Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userSecond-order cosmological perturbation theory and initial conditions for $N$-body simulations
110
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We use gauge-invariant cosmological perturbation theory to calculate the displacement field that sets the initial conditions for $N$-body simulations. Using first and second-order fully relativistic perturbation theory in the synchronous-comoving gauge, allows us to go beyond the Newtonian predictions and to calculate relativistic corrections to it. We use an Einstein--de Sitter model, including both growing and decaying modes in our solutions. The impact of our results should be assessed through the implementation of the featured displacement in cosmological $N$-body simulations.
rate research
Read More
Cosmology is entering an era of percent level precision due to current large observational surveys. This precision in observation is now demanding more accuracy from numerical methods and cosmological simulations. In this paper, we study the accuracy of $N$-body numerical simulations and their dependence on changes in the initial conditions and in the simulation algorithms. For this purpose, we use a series of cosmological $N$-body simulations with varying initial conditions. We test the influence of the initial conditions, namely the pre-initial configuration (preIC), the order of the Lagrangian perturbation theory (LPT), and the initial redshift, on the statistics associated with the large scale structures of the universe such as the halo mass function, the density power spectrum, and the maximal extent of the large scale structures. We find that glass or grid pre-initial conditions give similar results at $zlesssim 2$. However, the initial excess of power in the glass initial conditions yields a subtle difference in the power spectra and the mass function at high redshifts. The LPT order used to generate the ICs of the simulations is found to play a crucial role. First-order LPT (1LPT) simulations underestimate the number of massive haloes with respect to second-order (2LPT) ones, typically by 2% at $10^{14} h^{-1} M_odot$ for an initial redshift of 23, and the small-scale power with an underestimation of 6% near the Nyquist frequency for $z_mathrm{ini} = 23$. Moreover, at higher redshifts, the high-mass end of the mass function is significantly underestimated in 1LPT simulations. On the other hand, when the LPT order is fixed, the starting redshift has a systematic impact on the low-mass end of the halo mass function.
Initial conditions for (Newtonian) cosmological N-body simulations are usually set by re-scaling the present-day power spectrum obtained from linear (relativistic) Boltzmann codes to the desired initial redshift of the simulation. This back-scaling method can account for the effect of inhomogeneous residual thermal radiation at early times, which is absent in the Newtonian simulations. We analyse this procedure from a fully relativistic perspective, employing the recently-proposed Newtonian motion gauge framework. We find that N-body simulations for LambdaCDM cosmology starting from back-scaled initial conditions can be self-consistently embedded in a relativistic space-time with first-order metric potentials calculated using a linear Boltzmann code. This space-time coincides with a simple N-body gauge for z<50 for all observable modes. Care must be taken, however, when simulating non-standard cosmologies. As an example, we analyse the back-scaling method in a cosmology with decaying dark matter, and show that metric perturbations become large at early times in the back-scaling approach, indicating a breakdown of the perturbative description. We suggest a suitable forwards approach for such cases.
We give an explicit relation, up to second-order terms, between scalar-field fluctuations defined on spatially-flat slices and the curvature perturbation on uniform-density slices. This expression is a necessary ingredient for calculating observable quantities at second-order and beyond in multiple-field inflation. We show that traditional cosmological perturbation theory and the `separate universe approach yield equivalent expressions for superhorizon wavenumbers, and in particular that all nonlocal terms can be eliminated from the perturbation-theory expressions.
Deriving the Einstein field equations (EFE) with matter fluid from the action principle is not straightforward, because mass conservation must be added as an additional constraint to make rest-frame mass density variable in reaction to metric variation. This can be avoided by introducing a constraint $delta(sqrt{-g}) = 0$ to metric variations $delta g^{mu u}$, and then the cosmological constant $Lambda$ emerges as an integration constant. This is a removal of one of the four constraints on initial conditions forced by EFE at the birth of the universe, and it may imply that EFE are unnecessarily restrictive about initial conditions. I then adopt a principle that the theory of gravity should be able to solve time evolution starting from arbitrary inhomogeneous initial conditions about spacetime and matter. The equations of gravitational fields satisfying this principle are obtained, by setting four auxiliary constraints on $delta g^{mu u}$ to extract six degrees of freedom for gravity. The cost of achieving this is a loss of general covariance, but these equations constitute a consistent theory if they hold in the special coordinate systems that can be uniquely specified with respect to the initial space-like hypersurface when the universe was born. This theory predicts that gravity is described by EFE with non-zero $Lambda$ in a homogeneous patch of the universe created by inflation, but $Lambda$ changes continuously across different patches. Then both the smallness and coincidence problems of the cosmological constant are solved by the anthropic argument. This is just a result of inhomogeneous initial conditions, not requiring any change of the fundamental physical laws in different patches.
In this paper we present the implementation of an efficient formalism for the generation of arbitrary non-Gaussian initial conditions for use in N-body simulations. The methodology involves the use of a separable modal approach for decomposing a primordial bispectrum or trispectrum. This approach allows for the far more efficient generation of the non-Gaussian initial conditions already described in the literature, as well as the generation for the first time of non-separable bispectra and the special class of diagonal-free trispectra. The modal approach also allows for the reconstruction of the spectra from given realisations, a fact which is exploited to provide an accurate consistency check of the simulations.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
