The anisotropy of the power spectrum in periodic cosmological
  simulations
  The classical gravitational force on a torus is anisotropic and always lower
than Newton's $1/r^2$ law. We demonstrate the effects of periodicity in dark
matter only $N$-body simulations of spherical collapse and standard
$\Lambda$CDM initial conditions. Periodic boundary conditions cause an overall
negative and anisotropic bias in cosmological simulations of cosmic structure
formation. The lower amplitude of power spectra of small periodic simulations
are a consequence of the missing large scale modes and the equally important
smaller periodic forces. The effect is most significant when the largest mildly
non-linear scales are comparable to the linear size of the simulation box, as
often is the case for high-resolution hydrodynamical simulations. Spherical
collapse morphs into a shape similar to an octahedron. The anisotropic growth
distorts the large-scale $\Lambda$CDM dark matter structures. We introduce the
direction-dependent power spectrum invariant under the octahedral group of the
simulation volume and show that the results break spherical symmetry.
