66 research outputs found
Zeldovich flow on cosmic vacuum background: new exact nonlinear analytical solution
A new exact nonlinear Newtonian solution for a plane matter flow superimposed
on the isotropic Hubble expansion is reported. The dynamical effect of cosmic
vacuum is taken into account. The solution describes the evolution of nonlinear
perturbations via gravitational instability of matter and the termination of
the perturbation growth by anti-gravity of vacuum at the epoch of transition
from matter domination to vacuum domination. On this basis, an `approximate' 3D
solution is suggested as an analog of the Zeldovich ansatz.Comment: 9 pages, 1 figure
Gravitational backreaction in cosmological spacetimes
We develop a new formalism for the treatment of gravitational backreaction in
the cosmological setting. The approach is inspired by projective techniques in
non-equilibrium statistical mechanics. We employ group-averaging with respect
to the action of the isotropy group of homogeneous and isotropic spacetimes
(rather than spatial averaging), in order to define effective FRW variables for
a generic spacetime. Using the Hamiltonian formalism for gravitating perfect
fluids, we obtain a set of equations for the evolution of the effective
variables; these equations incorporate the effects of backreaction by the
inhomogeneities. Specializing to dust-filled spacetimes, we find regimes that
lead to a closed set of backreaction equations, which we solve for small
inhomogeneities. We then study the case of large inhomogeneities in relation to
the proposal that backreaction can lead to accelerated expansion. In
particular, we identify regions of the gravitational state space that
correspond to effective cosmic acceleration. Necessary conditions are (i) a
strong expansion of the congruences corresponding to comoving observers, and
(ii) a large negative value of a dissipation variable that appears in the
effective equations (i.e, an effective "anti-dissipation").Comment: 36 pages, latex. Extended discussion on results and on relation to
Lemaitre-Tolman-Bondi models. Version to appear in PR
Small Scale Perturbations in a General MDM Cosmology
For a universe with massive neutrinos, cold dark matter, and baryons, we
solve the linear perturbation equations analytically in the small-scale limit
and find agreement with numerical codes at the 1-2% level. The inclusion of
baryons, a cosmological constant, or spatial curvature reduces the small-scale
power and tightens limits on the neutrino density from observations of high
redshift objects. Using the asymptotic solution, we investigate neutrino infall
into potential wells and show that it can be described on all scales by a
growth function that depends on time, wavenumber, and cosmological parameters.
The growth function may be used to scale the present-day transfer functions
back in redshift. This allows us to construct the time-dependent transfer
function for each species from a single master function that is independent of
time, cosmological constant, and curvature.Comment: Submitted to ApJ; 13 pages, aastex, 4 figures included; also
available at http://www.sns.ias.edu/~wh
The Cosmic No-Hair Theorem and the Nonlinear Stability of Homogeneous Newtonian Cosmological Models
The validity of the cosmic no-hair theorem is investigated in the context of
Newtonian cosmology with a perfect fluid matter model and a positive
cosmological constant. It is shown that if the initial data for an expanding
cosmological model of this type is subjected to a small perturbation then the
corresponding solution exists globally in the future and the perturbation
decays in a way which can be described precisely. It is emphasized that no
linearization of the equations or special symmetry assumptions are needed. The
result can also be interpreted as a proof of the nonlinear stability of the
homogeneous models. In order to prove the theorem we write the general solution
as the sum of a homogeneous background and a perturbation. As a by-product of
the analysis it is found that there is an invariant sense in which an
inhomogeneous model can be regarded as a perturbation of a unique homogeneous
model. A method is given for associating uniquely to each Newtonian
cosmological model with compact spatial sections a spatially homogeneous model
which incorporates its large-scale dynamics. This procedure appears very
natural in the Newton-Cartan theory which we take as the starting point for
Newtonian cosmology.Comment: 16 pages, MPA-AR-94-
The Excursion Set Theory of Halo Mass Functions, Halo Clustering, and Halo Growth
I review the excursion set theory (EST) of dark matter halo formation and
clustering. I recount the Press-Schechter argument for the mass function of
bound objects and review the derivation of the Press-Schechter mass function in
EST. The EST formalism is powerful and can be applied to numerous problems. I
review the EST of halo bias and the properties of void regions. I spend
considerable time reviewing halo growth in the EST. This section culminates
with descriptions of two Monte Carlo methods for generating halo mass accretion
histories. In the final section, I emphasize that the standard EST approach is
the result of several simplifying assumptions. Dropping these assumptions can
lead to more faithful predictions and a more versatile formalism. One such
assumption is the constant height of the barrier for nonlinear collapse. I
review implementations of the excursion set approach with arbitrary barrier
shapes. An application of this is the now well-known improvement to standard
EST that follows from the ellipsoidal-collapse barrier. Additionally, I
emphasize that the statement that halo accretion histories are independent of
halo environments is a simplifying assumption, rather than a prediction of the
theory. I review the method for constructing correlated random walks of the
density field in more general cases. I construct a simple toy model with
correlated walks and I show that excursion set theory makes a qualitatively
simple and general prediction for the relation between halo accretion histories
and halo environments: regions of high density preferentially contain
late-forming halos and conversely for regions of low density. I conclude with a
brief discussion of this prediction in the context of recent numerical studies
of the environmental dependence of halo properties. (Abridged)Comment: 62 pages, 19 figures. Review article based on lectures given at the
Sixth Summer School of the Helmholtz Institute for Supercomputational
Physics. Accepted for Publication in IJMPD. Comments Welcom
Hydrodynamic approach to the evolution of cosmological structures
A hydrodynamic formulation of the evolution of large-scale structure in the
Universe is presented. It relies on the spatially coarse-grained description of
the dynamical evolution of a many-body gravitating system. Because of the
assumed irrelevance of short-range (``collisional'') interactions, the way to
tackle the hydrodynamic equations is essentially different from the usual case.
The main assumption is that the influence of the small scales over the
large-scale evolution is weak: this idea is implemented in the form of a
large-scale expansion for the coarse-grained equations. This expansion builds a
framework in which to derive in a controlled manner the popular ``dust'' model
(as the lowest-order term) and the ``adhesion'' model (as the first-order
correction). It provides a clear physical interpretation of the assumptions
involved in these models and also the possibility to improve over them.Comment: 14 pages, 3 figures. Version to appear in Phys. Rev.
On the Back Reaction Problem for Gravitational Perturbations
We derive the effective energy-momentum tensor for cosmological perturbations
and prove its gauge-invariance. The result is applied to study the influence of
perturbations on the behaviour of the Friedmann background in inflationary
Universe scenarios. We found that the back reaction of cosmological
perturbations on the background can become important already at energies below
the self-reproduction scale.Comment: 4 pages, uses LATE
Lagrangian theory of structure formation in relativistic cosmology I: Lagrangian framework and definition of a nonperturbative approximation
In this first paper we present a Lagrangian framework for the description of
structure formation in general relativity, restricting attention to
irrotational dust matter. As an application we present a self-contained
derivation of a general-relativistic analogue of Zel'dovich's approximation for
the description of structure formation in cosmology, and compare it with
previous suggestions in the literature. This approximation is then
investigated: paraphrasing the derivation in the Newtonian framework we provide
general-relativistic analogues of the basic system of equations for a single
dynamical field variable and recall the first-order perturbation solution of
these equations. We then define a general-relativistic analogue of Zel'dovich's
approximation and investigate its implications by functionally evaluating
relevant variables, and we address the singularity problem. We so obtain a
possibly powerful model that, although constructed through extrapolation of a
perturbative solution, can be used to put into practice nonperturbatively, e.g.
problems of structure formation, backreaction problems, nonlinear properties of
gravitational radiation, and light-propagation in realistic inhomogeneous
universe models. With this model we also provide the key-building blocks for
initializing a fully relativistic numerical simulation.Comment: 21 pages, content matches published version in PRD, discussion on
singularities added, some formulas added, some rewritten and some correcte
Evolution of density perturbations in a realistic universe
Prompted by the recent more precise determination of the basic cosmological
parameters and growing evidence that the matter-energy content of the universe
is now dominated by dark energy and dark matter we present the general solution
of the equation that describes the evolution of density perturbations in the
linear approximation. It turns out that as in the standard CDM model the
density perturbations grow very slowly during the radiation dominated epoch and
their amplitude increases by a factor of about 4000 in the matter and later
dark energy dominated epoch of expansion of the universe.Comment: 19 pages, 4 figure
Power Spectra for Cold Dark Matter and its Variants
The bulk of recent cosmological research has focused on the adiabatic cold
dark matter model and its simple extensions. Here we present an accurate
fitting formula that describes the matter transfer functions of all common
variants, including mixed dark matter models. The result is a function of
wavenumber, time, and six cosmological parameters: the massive neutrino
density, number of neutrino species degenerate in mass, baryon density, Hubble
constant, cosmological constant, and spatial curvature. We show how
observational constraints---e.g. the shape of the power spectrum, the abundance
of clusters and damped Lyman-alpha systems, and the properties of the
Lyman-alpha forest--- can be extended to a wide range of cosmologies, including
variations in the neutrino and baryon fractions in both high-density and
low-density universes.Comment: 20 pages, LaTeX, 4 figures. Submitted to ApJ. Electronic versions of
the fitting formula, as well as simple codes to output cosmological
quantities (e.g. sigma_8) as a function of parameters and illustrative
animations of parameter dependence, are available at
http://www.sns.ias.edu/~whu/transfer/transfer.htm
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