Modeling Dynamical Dark Energy

Cosmological models with different types of Dark Energy are becoming viable alternatives for standard models with the cosmological constant. Yet, such models are more difficult to analyze and to simulate. We present analytical approximations and discuss ways of making simulations for two families of models, which cover a wide range of possibilities and include models with both slow and fast changing ratio w=p\rho. More specifically, we give analytical expressions for the evolution of the matter density parameter Omega_m(z) and the virial density contrast Delta_c at any redshift z. The latter is used to identify halos and to find their virial masses. We also provide an approximation for the linear growth factor of linear fluctuations between redshift z=40 and z=0. This is needed to set the normalization of the spectrum of fluctuations. Finally, we discuss the expected behavior of the halo mass function and its time evolution.Comment: 10 pages, 10 figures ApJ submitte

Tracing the Nature of Dark Energy with Galaxy Distribution

Dynamical Dark Energy (DE) is a viable alternative to the cosmological constant. Yet, constructing tests to discriminate between Lambda and dynamical DE models is difficult because the differences are not large. In this paper we explore tests based on the galaxy mass function, the void probability function (VPF), and the number of galaxy clusters. At high z the number density of clusters shows large differences between DE models, but geometrical factors reduce the differences substantially. We find that detecting a model dependence in the cluster redshift distribution is a hard challenge. We show that the galaxy redshift distribution is potentially a more sensitive characteristics. We do so by populating dark matter halos in Nbody simulations with galaxies using well-tested Halo Occupation Distribution (HOD). We also estimate the Void Probability Function and find that, in samples with the same angular surface density of galaxies in different models, the VPF is almost model independent and cannot be used as a test for DE. Once again, geometry and cosmic evolution compensate each other. By comparing VPF's for samples with fixed galaxy mass limits, we find measurable differences.Comment: 12 pages, 11 figures, dependence on mass-luminosity relation discussed, minor changes to match the accepted version by MNRA

Halo Mass Functions in Early Dark Energy Cosmologies

We examine the linear density contrast at collapse time, $\delta_c$ for large-scale structure in dynamical dark energy cosmologies, including models with early dark energy. Contrary to previous results, we find that as long as dark energy is homogeneous on small scales, $\delta_c$ is insensitive to dark energy properties for parameter values fitting current data, including the case of early dark energy. This is significant since using the correct $\delta_c$ is crucial for accurate Press-Schechter prediction of the halo mass function. Previous results have found an apparent failing of the extended Press-Schechter approach (Sheth-Tormen) for early dark energy. Our calculations demonstrate that with the correct $\delta_c$ the accuracy of this approach is restored. We discuss the significance of this result for the halo mass function and examine what dark energy physics would be needed to cause significant change in $\delta_c$, and the observational signatures this would leave.Comment: 5 pages, 2 figures. Accepted for MNRAS Letter

Tracing the nature of dark energy with galaxy distribution

Dynamical dark energy (DE) is a viable alternative to the cosmological constant. Constructing tests to discriminate between Λ and dynamical DE models is difficult, however, because the differences are not large. In this paper we explore tests based on the galaxy mass function, the void probability function (VPF), and the number of galaxy clusters. At high z, the number density of clusters shows large differences between DE models, but geometrical factors reduce the differences substantially. We find that detecting a model dependence in the cluster redshift distribution is a significant challenge. We show that the galaxy redshift distribution is potentially a more sensitive characteristic. We do this by populating dark matter haloes in N-body simulations with galaxies using well-tested halo occupation distributions. We also estimate the VPF and find that samples with the same angular surface density of galaxies, in different models, exhibition almost model-independent VPF which therefore cannot be used as a test for DE. Once again, geometry and cosmic evolution compensate each other. By comparing VPFs for samples with fixed galaxy mass limits, we find measurable difference

Dynamical Dark Energy simulations: high accuracy Power Spectra at high redshift

Accurate predictions on non--linear power spectra, at various redshift z, will be a basic tool to interpret cosmological data from next generation mass probes, so obtaining key information on Dark Energy nature. This calls for high precision simulations, covering the whole functional space of w(z) state equations and taking also into account the admitted ranges of other cosmological parameters; surely a difficult task. A procedure was however suggested, able to match the spectra at z=0, up to k~3, hMpc^{-1}, in cosmologies with an (almost) arbitrary w(z), by making recourse to the results of N-body simulations with w = const. In this paper we extend such procedure to high redshift and test our approach through a series of N-body gravitational simulations of various models, including a model closely fitting WMAP5 and complementary data. Our approach detects w= const. models, whose spectra meet the requirement within 1% at z=0 and perform even better at higher redshift, where they are close to a permil precision. Available Halofit expressions, extended to (constant) w \neq -1 are unfortunately unsuitable to fit the spectra of the physical models considered here. Their extension to cover the desired range should be however feasible, and this will enable us to match spectra from any DE state equation.Comment: method definitely improved in semplicity and efficacy,accepted for publication on JCA

Scalar field-perfect fluid correspondence and nonlinear perturbation equations

The properties of dynamical Dark Energy (DE) and, in particular, the possibility that it can form or contribute to stable inhomogeneities, have been widely debated in recent literature, also in association to a possible coupling between DE and Dark Matter (DM). In order to clarify this issue, in this paper we present a general framework for the study of the nonlinear phases of structure formation, showing the equivalence between two possible descriptions of DE: a scalar field \phi self-interacting through a potential V(\phi) and a perfect fluid with an assigned negative equation of state w(a). This enables us to show that, in the presence of coupling, the mass of DE quanta may increase where large DM condensations are present, so that also DE may partake to the clustering process.Comment: 16 pages, accepted for publication in JCA