1,459 research outputs found
Initial conditions for cold dark matter particles and General Relativity
We describe the irrotational dust component of the universe in terms of a
relativistic gradient expansion and transform the resulting synchronous metric
to a Newtonian coordinate system. The two metrics are connected via a
space-like displacement field and a time-like perturbation, providing a
relativistic generalization of the transformation from Lagrangian to Eulerian
coordinates. The relativistic part of the displacement field generates already
at initial time a non-local density perturbation at second order. This is a
purely relativistic effect since it originates from space-time mixing. We give
two options, the passive and the active approach, on how to include the
relativistic corrections for example in N-body simulations. In the passive
approach we treat the corrections as a non-Gaussian modification of the initial
Gaussian field (primordial non-Gaussianity could be incorporated as well). The
induced non-Gaussianity depends on scale and the redshift at which initial
conditions are set, with f_NL ~ few for small enough scales and redshifts. In
the active approach we show how to use the relativistic trajectory to obtain
the initial displacement and velocity of particles for N-body simulations
without modifying the initial Gaussian field.Comment: Title adjusted, added a table for clarity, matches published versio
Zel'dovich approximation and General Relativity
We show how the Zel'dovich approximation and the second order displacement
field of Lagrangian perturbation theory can be obtained from a general
relativistic gradient expansion in \Lambda{}CDM cosmology. The displacement
field arises as a result of a second order non-local coordinate transformation
which brings the synchronous/comoving metric into a Newtonian form. We find
that, with a small modification, the Zel'dovich approximation holds even on
scales comparable to the horizon. The corresponding density perturbation is not
related to the Newtonian potential via the usual Poisson equation but via a
modified Helmholtz equation. This is a consequence of causality not present in
the Newtonian theory. The second order displacement field receives relativistic
corrections that are subdominant on short scales but are comparable to the
second order Newtonian result on scales approaching the horizon. The
corrections are easy to include when setting up initial conditions in large
N-body simulations.Comment: 5 pages, corrected a typo, accepted for publication in MNRAS Letter
Self Regulation of Infrared Correlations for Massless Scalar Fields during Inflation
Self-energies of a minimally coupled scalar field with quartic and trilinear
interactions are calculated in a de Sitter background, using a position space
propagator. For quartic interactions, we recover earlier results for the
seagull diagram, namely that it contributes an effective mass for the scalar
field at leading order in the infrared enhancement in a steady-state de Sitter
background. We further show that the sunset diagram also contributes to this
effective mass and argue that these two contributions are sufficient in order
to determine a self-consistent dynamical mass. In addition, trilinear
interactions also induce a dynamical mass for the scalar field which we
calculate. Since an interacting scalar field in de Sitter acquires a dynamical
mass through these loop corrections, the infrared divergences of the two-point
correlator are naturally self-regulated.Comment: 16 pages, 4 figure
Modelling of soot formation in laminar diffusion flames using a comprehensive CFD-PBE model with detailed gas-phase chemistry
A discretised population balance equation (PBE) is coupled with an in-house computational fluid dynamics (CFD) code in order to model soot formation in laminar diffusion flames. The unsteady Navier–Stokes, species and enthalpy transport equations and the spatially-distributed discretised PBE for the soot particles are solved in a coupled manner, together with comprehensive gas-phase chemistry and an optically thin radiation model, thus yielding the complete particle size distribution of the soot particles. Nucleation, surface growth and oxidation are incorporated into the PBE using an acetylene-based soot model. The potential of the proposed methodology is investigated by comparing with experimental results from the Santoro jet burner [Santoro, Semerjian and Dobbins, Soot particle measurements in diffusion flames, Combustion and Flame, Vol. 51 (1983), pp. 203–218; Santoro, Yeh, Horvath and Semerjian, The transport and growth of soot particles in laminar diffusion flames, Combustion Science and Technology, Vol. 53 (1987), pp. 89–115] for three laminar axisymmetric non-premixed ethylene flames: a non-smoking, an incipient smoking and a smoking flame. Overall, good agreement is observed between the numerical and the experimental results
On the accuracy of N-body simulations at very large scales
We examine the deviation of Cold Dark Matter particle trajectories from the
Newtonian result as the size of the region under study becomes comparable to or
exceeds the particle horizon. To first order in the gravitational potential,
the general relativistic result coincides with the Zel'dovich approximation and
hence the Newtonian prediction on all scales. At second order, General
Relativity predicts corrections which overtake the corresponding second order
Newtonian terms above a certain scale of the order of the Hubble radius.
However, since second order corrections are very much suppressed on such
scales, we conclude that simulations which exceed the particle horizon but use
Newtonian equations to evolve the particles, reproduce the correct trajectories
very well. The dominant relativistic corrections to the power spectrum on
scales close to the horizon are at most of the order of at
and at . The differences in the positions of real
space features are affected at a level below at both redshifts. Our
analysis also clarifies the relation of N-body results to relativistic
considerations.Comment: 7 pages, 2 figures; v2: 7 pages, 3 figures, matches version published
in MNRA
Fluctuations along supersymmetric flat directions during Inflation
We consider a set of scalar fields, consisting of a single flat direction and
one or several non-flat directions. We take our cue from the MSSM, considering
separately D-flat and F-flat directions, but our results apply to any
supersymmetric scenario containing flat directions. We study the field
fluctuations during pure de Sitter Inflation, following the evolution of the
infrared modes by numerically solving the appropriate Langevin equations. We
demonstrate that for the Standard Model U(1), SU(2) or SU(3) gauge couplings,
as well as for large enough Yukawa couplings, the fluctuations along the
non-flat directions effectively block the fluctuations along the flat
directions. The usual expected behaviour \propto N, with N the
number of efolds, may be strongly violated, depending on the coupling
strengths. As a consequence, those cosmological considerations, which are
derived assuming that during inflation flat directions fluctuate freely, should
be revised.Comment: 19 pages, 5 figures, Submitted to JCA
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