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 .