Exact analytic solution for non-linear density fluctuation in a ΛCDM universe

Yoo, Jaiyul; Gong, Jinn‐Ouk

doi:10.1088/1475-7516/2016/07/017

Cited by 11 publications

(16 citation statements)

References 57 publications

(180 reference statements)

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“…Using the Einstein equations in the comoving gauge (γ = v = 0 , ϕ ≡ ζ), the perturbations can be expressed in terms of the spatial configuration δ + (x) of the density contrast or the curvature perturbation ζ(x) as [58] ζ(x) = C ∆ −1 δ + (x) ,…”

Section: Summary and Discussionmentioning

confidence: 99%

Galaxy two-point correlation function in general relativity

Scaccabarozzi

Yoo

Biern

2018

J. Cosmol. Astropart. Phys.

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We perform theoretical and numerical studies of the full relativistic two-point galaxy correlation function, considering the linear-order scalar and tensor perturbation contributions and the wide-angle effects. Using the gauge-invariant relativistic description of galaxy clustering and accounting for the contributions at the observer position, we demonstrate that the complete theoretical expression is devoid of any long-mode contributions from scalar or tensor perturbations and it lacks the infrared divergences in agreement with the equivalence principle. By showing that the gravitational potential contribution to the correlation function converges in the infrared, our study justifies an IR cut-off (k IR ≤ H 0 ) in computing the gravitational potential contribution. Using the full gauge-invariant expression, we numerically compute the galaxy two-point correlation function and study the individual contributions in the conformal Newtonian gauge. We find that the terms at the observer position such as the coordinate lapses and the observer velocity (missing in the standard formalism) dominate over the other relativistic contributions in the conformal Newtonian gauge such as the source velocity, the gravitational potential, the integrated Sachs-Wolf effect, the Shapiro time-delay and the lensing convergence. Compared to the standard Newtonian theoretical predictions that consider only the density fluctuation and redshift-space distortions, the relativistic effects in galaxy clustering result in a few percent-level systematic errors beyond the scale of the baryonic acoustic oscillation (∼ 2% at 150 Mpc/h and redshift one). Our theoretical and numerical study provides a comprehensive understanding of the relativistic effects in the galaxy two-point correlation function, as it proves the validity of the theoretical prediction and accounts for effects that are often neglected in its numerical evaluation. arXiv:1807.09796v2 [astro-ph.CO]

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Section: Summary and Discussionmentioning

confidence: 99%

Galaxy two-point correlation function in general relativity

Scaccabarozzi

Yoo

Biern

2018

J. Cosmol. Astropart. Phys.

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“…also [35] for other second order results). At third and fourth order, our solutions are new (other third order results, using a different gauge, were derived by [65], cf. also [36,54]).…”

Section: Discussionmentioning

confidence: 81%

“…for higher-order statistics such as the bispectrum, cf. [54,65]. In addition, they may help in setting initial conditions -and extract relativistic effects -from simulations of the growth of large scale structure in cosmology, both Newtonian, cf.…”

Section: Discussionmentioning

confidence: 99%

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f_NL−g_NL mixing in the matter density field at higher orders

Gressel

Bruni

2018

J. Cosmol. Astropart. Phys.

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In this paper we examine how primordial non-Gaussianity contributes to nonlinear perturbative orders in the expansion of the density field at large scales in the matter dominated era. General Relativity is an intrinsically nonlinear theory, establishing a nonlinear relation between the metric and the density field. Representing the metric perturbations with the curvature perturbation ζ, it is known that nonlinearity produces effective non-Gaussian terms in the nonlinear perturbations of the matter density field δ, even if the primordial ζ is Gaussian. Here we generalise these results to the case of a non-Gaussian primordial ζ. Using a standard parametrization of primordial non-Gaussianity in ζ in terms of f NL , g NL , h NL ..., we show how at higher order (from third and higher) nonlinearity also produces a mixing of these contributions to the density field at large scales, e.g. both f NL and g NL contribute to the third order in δ. This is the main result of this paper. Our analysis is based on the synergy between a gradient expansion (aka long-wavelength approximation) and standard perturbation theory at higher order. In essence, mathematically the equations for the gradient expansion are equivalent to those of first order perturbation theory, thus first-order results convert into gradient expansion results and, vice versa, the gradient expansion can be used to derive results in perturbation theory at higher order and large scales.

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“…[29,30]) in the comoving gauge to obtain the curvature power spectrum P ζ (k) and the growth function of the metric perturbations in that gauge, and then apply the transformation to the Newtonian gauge used in this work. We refer to [24,31] for the details, and only state the results here.…”

Section: B Perturbation Variables and Their Power Spectramentioning

confidence: 99%

General relativistic effects in weak lensing angular power spectra

Grimm

Yoo

2021

Phys. Rev. D

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Advances in upcoming weak lensing surveys pose new challenges for an accurate modeling of the lensing observables. The wide sky coverage of Euclid makes angular scales down to lmin=10 accessible. At such large angular scales, general relativistic effects manifest themselves, and the lensing magnification cannot be correctly described by the standard lensing convergence only. The impact of lineof-sight velocities on the magnification angular power spectrum, referred to as the Doppler magnification, is already well recognized in literature. In particular, it was suggested that the Doppler magnification could be extracted by measurements of both cosmic shear and magnification. In this work, we point out two previously neglected aspects with respect to this method. First, the impact of the Doppler magnification is reduced through nonvanishing cross terms with the standard lensing convergence. This is particularly relevant when the sources are averaged over a bin of width Δz0.1, such as in Euclid's tomographic weak lensing survey. Second, general relativistic potential terms slightly enhance the signal. We present numerical calculations of all relativistic effects in the weak lensing angular power spectra on large scales.

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Exact analytic solution for non-linear density fluctuation in a ΛCDM universe

Cited by 11 publications

References 57 publications

Galaxy two-point correlation function in general relativity

Galaxy two-point correlation function in general relativity

f_NL−g_NL mixing in the matter density field at higher orders

General relativistic effects in weak lensing angular power spectra

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Exact analytic solution for non-linear density fluctuation in a ΛCDM universe

Cited by 11 publications

References 57 publications

Galaxy two-point correlation function in general relativity

Galaxy two-point correlation function in general relativity

fNL−gNL mixing in the matter density field at higher orders

General relativistic effects in weak lensing angular power spectra

Contact Info

Product

Resources

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f_NL−g_NL mixing in the matter density field at higher orders