Angular-averaged consistency relations of large-scale structures

Valageas, Patrick

doi:10.1103/physrevd.89.123522

Cited by 33 publications

(89 citation statements)

References 44 publications

(121 reference statements)

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“…In Fig. 4, we compare the results reported in [42] with the (VKPR) approximation implicitly used in [36,37], see also [14], Figure 4: The response of the power spectrum to a long-wavelength perturbation, G 1 (k, z), at redshifts z = 0 (left) and z = 2 (right), as introduced in [42]. The red solid line uses the approximation in (5.6) [36,37] (see footnote 4).…”

Section: Discussionmentioning

confidence: 99%

On the soft limit of the large scale structure power spectrum: UV dependence

Garny

Konstandin

Porto³

et al. 2015

J. Cosmol. Astropart. Phys.

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We derive a non-perturbative equation for the large scale structure power spectrum of longwavelength modes. Thereby, we use an operator product expansion together with relations between the three-point function and power spectrum in the soft limit. The resulting equation encodes the coupling to ultraviolet (UV) modes in two time-dependent coefficients, which may be obtained from response functions to (anisotropic) parameters, such as spatial curvature, in a modified cosmology. We argue that both depend weakly on fluctuations deep in the UV. As a byproduct, this implies that the renormalized leading order coefficient(s) in the effective field theory (EFT) of large scale structures receive most of their contribution from modes close to the non-linear scale. Consequently, the UV dependence found in explicit computations within standard perturbation theory stems mostly from counter-term(s). We confront a simplified version of our non-perturbative equation against existent numerical simulations, and find good agreement within the expected uncertainties. Our approach can in principle be used to precisely infer the relevance of the leading order EFT coefficient(s) using small volume simulations in an 'anisotropic separate universe' framework. Our results suggest that the importance of these coefficient(s) is a ∼ 10% effect, and plausibly smaller. Introduction and SummaryThe measurement of anisotropies in the cosmic microwave background (CMB) by the Planck collaboration has provided invaluable information about the origin of the seed of structure [1], plausibly created during an early phase of accelerated expansion [2]. While this is a remarkable achievement, many questions still remain open regarding the nature of an inflationary cosmology.Perhaps the most outstanding one is whether a slowly-rolling, weakly coupled, fundamental scalar field played the role of the Higgs mechanism for the early universe; or if the universe chose a different path, such as dynamics at strong coupling or supersymmetry, e.g. [3][4][5]. These possibilities remain viable candidates to play a role in the early universe, and have not been considerably hindered by the Planck data [3]. In particular, the existent bounds on (equilateral) non-Gaussianity [6] are still above some well-motivated thresholds [3,7].Large-scale structure (LSS) surveys are due to become the next leading probe for precision cosmology, providing new information about the history of the universe through ambitious observational programs, currently under way to make very precise measurements. Therefore, the analytic control for the largest number of modes in the process of structure formation will allow us to place better constraints on cosmological parameters, and to further our understanding on the seed of structure. Unfortunately, quantitative predictions even for the simplest of the cosmologies is a daunting task, due to the non-linear nature of dark matter clustering. Moreover, even if one adopts a numerical approach, including baryonic matter is far from straightforward.He...

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Section: Discussionmentioning

confidence: 99%

On the soft limit of the large scale structure power spectrum: UV dependence

Garny

Konstandin

Porto³

et al. 2015

J. Cosmol. Astropart. Phys.

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“…Assuming that c s is known, we can measurec b from N-body data, and thus determine the principal EFT shape that renormalizes the angle-averaged bispectrum in the whole kinematic plane, up to corrections of O(10%). Before moving on to the measurement ofc b in the next section, let us note that Valageas [29] as well as Kehagias, Perrier and Riotto [30] have proposed an ansatz for G 1 (k) based on the form of the linear growth function in the curved background. In the VKPR ansatz, G 1 (k) can be written in terms of the power spectrum of the fiducial cosmology at all orders in perturbation theory (see Appendix C.3 for a brief review).…”

Section: Squeezed Angle-averaged Bispectrummentioning

confidence: 99%

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

Bertolini

Solon

2016

J. Cosmol. Astropart. Phys.

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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 O(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.

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“…A different kind of consistency relation has been tested in[31] using N -body simulations as well. That interesting relation concerns the higher order coefficients of the low q expansion of the bispectrum[32,33]. More specifically, it concerns the q 0 behavior in the context of (5), and its derivation crucially rely on the hard observables being mass fluctuations as opposed to galaxy fluctuations.…”

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confidence: 99%

Nonperturbative test of consistency relations and their violation

Esposito

Hui

2019

Phys. Rev. D

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In this paper, we verify the large scale structure consistency relations using N -body simulations, including modes in the highly non-linear regime. These relations (pointed out by Kehagias & Riotto and Peloso & Pietroni) follow from the symmetry of the dynamics under a shift of the Newtonian potential by a constant and a linear gradient, and predict the absence of certain poles in the ratio between the (equal time) squeezed bispectrum and power spectrum. The consistency relations, as symmetry statements, are exact, but have not been previously checked beyond the perturbative regime. Our test using N -body simulations not only offers a non-perturbative check, but also serves as a warm-up exercise for applications to observational data. A number of subtleties arise when taking the squeezed limit of the bispectrum-we show how to circumvent or address them. An interesting by-product of our investigation is an explicit demonstration that the linear-gradientsymmetry is unaffected by the periodic boundary condition of the simulations. Lastly, we verify using simulations that the consistency relations are violated when the initial conditions are nongaussian (of the local f NL type). The methodology developed here paves the way for constraining primordial non-gaussianity using large scale structure data, including (numerous) highly non-linear modes that are otherwise hard to interpret and utilize.1 The split into two separate symmetries here follows the discussion of [17].

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Angular-averaged consistency relations of large-scale structures

Cited by 33 publications

References 44 publications

On the soft limit of the large scale structure power spectrum: UV dependence

On the soft limit of the large scale structure power spectrum: UV dependence

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

Nonperturbative test of consistency relations and their violation

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