Download Horizon Initial Conditions and Related Softwares (expert only)

WMAP I

CMB temperature fluctuations as seen by WMAP after one year of operation

The initial cosmological conditions are built by linearly integrating an almost scale-invariant fluctuations spectrum produced by the assumed early inflation. These density fluctuations are integrated in the linear regime until the non-linear evolution has to be treated by numerical simulations.

The linear integration is performed using the COSMICS package, including LINGER (linear equations in general relativity) and GRAFIC (Gaussian RAndom Field Initial Conditions). This package has been created by E. Bertschinger (see the web site http://web.mit.edu/edbert and the related paper).

The program uses a set of parameters to define the model of universe used (flat curvature, densities of baryonic and dark matter and dark energy content), selects the power spectrum shape, and its normalisation, and outputs the density and velocity field on a regular lattice, with periodic boundary conditions.

The density perturbations are given by a displacement field at each position of the cartesian lattice, and a velocity field, obeying the Zeldovich approximation (displacement and velocities are coherent to produce the density perturbations).

The method uses the key equation which develops the density perturbation field as the convolution of a white noise function with a transfer function, which represents the power spectrum P(k). The largest and smallest scale that can be treated is limited by the size of the cartesian grid, and the smallest cell used (the resolution).

The challenge of the Horizon project is to study galaxy formation at the smallest scale, taking into account the cosmological context, widely using multi-scale resolution. It is now possible with GRAFIC2 to generate Gaussian random fields, with adaptive mesh refinement (Bertschinger 2001). The advantage of this package is to provide codes able to relate the large scale density perturbations to the refined small scales ones. Indeed, it is not only dividing the smallest cells in the refined zone by a certain refinement factor r, but also ensures that the phase of the coarse grid fluctuations are the same as those in the fine grid, for the same wave-number. The convolution with multi-scale resolution enforces a constraint on the white noise functions that made them coherent at the relevant scales, and not completely independent. This ensures that the small-scale structures that will develop in the high resolution simulations through gravitational collapse will know in which large-scale structure they form, at low resolution.

Before recombination, the ionized baryons are tightly coupled to the photons and participate closely to the acoustic oscillations, which are visible as the characterictics peaks in the anisotropy power spectrum of the CMB (Cosmic Microwave Background) . These peaks occur at low and intermediate scale, and then are damped at small scale. Although the baryonic fraction (4-5% in Omega_b) is low, these perturbations remain imprinted in the density power spectrum, and could be an interesting signature, that can be observed in large-scale structures. The cosmological initial conditions will therefore also include the baryon wiggles and damping, according to the precise treatment by Eisenstein and Hu (1998). The baryons affect the transfer function of dark matter through the acoustic oscillations, and suppression of power below the sound horizon.