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Lattice Universe: examples and problems.

Maxim Brilenkov1, Maxim Eingorn2, Alexander Zhuk3

  • 1Department of Theoretical Physics, Odessa National University, Dvoryanskaya st. 2, Odessa, 65082 Ukraine.

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Smearing masses in lattice universes is physically necessary to avoid nonphysical gravitational potentials. Other lattice topologies either lead to unphysical results or reduce to the simplest topology.

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Area of Science:

  • Cosmology
  • General Relativity
  • Computational Astrophysics

Background:

  • Lattice universes are theoretical models used to study the large-scale structure of the cosmos.
  • The Newtonian limit of General Relativity provides a simplified framework for understanding gravity on cosmic scales.
  • The spatial topology of the universe significantly impacts cosmological models.

Purpose of the Study:

  • To investigate the behavior of gravitational potential in lattice universes with different spatial topologies.
  • To determine the physical implications of point-like versus smeared mass distributions in these models.
  • To assess the validity and necessity of mass-smearing techniques in N-body simulations.

Main Methods:

  • Solving the Poisson equation for the gravitational potential within various lattice universe topologies.
  • Analyzing the gravitational field behavior around point-like mass distributions.
  • Comparing results for different spatial topologies ([Formula: see text], [Formula: see text], [Formula: see text]).

Main Results:

  • In the [Formula: see text] topology, point-like masses lead to nonphysical, undefined gravitational potentials along lines connecting identical masses.
  • Mass-smearing is demonstrated as a physically necessary procedure to obtain regular and meaningful solutions in the [Formula: see text] model.
  • The [Formula: see text] and [Formula: see text] topologies do not yield physically reasonable nontrivial solutions and effectively reduce to the [Formula: see text] topology.

Conclusions:

  • Mass-smearing in N-body simulations is not merely a numerical technique but a physically justified requirement for lattice universes.
  • The simplest lattice topology ([Formula: see text]) is the only one that allows for physically consistent gravitational dynamics when mass-smearing is applied.
  • More complex topologies ([Formula: see text], [Formula: see text]) are either unphysical or degenerate to the simplest case, limiting their independent relevance in cosmological simulations.