Modeling Dynamical Dark Energy

Cosmological models with different types of Dark Energy are becoming viablealternatives for standard models with the cosmological constant. Yet, suchmodels are more difficult to analyze and to simulate. We present analyticalapproximations and discuss ways of making simulations for two families ofmodels, which cover a wide range of possibilities and include models with bothslow and fast changing ratio w=p\rho. More specifically, we give analyticalexpressions for the evolution of the matter density parameter Omega_m(z) andthe virial density contrast Delta_c at any redshift z. The latter is used toidentify halos and to find their virial masses. We also provide anapproximation for the linear growth factor of linear fluctuations betweenredshift z=40 and z=0. This is needed to set the normalization of the spectrumof fluctuations. Finally, we discuss the expected behavior of the halo massfunction and its time evolution.Comment: 10 pages, 10 figures ApJ submitte