-amplitude comparison, for example, between theory and N-body results.

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“…12,14,18,[20][21][22][23]. For example, the EFTofLSS extends the k-reach of the models for the matter power spectrum by a factor of 2-3 [24]. The formalism has also incorporated biased tracers [e.g.…”

Section: Jcap01(2024)051mentioning

confidence: 99%

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

Karandikar,

Porciani,

Hahn

2024

J. Cosmol. Astropart. Phys.

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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.

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The reach of next-to-leading-order perturbation theory for the matter bispectrum

Cited by 22 publications

References 105 publications

Perturbation theory of LSS in the $Λ$CDM Universe: exact time evolution and the two-loop power spectrum

Perturbation theory of LSS in the $Λ$CDM Universe: exact time evolution and the two-loop power spectrum

Perturbation Theory vs Simulation: Quasi-linear Scale, Binning Effect, and Visualization of Bispectrum

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

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