Unified treatment of cosmological perturbations from superhorizon to small scales

Carbone, C.; Matarrese, S.

doi:10.1103/physrevd.71.043508

Cited by 106 publications

(101 citation statements)

References 27 publications

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“…The final limit comes from recognizing that anisotropic stress, inducing a ψ − φ = 0 term, is a post-Newtonian second-order contribution; this can only be relevant either on very large scales or on very small highly non-linear scales [23], so ψ = φ to a good approximation for the range of wavelenghts of interest here.…”

Section: H the First Order Perturbation In Xmentioning

confidence: 99%

Second order geodesic corrections to cosmic shear

et al. 2005

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We consider the impact of second order corrections to the geodesic equation governing gravitational lensing. We start from the full second order metric, including scalar, vector and tensor perturbations, and retain all relevant contributions to the cosmic shear corrections that are second order in the gravitational potential. The relevant terms are: the nonlinear evolution of the scalar gravitational potential, the Born correction, and lens-lens coupling. No other second order terms contribute appreciably to the lensing signal. Since ray-tracing algorithims currently include these three effects, this derivation serves as rigorous justification for the numerical predictions.

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Section: H the First Order Perturbation In Xmentioning

confidence: 99%

Second order geodesic corrections to cosmic shear

et al. 2005

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“…On the largest scales, a perturbative approach is used in a general-relativistic framework. On small scales, non-linearities are treated in a Newtonian fashion, often with the use of N-body simulations.Few attempts have been made to go beyond the Newtonian approximation on non-linear scales by including post-Newtonian type corrections [1][2][3][4][5][6]. However, no attempt has been made to include post-Newtonian corrections in N-body simulations of cosmological large scale structure.…”

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confidence: 99%

Computing general-relativistic effects from Newtonian N-body simulations: Frame dragging in the post-Friedmann approach

2014

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We present the first calculation of an intrinsically relativistic quantity in fully non-linear cosmological large-scale structure studies. Traditionally, non-linear structure formation in standard ΛCDM cosmology is studied using N-body simulations, based on Newtonian gravitational dynamics on an expanding background. When one derives the Newtonian regime in a way that is a consistent approximation to the Einstein equations, a gravito-magnetic vector potential -giving rise to frame dragging -is present in the metric in addition to the usual Newtonian scalar potential. At leading order, this vector potential does not affect the matter dynamics, thus it can be computed from Newtonian N-body simulations. We explain how we compute the vector potential from simulations in ΛCDM and examine its magnitude relative to the scalar potential. We also discuss some possible observable effects.Introduction. Modern Cosmology is usually studied in two limits. On the largest scales, a perturbative approach is used in a general-relativistic framework. On small scales, non-linearities are treated in a Newtonian fashion, often with the use of N-body simulations.Few attempts have been made to go beyond the Newtonian approximation on non-linear scales by including post-Newtonian type corrections [1][2][3][4][5][6]. However, no attempt has been made to include post-Newtonian corrections in N-body simulations of cosmological large scale structure. Investigations have been carried out into the interpretation of N-body simulations on large scales, of the order of the Hubble length [7,8]. In [8], they go further and examine the dictionary between Newtonian and relativistic cosmologies on all scales and how accurately Newtonian cosmology satisfy the Einstein equations. Of course, no matter how well the Newtonian dynamics capture the full GR dynamics, there are GR quantities on all scales that have no counterpart in Newtonian theory.Recently, a new approximation scheme has been developed, dubbed the post-Friedmann approach [9], with the aim of providing a unified framework for all scales, from the fully non-linear Newtonian regime to the largest scales where relativistic effects become important [10]. It is based on an expansion in inverse powers of the speed of light, c, in a post-Newtonian [11] fashion, adapted to cosmology. When linearised, this approach correctly reproduces the linear general-relativistic perturbation theory. When one derives the Newtonian regime in this approach, in a way that is a consistent approximation to the Einstein equations, a vector potential must be present in the metric in addition to the usual Newtonian scalar gravitational potential.This vector potential is non-dynamical at leading order, therefore it does not affect the matter dynamics.

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“…In the present paper, we are interested in the cosmological stochastic GW background produced by Cold Dark Matter (CDM) halos via power transfer from scalar and possible vector perturbations to tensor metric modes, during the strongly nonlinear stage of their evolution [21]. It differs from other cosmological backgrounds, as that produced during the mildly nonlinear stage [22], since density and velocity fields can be, in this case, highly nonlinear.…”

Section: Introductionmentioning

confidence: 99%

Stochastic gravitational wave background from cold dark matter halos

2006

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The current knowledge of cosmological structure formation suggests that Cold Dark Matter (CDM) halos possess a nonspherical density profile, implying that cosmic structures can be potential sources of gravitational waves via power transfer from scalar perturbations to tensor metric modes in the nonlinear regime. By means of a previously developed mathematical formalism and a triaxial collapse model, we numerically estimate the stochastic gravitational-wave background generated by CDM halos during the fully nonlinear stage of their evolution. Our results suggest that the energy density associated with this background is comparable to that produced by primordial tensor modes at frequencies 10 ÿ18 -10 ÿ17 Hz if the energy scale of inflation is V 1=4 1-2 10 15 GeV, and that these gravitational waves could give rise to several cosmological effects, including secondary CMB anisotropy and polarization.

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Unified treatment of cosmological perturbations from superhorizon to small scales

Cited by 106 publications

References 27 publications

Second order geodesic corrections to cosmic shear

Second order geodesic corrections to cosmic shear

Computing general-relativistic effects from Newtonian N-body simulations: Frame dragging in the post-Friedmann approach

Stochastic gravitational wave background from cold dark matter halos

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