21 research outputs found
Estimating the amount of vorticity generated by cosmological perturbations in the early universe
We estimate the amount of vorticity generated at second order in cosmological
perturbation theory from the coupling between first order energy density and
non-adiabatic pressure, or entropy, perturbations. Assuming power law input
spectra for the source terms, and working in a radiation background, we
calculate the wave number dependence of the vorticity power spectrum and its
amplitude. We show that the vorticity generated by this mechanism is
non-negligible on small scales, and hence should be taken into consideration in
current and future CMB experiments.Comment: 9 pages, revtex4, 1 figure; v2: typos and minor error corrected,
result unchange
Transverse frames for Petrov type I spacetimes: a general algebraic procedure
We develop an algebraic procedure to rotate a general Newman-Penrose tetrad
in a Petrov type I spacetime into a frame with Weyl scalars and
equal to zero, assuming that initially all the Weyl scalars are non
vanishing. The new frame highlights the physical properties of the spacetime.
In particular, in a Petrov Type I spacetime, setting and
to zero makes apparent the superposition of a Coulomb-type effect
with transverse degrees of freedom and .Comment: 10 pages, submitted to Classical Quantum Gravit
Stress effects in structure formation
Residual velocity dispersion in cold dark matter induces stresses which lead
to effects that are absent in the idealized dust model. A previous Newtonian
analysis showed how this approach can provide a theoretical foundation for the
phenomenological adhesion model. We develop a relativistic kinetic theory
generalization which also incorporates the anisotropic velocity dispersion that
will typically be present. In addition to density perturbations, we consider
the rotational and shape distortion properties of clustering. These quantities
together characterize the linear development of density inhomogeneity, and we
find exact solutions for their evolution. As expected, the corrections are
small and arise only in the decaying modes, but their effect is interesting.
One of the modes for density perturbations decays less rapidly than the
standard decaying mode. The new rotational mode generates precession of the
axis of rotation. The new shape modes produce additional distortion that
remains frozen in during the subsequent (linear) evolution, despite the rapid
decay of the terms that caused it.Comment: significantly improved discussion of kinetic theory of CDM velocity
dispersion; to appear Phys. Rev.
Vorticity generation at second order in cosmological perturbation theory
We show that at second order in cosmological perturbation theory vorticity
generation is sourced by entropy gradients. This is an extension of Crocco's
theorem to a cosmological setting.Comment: 4 pages, revtex4; v2: discussion expanded, references added, version
being submitted; v3: corresponds to version published in PR
A Concise Introduction to Perturbation Theory in Cosmology
We give a concise, self-contained introduction to perturbation theory in
cosmology at linear and second order, striking a balance between mathematical
rigour and usability. In particular we discuss gauge issues and the active and
passive approach to calculating gauge transformations. We also construct
gauge-invariant variables, including the second order tensor perturbation on
uniform curvature hypersurfaces.Comment: revtex4, 16 pages, 3 figures; v2: minor changes, typos corrected,
reference added, version accepted by CQ
Regular spherical dust spacetimes
Physical (and weak) regularity conditions are used to determine and classify
all the possible types of spherically symmetric dust spacetimes in general
relativity. This work unifies and completes various earlier results. The
junction conditions are described for general non-comoving (and non-null)
surfaces, and the limits of kinematical quantities are given on all comoving
surfaces where there is Darmois matching. We show that an inhomogeneous
generalisation of the Kantowski-Sachs metric may be joined to the
Lemaitre-Tolman-Bondi metric. All the possible spacetimes are explicitly
divided into four groups according to topology, including a group in which the
spatial sections have the topology of a 3-torus. The recollapse conjecture (for
these spacetimes) follows naturally in this approach.Comment: Minor improvements, additional references. Accepted by GR
Comments on gauge-invariance in cosmology
We revisit the gauge issue in cosmological perturbation theory, and highlight
its relation to the notion of covariance in general relativity. We also discuss
the similarities and differences of the covariant approach in perturbation
theory to the Bardeen or metric approach in a non-technical fashion.Comment: 7 pages, 1 figure, revtex4; v3: minor changes, typos corrected,
discussion extended; v4: typos corrected, corresponding to published versio
Exact isotropic cosmologies with local fractal number counts
We construct an exact relativistic cosmology in which an inhomogeneous but
isotropic local region has fractal number counts and matches to a homogeneous
background at a scale of the order of Mpc. We show that Einstein's
equations and the matching conditions imply either a nonlinear Hubble law or a
very low large-scale density.Comment: revised version, to appear Class. Q. Grav.; minor corrections
following eqn 16, additional comments on relation to other work, some new
reference
Dark Energy or Apparent Acceleration Due to a Relativistic Cosmological Model More Complex than FLRW?
We use the Szekeres inhomogeneous relativistic models in order to fit
supernova combined data sets. We show that with a choice of the spatial
curvature function that is guided by current observations, the models fit the
supernova data almost as well as the LCDM model without requiring a dark energy
component. The Szekeres models were originally derived as an exact solution to
Einstein's equations with a general metric that has no symmetries and are
regarded as good candidates to model the true lumpy universe that we observe.
The null geodesics in these models are not radial. The best fit model found is
also consistent with the requirement of spatial flatness at CMB scales. The
first results presented here seem to encourage further investigations of
apparent acceleration using various inhomogeneous models and other constraints
from CMB and large structure need to be explored next.Comment: 6 pages, 1 figure, matches version published in PR