Initial conditions are generated assuming gaussian random fields.
In this case the initial density field is entirely characterized by its power spectrum. The power spectrum was computed using a modified version of CAMB (Lewis et al, 1999) including the fluctuations of dark energy (Alimi et al, 2010).
Linear power spectrum at z=0 for ΛCDM (red), SUGRA (green) and Ratra-Peebles (blue). The normalization is different because models have been calibrated on SNIa and CMB. Corresponding two-column ASCII files can be found here pk_lcdmw5.dat pk_sucdmw5.dat pk_rpcdmw5.dat
We have modified MPGRAFIC (Prunet et al, 2008), a parallel version of GRAFIC (Bertschinger et al, 2001) in order to take into account quintessence cosmologies including the fluctuations of scalar field. This code computes dark matter particles displacements and velocities using Zel’dovich approximation. The choice of initial redshift is particularly critical, it should be high enough for Zel’dovich approximation to be valid. We start the simulations, for all cosmologies, when the level of fluctuation at the resolution of the code is 0.05 (leading to starting redshift between 50 and 150 depending on cosmology and box length, see section Run).
We first generate 2048^3 initial conditions and then degrade them down to 256^3 using the Degraf code within MPGRAFIC package. Here is the measured power spectrum for various resolution compared to the linear power spectrum.
Measured power spectrum for 256^3 (light blue), 512^3 (dark blue), 1024^3 (green) and 2048^3 (red) initial conditions versus linear power spectrum (black). The box length is L=648 Mpc/h, cosmology is Ratra-Peebles, expansion factor is a=0.0121622.
Error diagram P(k)/Plin(k)-1 (same convention as previous plot). The agreement between the linear and generated power spectrum is pretty good, deviations are essentially Poisson noise.
For completeness we should mention that initial conditions have been generated on 256 cores and the seed of « DEUSS white noise » is 1415926.