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We perform N-body simulations for models with a DE component. Besides of DE with constant negative state parameter w, we consider DE due to scalar fields, self-interacting through RP or SUGRA potentials. According to our post-linear analysis, at z=0, DM power spectra and halo mass functions do not depend on DE nature. This is welcome, as LCDM fits observations. Halo profiles, instead, are denser than LCDM. For example, the density at 15 kpc of a DE halo with M=10^13 exceeds LCDM by ~45%. Differences, therefore, are small but, however, DE does not ease the problem with cuspy DM profiles. We study also subhalos and find that, at $z=0$, the number of satellites coincides in all DE models. At higher z, DE models show increasing differences from LCDM and among themselves (i.e. in the mass function evolution); this is the obvious pattern to distinguish between different DE state equations.
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We study the impact of Early Dark Energy fluctuations in the linear and non-linear regimes of structure formation. In these models the energy density of dark energy is non-negligible at high redshifts and the fluctuations in the dark energy component can have the same order of magnitude of dark matter fluctuations. Since two basic approximations usually taken in the standard scenario of quintessence models, that both dark energy density during the matter dominated period and dark energy fluctuations on small scales are negligible, are not valid in such models, we first study approximate analytical solutions for dark matter and dark energy perturbations in the linear regime. This study is helpful to find consistent initial conditions for the system of equations and to analytically understand the effects of Early Dark Energy and its fluctuations, which are also verified numerically. In the linear regime we compute the matter growth and variation of the gravitational potential associated with the Integrated Sachs-Wolf effect, showing that these observables present important modifications due to Early Dark Energy fluctuations, though making them more similar to $Lambda$CDM model. We also make use of the Spherical Collapse model to study the influence of Early Dark Energy fluctuations in the nonlinear regime of structure formation, especially on $delta_c$ parameter, and their contribution to the halo mass, which we show can be of the order of 10%. We finally compute how the number density of halos is modified in comparison to $Lambda$CDM model and address the problem of how to correct the mass function in order to take into account the contribution of clustered dark energy. We conclude that the inhomogeneous Early Dark Energy models are more similar to $Lambda$CDM model than its homogeneous counterparts.
We study properties of dark matter halos in a variety of models which include Dark Energy (DE). We consider both DE due to a scalar field self--interacting through Ratra-Peebles or SUGRA potentials, and DE with constant negative w=prho >-1. We find that at redshift zero the nonlinear power spectrum of the dark matter, and the mass function of halos, practically do not depend on DE state equation and are almost indistinguishable from predictions of the LCDM model. This is consistent with the nonlinear analysis presented in the accompanying paper. It is also a welcome feature because LCDM models fit a large variety of data. On the other hand, at high redshifts DE models show substantial differences from LCDM and substantial differences among themselves. Halo profiles differ even at z=0. DE halos are denser than LCDM in their central parts because the DE halos collapse earlier. Nevertheless, differences between the models are not so large. For example, the density at 10 kpc of a DE ~10^{13}Msun halo deviates from LCDM by not more than 50%. This, however, means that DE is not a way to ease the problem with cuspy dark matter profiles. Addressing another cosmological problem - abundance of subhalos -- we find that the number of satellites of halos in various DE models does not change relative to the LCDM, when normalized to the same circular velocity of the parent halo. To summarize, the best way to find which DE model fits the observed Universe is to look for evolution of halo properties. For example, the abundance of galaxy groups with mass larger than 10^{13}Msun at z> 2 can be used to discriminate between the models, and, thus, to constrain the nature of DE.
The standard cold dark matter (CDM) model predicts too many and too dense small structures. We consider an alternative model that the dark matter undergoes two-body decays with cosmological lifetime $tau$ into only one type of massive daughters with non-relativistic recoil velocity $V_k$. This decaying dark matter model (DDM) can suppress the structure formation below its free-streaming scale at time scale comparable to $tau$. Comparing with warm dark matter (WDM), DDM can better reduce the small structures while being consistent with high redshfit observations. We study the cosmological structure formation in DDM by performing self-consistent N-body simulations and point out that cosmological simulations are necessary to understand the DDM structures especially on non-linear scales. We propose empirical fitting functions for the DDM suppression of the mass function and the mass-concentration relation, which depend on the decay parameters lifetime $tau$ and recoil velocity $V_k$, and redshift. The fitting functions lead to accurate reconstruction of the the non-linear power transfer function of DDM to CDM in the framework of halo model. Using these results, we set constraints on the DDM parameter space by demanding that DDM does not induce larger suppression than the Lyman-$alpha$ constrained WDM models. We further generalize and constrain the DDM models to initial conditions with non-trivial mother fractions and show that the halo model predictions are still valid after considering a global decayed fraction. Finally, we point out that the DDM is unlikely to resolve the disagreement on cluster numbers between the Planck primary CMB prediction and the Sunyaev-Zeldovich (SZ) effect number count for $tau sim H_{0}^{-1}$.
The standard model of cosmology assumes that the Universe can be described to hover around a homogeneous-isotropic solution of Einsteins general theory of relativity. This description needs (sometimes hidden) hypotheses that restrict the generality, and relaxing these restrictions is the headline of a new physical approach to cosmology that refurnishes the cosmological framework. Considering a homogeneous geometry as a template geometry for the in reality highly inhomogeneous Universe must be considered a strong idealization. Unveiling the limitations of the standard model opens the door to rich consequences of general relativity, giving rise to effective (i.e. spatially averaged) cosmological models that may even explain the longstanding problems of dark energy and dark matter. We explore in this talk the influence of structure formation on average properties of the Universe by discussing: (i) general thoughts on why considering average properties, on the key-issue of non-conserved curvature, and on the global gravitational instability of the standard model of cosmology; (ii) the general set of cosmological equations arising from averaging the scalar parts of Einsteins equations, the generic property of structure formation interacting with the average properties of the Universe in a scale-dependent way, and the description of cosmological backreaction in terms of an effective scalar field.
We determine constraints on spatially-flat tilted dynamical dark energy XCDM and $phi$CDM inflation models by analyzing Planck 2015 cosmic microwave background (CMB) anisotropy data and baryon acoustic oscillation (BAO) distance measurements. XCDM is a simple and widely used but physically inconsistent parameterization of dynamical dark energy, while the $phi$CDM model is a physically consistent one in which a scalar field $phi$ with an inverse power-law potential energy density powers the currently accelerating cosmological expansion. Both these models have one additional parameter compared to standard $Lambda$CDM and both better fit the TT + lowP + lensing + BAO data than does the standard tilted flat-$Lambda$CDM model, with $Delta chi^2 = -1.26 (-1.60)$ for the XCDM ($phi$CDM) model relative to the $Lambda$CDM model. While this is a 1.1$sigma$ (1.3$sigma$) improvement over standard $Lambda$CDM and so not significant, dynamical dark energy models cannot be ruled out. In addition, both dynamical dark energy models reduce the tension between the Planck 2015 CMB anisotropy and the weak lensing $sigma_8$ constraints.
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