Proper-time hypersurface of nonrelativistic matter flows: Galaxy bias in general relativity

Yoo, Jaiyul

doi:10.1103/physrevd.90.123507

Cited by 26 publications

(85 citation statements)

References 61 publications

(178 reference statements)

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“…In the comoving gauge, the dynamical equations of motion are shown to be identical to the Newtonian ones to the second order in perturbations [31,32] with the relativistic effects appearing only from the third order [33]. This gauge condition is later shown [13] to correspond to the proper-time hypersurface of nonrelativistic matter flows. In the proper-time hypersurface, the local observer moving with the nonrelativistic matter flows can measure the energy density in its rest frame, providing the most natural description of the matter density fluctuation.…”

Section: Dynamical Equations Of Motionmentioning

confidence: 92%

“…The observer four velocity is then decomposed in terms of the shear σ ij and the expansion θ [24,25] as 5) where the semicolon is the covariant derivative with respect to the spacetime metric g ab and the induced metric h ab = g ab + u a u b is indeed the projection to the 3-hypersurface. The normal observer is irrotational u [a;b] = 0, and the energy-momentum conservation of the nonrelativistic matter flows imposes that the observer follows the geodesic a a = u a;b u b = 0 and N = 1 [13]. Thus the coordinate time exactly corresponds to the proper time.…”

Section: Nonlinear Dynamical Equationsmentioning

confidence: 99%

“…This can be described by any choice of gauge conditions, but the comoving gauge choice in a universe with a presureless medium allows the global coordinate system to be aligned to the proper-time hypersurface, facilitating the computation of the matter density fluctuation in the proper-time hypersurface [13]. This aspect is of particular importance when galaxy bias is considered.…”

Section: Introductionmentioning

confidence: 99%

“…In [11], the synchronous comoving gauge was advocated for galaxy bias. However, it was shown [13,14] that the spatial coordinates in this gauge condition trace the nonrelativistic matter flows and the direct computation of the matter power spectrum in this coordinate is inadequate for galaxy bias. In contrast, the comoving gauge condition with the spatial C-gauge condition fixes the spatial coordinates, providing a natural framework to describe local dynamics in the relativistic context [13].…”

Section: Introductionmentioning

confidence: 99%

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

Yoo

Gong

2016

J. Cosmol. Astropart. Phys.

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We derive the exact third-order analytic solution of the matter density fluctuation in the propertime hypersurface in a ΛCDM universe, accounting for the explicit time-dependence and clarifying the relation to the initial condition. Furthermore, we compare our analytic solution to the previous calculation in the comoving gauge, and to the standard Newtonian perturbation theory by providing Fourier kernels for the relativistic effects. Our results provide an essential ingredient for a complete description of galaxy bias in the relativistic context. AbstractWe derive the exact third-order analytic solution of the matter density fluctuation in the proper-time hypersurface in a ΛCDM universe, accounting for the explicit time-dependence and clarifying the relation to the initial condition. Furthermore, we compare our analytic solution to the previous calculation in the comoving gauge, and to the standard Newtonian perturbation theory by providing Fourier kernels for the relativistic effects. Our results provide an essential ingredient for a complete description of galaxy bias in the relativistic context.

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Section: Dynamical Equations Of Motionmentioning

confidence: 92%

Section: Nonlinear Dynamical Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Yoo

Gong

2016

J. Cosmol. Astropart. Phys.

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“…Thus the coordinate time precisely coincides with the proper time [21] so that we can up to second order, in the absence of the tensor perturbations, reproduce the Newtonian hydrodynamical equations, giving rise to the correspondence between the Newtonian and relativistic cosmologies [11,22].…”

Section: Exact Equations For Cosmological Perturbationsmentioning

confidence: 99%

Exact non-linear equations for cosmological perturbations

Gong¹,

Hwang

Noh

et al. 2017

J. Cosmol. Astropart. Phys.

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We present a complete set of exact and fully non-linear equations describing all three types of cosmological perturbations -scalar, vector and tensor perturbations. We derive the equations in a thoroughly gauge-ready manner, so that any spatial and temporal gauge conditions can be employed. The equations are completely general without any physical restriction except that we assume a flat homogeneous and isotropic universe as a background. We also comment briefly on the application of our formulation to the non-expanding Minkowski background.

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Relativistic effects and primordial non-Gaussianity in the matter density fluctuation

Yoo¹,

Gong²

2016

Physics Letters B

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We present the third-order analytic solution of the matter density fluctuation in the proper-time hypersurface of nonrelativistic matter flows by solving the nonlinear general relativistic equations. The proper-time hypersurface provides a coordinate system that a local observer can set up without knowledge beyond its neighborhood, along with physical connections to the local Newtonian descriptions in the relativistic context. The initial condition of our analytic solution is set up by the curvature perturbation in the comoving gauge, clarifying its impact on the nonlinear evolution. We compute the effective non-Gaussian parameters due to the nonlinearity in the relativistic equations. With proper coordinate rescaling, we show that the equivalence principle is respected and the relativistic effect vanishes in the large-scale limit. 98.80.Jk,98.62.Py Rapid developments in large-scale galaxy surveys over the past decades have enabled the precision measurements of galaxy clustering, which can be used to probe the nature of dark energy and the perturbation generation mechanism in the early Universe [1]. In parallel, the recent theoretical development ([2-6]; see [7] for review) has revealed that the subtle relativistic effects are present in galaxy clustering, providing new opportunities to extract additional and critical information about the gravity on large scales and the initial conditions for structure formation. In particular, the relativistic formalism has been extended [8-10] to the second-order in perturbations for the computation of higher-order statistics such as the bispectrum.One of the critical elements in the relativistic formalism is galaxy bias, which relates the galaxy number density to the underlying matter distribution. Beyond the linear order in perturbations, however, galaxy bias poses a nontrivial problem due to the gauge issues in general relativity. It was shown [11] that the proper-time hypersurface of nonrelativistic matter flows provides a physical description of the local observer, moving with dark matter and baryons that will collapse to form galaxies. This physical justification has led us to study the nonlinear relativistic effects of the matter density fluctuation in the proper-time hypersurface of nonrelativistic matter flows. This is timely and interesting, for there has been recent conflict in literature -It is argued in [12,13] by performing the second-order relativistic calculations that the nonlinear evolution of gravity generates the local-type non-Gaussianity, which would in turn exhibit a prominent signature in galaxy clustering on large scales. On the other hands, in [14-16] the opposite claim is asserted that the observable quantities are not affected by these nonlinear relativistic effects of gravity, while the calculations are in general based on studying the special case (or the squeezed limit), where only the linear- * Electronic address: jyoo@physik.uzh.ch † Electronic address: jinn-ouk.gong@apctp.org order calculations are required. In this article, we present the ...

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Proper-time hypersurface of nonrelativistic matter flows: Galaxy bias in general relativity

Cited by 26 publications

References 61 publications

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

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

Exact non-linear equations for cosmological perturbations

Relativistic effects and primordial non-Gaussianity in the matter density fluctuation

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