Cosmic variance limited Baryon Acoustic Oscillations from the DEUS-FUR
  $\Lambda$CDM simulation
  We investigate the non-linear evolution of Baryon Acoustic Oscillations (BAO)
in the low-redshift matter power spectrum from the DEUS-FUR $\Lambda$CDM model
simulation. This is the first cosmological N-body simulation encompassing the
full observable cosmic volume, thus allowing cosmic variance limited
predictions at BAO scales. We control the effect of numerical systematic errors
using a series of large volume high-resolution simulations. The combined
analysis allows us to measure the matter power spectrum between $z=0$ and $1$
to 1% over the entire BAO range, $0.03<k [\textrm{h Mpc}^{-1}]<0.3$, in bins of
size $\Delta k/k\lesssim$ 1%. We define the BAO with respect to a non-linearly
evolved wiggle-free spectrum and determine the characteristics of the BAO
without recurring to extrapolation from global fitting functions. We quantify
the effects of non-linearities on the position and amplitude of the BAO
extrema, and the coupling to the broadband slope of the power spectrum. We use
these estimates to test non-linear predictions from semi-analytical models.
Quite remarkably from the analysis of the redshift evolution of BAO we find
that the second dip and third peak remains unaltered by non-linear effects.
Furthermore, we find that the square of the damping factor and the shift of the
position of BAO extrema scale to good approximation as the square of the growth
factor, in agreement with expectations from perturbation theory. This confirms
the idea that, besides cosmic distances, an accurate measurement of BAO at
different redshifts can directly probe the growth of cosmic structures.
