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 $tau sim H_{0}^{-1}$.
We study the empirical relation between an astronomical objects angular momentum $J$ and mass $M$, $J=beta M^alpha$, the $J-M$ relation, using N-body simulations. In particular, we investigate the time evolution of the $J-M$ relation to study how the
initial power spectrum and cosmological model affect this relation, and to test two popular models of its origin - mechanical equilibrium and tidal torque theory. We find that in the $Lambda$CDM model, $alpha$ starts with a value of $sim 1.5$ at high redshift $z$, increases monotonically, and finally reaches $5/3$ near $z=0$, whereas $beta$ evolves linearly with time in the beginning, reaches a maximum and decreases, and stabilizes finally. A three-regime scheme is proposed to understand this newly observed picture. We show that the tidal torque theory accounts for this time evolution behaviour in the linear regime, whereas $alpha=5/3$ comes from the virial equilibrium of haloes. The $J-M$ relation in the linear regime contains the information of the power spectrum and cosmological model. The $J-M$ relations for haloes in different environments and with different merging histories are also investigated to study the effects of a halos non-linear evolution. An updated and more complete understanding of the $J-M$ relation is thus obtained.
We study the equilibrium structures of white dwarfs with dark matter cores formed by non-self-annihilating dark matter DM particles with mass ranging from 1 GeV to 100 GeV, which are assumed to form an ideal degenerate Fermi gas inside the stars. For
DM particles of mass 10 GeV and 100 GeV, we find that stable stellar models exist only if the mass of the DM core inside the star is less than O(10^-3) Msun and O(10^-6) Msun, respectively. The global properties of these stars, and in particular the corresponding Chandrasekhar mass limits, are essentially the same as those of traditional white dwarf models without DM. Nevertheless, in the 10 GeV case, the gravitational attraction of the DM core is strong enough to squeeze the normal matter in the core region to densities above neutron drip, far above those in traditional white dwarfs. For DM with particle mass 1 GeV, the DM core inside the star can be as massive as around 0.1 Msun and affects the global structure of the star significantly. In this case, the radius of a stellar model with DM can be about two times smaller than that of a traditional white dwarf. Furthermore, the Chandrasekhar mass limit can also be decreased by as much as 40%. Our results may have implications on to what extent type Ia supernovae can be regarded as standard candles - a key assumption in the discovery of dark energy.
One of the main goals of modern cosmic microwave background (CMB) missions is to measure the tensor-to-scalar ratio $r$ accurately to constrain inflation models. Due to ignorance about the reionization history $X_{e}(z)$, this analysis is usually don
e by assuming an instantaneous reionization $X_{e}(z)$ which, however, can bias the best-fit value of $r$. Moreover, due to the strong mixing of B-mode and E-mode polarizations in cut-sky measurements, multiplying the sky coverage fraction $f_{sky}$ by the full-sky likelihood would not give satisfactory results. In this work, we forecast constraints on $r$ for the Planck mission taking into account the general reionization scenario and cut-sky effects. Our results show that by applying an N-point interpolation analysis to the reionization history, the bias induced by the assumption of instantaneous reionization is removed and the value of $r$ is constrained within $5%$ error level, if the true value of $r$ is greater than about 0.1 .
