Integration of inhomogeneous cosmological spacetimes in the BSSN formalism

Mertens, James B.; Giblin, John T.; Starkman, Glenn D.

doi:10.1103/physrevd.93.124059

Cited by 63 publications

(77 citation statements)

References 23 publications

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“…For example, for our chosen threshold value for , the O(10 −5 ) error in the numerical solution for Ψ shown in Fig. 4 (middle panel) is comparable to the level of Hamiltonian constraint violations typically found in other numerical relativity codes [26,37].…”

Section: Point-like Sinusoidal and Spherically Symmetric Sourcessupporting

confidence: 68%

GRAMSES: a new route to general relativistic N-body simulations in cosmology. Part I. Methodology and code description

Barrera-Hinojosa

2020

J. Cosmol. Astropart. Phys.

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We present GRAMSES, a new pipeline for nonlinear cosmological N -body simulations in General Relativity (GR). This code adopts the Arnowitt-Deser-Misner (ADM) formalism of GR, with constant mean curvature and minimum distortion gauge fixings, which provides a fully nonlinear and background independent framework for relativistic cosmology. Employing a fully constrained formulation, the Einstein equations are reduced to a set of ten elliptical equations which are solved using multigrid relaxation with adaptive mesh refinements (AMR), and three hyperbolic equations for the evolution of tensor degrees of freedom. The current version of GRAMSES neglects the latter by using the conformal flatness approximation, which allows it to compute the two scalar and two vector degrees of freedom of the metric. In this paper we describe the methodology, implementation, code tests and first results for cosmological simulations in a ΛCDM universe, while the generation of initial conditions and physical results will be discussed elsewhere. Inheriting the efficient AMR and massive parallelisation infrastructure from the publicly-available N -body and hydrodynamic simulation code RAMSES, GRAMSES is ideal for studying the detailed behaviour of spacetime inside virialised cosmic structures and hence accurately quantifying the impact of backreaction effects on the cosmic expansion, as well as for investigating GR effects on cosmological observables using cosmic-volume simulations.

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Section: Point-like Sinusoidal and Spherically Symmetric Sourcessupporting

confidence: 68%

GRAMSES: a new route to general relativistic N-body simulations in cosmology. Part I. Methodology and code description

Barrera-Hinojosa

2020

J. Cosmol. Astropart. Phys.

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“…On the other hand, we may also parametrize the null geodesics by the endpoints δx E and δx O , or -more precisely -by their equivalence classes in Q O and Q E respectively. In the second parametrization, we need to impose the linear condition given by the time lapse formula (50). The resulting dimension of the null geodesic family is therefore again 3 + 3 − 1 = 5.…”

Section: Direction Variation Formulamentioning

confidence: 99%

Geometric optics in general relativity using bilocal operators

2019

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We consider the standard problem of observational astronomy, i.e. the observations of light emission from a distant region of spacetime in general relativity. The goal is to describe the changes between the measurements of the light performed by a sample of observers slightly displaced with respect to each other and moving with different 4-velocities and 4-accelerations. In our approach, all results of observations can be expressed as functions of the kinematic variables, describing the motions of the observers and the emitting bodies with respect to their local inertial frames, and four linear bilocal geodesic operators, describing the influence of the spacetime geometry on light propagation. The operators are functionals of the curvature tensor along the line of sight. The results are based on the assumption that the regions of emissions and observations are sufficiently small so that the spacetime curvature effects are negligible within each of them, although they are significant for the light propagation between them. The new formulation provides a uniform approach to optical phenomena in curved spacetimes and, as an application, we discuss the problem of a fully relativistic definition of the parallax and position drifts (or proper motions). We then use the results to construct combinations of observables which are completely insensitive to the motion of both the observer and the emitter. These combinations by construction probe the spacetime geometry between the observation and emission regions and in our formalism we may express them as functionals of the Riemann tensor along the line of sight. For short distances one of these combinations depends only on the matter content along the line of sight. This opens up the possibility to measure the matter content of a spacetime in a tomographylike manner irrespective of the motions of the emitter and the observer.Even if A enters the differential equation linearly, the general solution contains a nonlinear dependence.

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“…The work by Giblin et al (2016a,b) and Mertens et al (2016) has been mentioned above in Sect. 12; a similar approach was adopted by Bentivegna & Bruni (2016).…”

Section: More-detailed Modelsmentioning

confidence: 88%

Calculation of distances in cosmological models with small-scale inhomogeneities and their use in observational cosmology: a review

Helbig¹

2020

TheOJA

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The Universe is not completely homogeneous. Even if it is sufficiently so on large scales, it is very inhomogeneous at small scales, and this has an effect on light propagation, so that the distance as a function of redshift, which in many cases is defined via light propagation, can differ from the homogeneous case. Simple models can take this into account. I review the history of this idea, its generalization to a wide variety of cosmological models, analytic solutions of simple models, comparison of such solutions with exact solutions and numerical simulations, applications, simpler analytic approximations to the distance equations, and (for all of these aspects) the related concept of a 'Swiss-cheese' universe.

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Integration of inhomogeneous cosmological spacetimes in the BSSN formalism

Cited by 63 publications

References 23 publications

GRAMSES: a new route to general relativistic N-body simulations in cosmology. Part I. Methodology and code description

GRAMSES: a new route to general relativistic N-body simulations in cosmology. Part I. Methodology and code description

Geometric optics in general relativity using bilocal operators

Calculation of distances in cosmological models with small-scale inhomogeneities and their use in observational cosmology: a review

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