Discrete Newtonian Cosmology: Perturbations

Abstract

In a previous paper [arXiv:1308.1852] we showed how a finite system of discrete particles interacting with each other via Newtonian gravitational attraction would lead to precisely the same dynamical equations for homothetic motion as in the case of the pressure-free Friedmann-Lemaître-Robertson-Walker cosmological models of General Relativity Theory, provided the distribution of particles obeys the central configuration equation. In this paper we show one can obtain perturbed such Newtonian solutions that give the same linearised structure growth equations as in the general relativity case. We also obtain the Dmitriev-Zeldovich equations for subsystems in this discrete gravitational model, and show how it leads to the conclusion that voids have an apparent negative mass.

arXiv comment24 pages

References in corpus (10)

• Celestial Mechanics, Conformal Structures, and Gravitational Waves
• A New Method for Determining Cumulative Gravitational Lensing Effects in Inhomogeneous Universes
• Influence of global cosmological expansion on local dynamics and kinematics
• Newton-Hooke spacetimes, Hpp-waves and the cosmological constant
• On the stability of naked singularities
• On Gravitational Repulsion
• Remarks on mechanical approach to observable Universe
• Central Configurations in Three Dimensions
• Generalizing the Cosmic Energy Equation
• Generalized Layzer-Irvine equation: the role of dark energy perturbations in cosmic structure formation

Cited by in corpus (14)

• First-order Cosmological Perturbations Engendered by Point-like Masses
• Cosmological aspects of the Eisenhart-Duval lift
• Eisenhart lifts and symmetries of time-dependent systems
• Conformal and projective symmetries in Newtonian cosmology
• Cosmological backreaction within the Szekeres model and emergence of spatial curvature
• The late Universe with non-linear interaction in the dark sector: the coincidence problem
• Scalar perturbations in cosmological models with dark energy - dark matter interaction
• Cosmological law of universal gravitation
• "Kepler Harmonies" and conformal symmetries
• Time arrow is influenced by the dark energy
• Coupled scalar fields in the late Universe: The mechanical approach and the late cosmic acceleration
• Noether Symmetry in Newtonian Dynamics and Cosmology
• The stability of galaxies in an expanding universe obtained by Newtonian dynamics
• On the magnetic 2+1- D space-time and its non-relativistic counterpart