Cosmological post-Newtonian equations from nonlinear perturbation theory

Mon. Not. R. Astron. Soc.

Park

2016

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We present fully nonlinear and exact cosmological perturbation equations in the presence of multiple components of fluids and minimally coupled scalar fields. We ignore the tensor-type perturbation. The equations are presented without taking the temporal gauge condition in the Friedmann background with general curvature and the cosmological constant. For each fluid component we ignore the anisotropic stress. The multiple component nature, however, introduces the anisotropic stress in the collective fluid quantities. We prove the Newtonian limit of multiple fluids in the zero-shear gauge and the uniform-expansion gauge conditions, present the Newtonian hydrodynamic equations in the presence of general relativistic pressure in the zero-shear gauge, and present the fully nonlinear equations and the third-order perturbation equations of the nonrelativistic pressure fluids in the CDM-comoving gauge.

“…We take the CDM-comoving gauge by setting v c ≡ 0 as the temporal gauge condition. The momentum conservation equation in equation (31) for the CDM component gives…”

Section: Non Relativistic Pressure Fluids In the Cdm-comoving Gaugementioning

confidence: 99%

“…To the linear order in perturbation, equations ( 6)-( 10) and ( 28)- (31) give (Bardeen 1988, Hwang 1991, Hwang & Noh 2013a)…”

Section: Linear Ordermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Fully non-linear cosmological perturbations of multicomponent fluid and field systems

Mon. Not. R. Astron. Soc.

Park

2016

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“…The formulation is powerful in producing higher-order perturbation equations easily, but more interesting aspect is its fully nonlinear and exact nature. We have successfully applied the formulation to Newtonian limit [5], first-order post-Newtonian limit [6], and Newtonian theory with relativistic pressure [7]. In [8,9] we applied the formulation to special relativistic hydrodynamics combined with weak gravity in Minkowski background.…”

Section: Introductionmentioning

confidence: 99%

Cosmological hydrodynamics with relativistic pressure and velocity

J. Cosmol. Astropart. Phys.

Park

2018

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We present hydrodynamic equations with relativistic pressure and velocity in the presence of weak gravity, in a cosmological context. Previously we consistently derived special relativistic hydrodynamic equations with weak gravity in Minkowski background. With the relativistic pressure and velocity one cannot derive the cosmological counterpart by a simple transformation from equations in the Minkowski background. Here we present a proper derivation. We point out the potential importance of relativistic pressure and velocity in gravitational lensing.

Newtonian hydrodynamics with general relativistic pressure

J. Cosmol. Astropart. Phys.

2013

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We present the general relativistic pressure correction terms in Newtonian hydrodynamic equations to the nonlinear order: these are equations (1)-(3). The derivation is made in the zero-shear gauge based on the fully nonlinear formulation of cosmological perturbation in Einstein's gravity. The correction terms differ from many of the previously suggested forms in the literature based on hand-waving manners. We confirm our results by comparing with (i) the nonlinear perturbation theory, (ii) the first order post-Newtonian approximation, and (iii) the special relativistic limit, and by checking (iv) the consistency with full Einstein's equation.