Newtonian and Relativistic Cosmologies

Abstract

Cosmological N-body simulations are now being performed using Newtonian gravity on scales larger than the Hubble radius. It is well known that a uniformly expanding, homogeneous ball of dust in Newtonian gravity satisfies the same equations as arise in relativistic FLRW cosmology, and it also is known that a correspondence between Newtonian and relativistic dust cosmologies continues to hold in linearized perturbation theory in the marginally bound/spatially flat case. Nevertheless, it is far from obvious that Newtonian gravity can provide a good global description of an inhomogeneous cosmology when there is significant nonlinear dynamical behavior at small scales. We investigate this issue in the light of a perturbative framework that we have recently developed, which allows for such nonlinearity at small scales. We propose a relatively straightforward "dictionary"---which is exact at the linearized level---that maps Newtonian dust cosmologies into general relativistic dust cosmologies, and we use our "ordering scheme" to determine the degree to which the resulting metric and matter distribution solve Einstein's equation. We find that Einstein's equation fails to hold at "order 1" at small scales and at "order $\epsilon$" at large scales. We then find the additional corrections to the metric and matter distribution needed to satisfy Einstein's equation to these orders. While these corrections are of some interest in their own right, our main purpose in calculating them is that their smallness should provide a criterion for the validity of the original dictionary (as well as simplified versions of this dictionary). We expect that, in realistic Newtonian cosmologies, these additional corrections will be very small; if so, this should provide strong justification for the use of Newtonian simulations to describe relativistic cosmologies, even on scales larger than the Hubble radius.

35 pages; minor changes

References in corpus (5)

• A new framework for analyzing the effects of small scale inhomogeneities in cosmology
• Full-Sky Weak Lensing Simulation with 70 Billion Particles
• Unified treatment of cosmological perturbations from super-horizon to small scales
• Applicability of the linearly perturbed FRW metric and Newtonian cosmology
• Geometrical order-of-magnitude estimates for spatial curvature in realistic models of the Universe

Cited by in corpus (98)

• Backreaction in late-time cosmology
• General relativity and cosmic structure formation
• Is there proof that backreaction of inhomogeneities is irrelevant in cosmology?
• gevolution: a cosmological N-body code based on General Relativity
• How well is our universe described by an FLRW model?
• General Relativistic N-body simulations in the weak field limit
• Schrödinger method as N-body double and UV completion of dust
• Cosmological simulations of screened modified gravity out of the static approximation: effects on matter distribution
• Relativistic N-body simulations with massive neutrinos
• Computing General Relativistic effects from Newtonian N-body simulations: Frame dragging in the post-Friedmann approach
• General relativistic corrections to $N$-body simulations and the Zel'dovich approximation
• N-body methods for relativistic cosmology
• Inhomogeneous Cosmology with Numerical Relativity
• Einstein's Universe: Cosmological structure formation in numerical relativity
• Lagrangian theory of structure formation in relativistic cosmology II: average properties of a generic evolution model
• First-order Cosmological Perturbations Engendered by Point-like Masses
• The missing link: a nonlinear post-Friedmann framework for small and large scales
• Solving the Vlasov equation in two spatial dimensions with the Schrödinger method
• LIGER: mock relativistic light-cones from Newtonian simulations
• Fully relativistic treatment of light neutrinos in $N$-body simulations
• Examples of backreaction of small scale inhomogeneities in cosmology
• Viscous dark matter growth in (neo-)Newtonian cosmology
• General relativistic weak-field limit and Newtonian N-body simulations
• Does small scale structure significantly affect cosmological dynamics?
• Comparing Fully General Relativistic and Newtonian Calculations of Structure Formation
• Einstein's signature in cosmological large-scale structure
• The effect of early radiation in N-body simulations of cosmic structure formation
• The fully non-linear post-Friedmann frame-dragging vector potential: Magnitude and time evolution from N-body simulations
• Newtonian versus relativistic cosmology
• Second order solutions of cosmological perturbation in the matter dominated era
• Backreaction in Cosmology
• A Simple, Heuristic Derivation of our "No Backreaction" Results
• Nonlinear cosmological consistency relations and effective matter stresses
• Studying the precision of ray tracing techniques with Szekeres models
• Cosmological Newtonian limits on large spacetime scales
• Methods for studying the accuracy of light propagation in N-body simulations
• A new approach to cosmological structure formation with massive neutrinos
• Cosmology on all scales: a two-parameter perturbation expansion
• Coarse-grained description of cosmic structure from Szekeres models
• Newtonian Limits of Isolated Cosmological Systems on Long Time Scales
• Cosmological gravity on all scales: simple equations, required conditions, and a framework for modified gravity
• General relativistic corrections and non-Gaussianity in large scale structure
• Simulation techniques for modified gravity
• Dark energy perturbations in $N$-body simulations
• Relativistic cosmological large scale structures at one-loop
• Scalar and vector perturbations in a universe with discrete and continuous matter sources
• The strongest gravitational lenses: II. Is the large Einstein radius of MACS J0717.5+3745 in conflict with LCDM?
• Frame dragging and Eulerian frames in General Relativity
• The Local Value of $H_0$ in an Inhomogeneous Universe
• Distance-redshift relation in plane symmetric universes
• The relativistic galaxy number counts in the weak field approximation
• Finding closure: approximating Vlasov-Poisson using finitely generated cumulants
• $\text{fRevolution}$ $-$ Relativistic Cosmological Simulations in $f(R)$ Gravity I: Methodology
• The Poisson equation at second order in relativistic cosmology
• The large-scale general-relativistic correction for Newtonian mocks
• Gravothermal Catastrophe with a Cosmological Constant
• General Relativistic Cosmological N-body Simulations I: time integration
• Observing relativistic features in large-scale structure surveys -- II: Doppler magnification in an ensemble of relativistic simulations
• Initial conditions for cosmological N-body simulations of the scalar sector of theories of Newtonian, Relativistic and Modified Gravity
• The Newtonian limit on cosmological scales
• Simple expressions for second order density perturbations in standard cosmology
• Do Newtonian large-scale structure simulations fail to include relativistic effects?
• Dynamic Field Theory and Equations of Motion in Cosmology
• Gravitational Lensing by a structure in a cosmological background
• Perturbation theory for cosmologies with non-linear structure
• Structure formation in an anisotropic universe: Eulerian perturbation theory
• A numerical relativity scheme for cosmological simulations
• A Relativistic view on large scale N-body simulations
• On the accuracy of N-body simulations at very large scales
• Einstein-Vlasov Calculations of Structure Formation
• Cosmological applications of the Brown-York quasilocal mass
• Gravitational instabilities of isothermal spheres in the presence of a cosmological constant
• Spherically Symmetric N-body Simulations with General Relativistic Dynamics
• Understanding the Dyer-Roeder approximation as a consequence of local cancellations of projected shear and expansion rate fluctuations
• Fully relativistic predictions in Horndeski gravity from standard Newtonian N-body simulations
• Redshift drift in a universe with structure II: Light rays propagated through a Newtonian N-body simulation
• Cosmological Newtonian limit
• Perturbed redshifts from N-body simulations
• 1+3 formulation of Newton's equations
• Wave Propagation in Modified Gravity
• Second-order effective energy-momentum tensor of gravitational scalar perturbations with perfect fluid
• Cosmological Perturbations: Vorticity, Isocurvature and Magnetic Fields
• Relativistic rotation curve for cosmological structures
• Electrodynamics on Cosmological Scales
• Testing inhomogeneous cosmography in our cosmic neighborhood using CosmicFlows-4
• Gravothermal instability with a cosmological constant in the canonical ensemble
• Beyond boundaries of redshift surveys: assessing mass fluctuations on "super-survey" scales
• The Schr$\ddot{o}$dinger-Poisson equations as the large-N limit of the Newtonian N-body system: applications to the large scale dark matter dynamics
• Averaged universe confronted with cosmological observations: A fully covariant approach
• Remarks on overestimating the effects of inhomogeneities on the Hubble constant
• Suppression of matter density growth at scales exceeding the cosmic screening length
• Direct correspondence between Newtonian gravitation and general relativity
• Redshift Drift fluctuations from N-body simulations
• Friedmann-Lemaître-Robertson-Walker cosmology through the lens of gravitoelectromagnetism
• Tracing Cosmological Signature with Doppler Lensing: Insights from Cosmological Simulations
• Ringing the universe with cosmic emptiness: void properties through a combined analysis of stacked weak gravitational and Doppler lensing
• The perturbed FLRW metric on all scales: Newtonian limit and top-hat collapse
• Mapping the cosmic mass distribution with stacked weak gravitational lensing and Doppler lensing