61 research outputs found
The future of cosmology and the role of non-linear perturbations
Cosmological perturbation theory is a key tool to study the universe. The
linear or first order theory is well understood, however, developing and
applying the theory beyond linear order is at the cutting edge of current
research in theoretical cosmology. In this article, I will describe some
signatures of non-linear perturbation theory that do not exist at linear order,
focusing on vorticity generation at second order. In doing so, we discuss why
this, among other features such as induced gravitational waves and
non-Gaussianities, shows that cosmological perturbation theory is crucial for
testing models of the universe.Comment: 6 pages, essay originally submitted to GRF competition, to appear in
Commun. Theor. Phy
The curvature perturbation at second order
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
Effects of non-linearities on magnetic field generation
Magnetic fields are present on all scales in the Universe. While we
understand the processes which amplify the fields fairly well, we do not have a
"natural" mechanism to generate the small initial seed fields. By using fully
relativistic cosmological perturbation theory and going beyond the usual
confines of linear theory we show analytically how magnetic fields are
generated. This is the first analytical calculation of the magnetic field at
second order, using gauge-invariant cosmological perturbation theory, and
including all the source terms. To this end, we have rederived the full set of
governing equations independently. Our results suggest that magnetic fields of
the order of G can be generated (although this depends on the small
scale cut-off of the integral), which is largely in agreement with previous
results that relied upon numerical calculations. These fields are likely too
small to act as the primordial seed fields for dynamo mechanisms.Comment: 21 pages; v2: minor changes, added references; v3: version accepted
for publication in JCA
Modelling non-dust fluids in cosmology
Currently, most of the numerical simulations of structure formation use
Newtonian gravity. When modelling pressureless dark matter, or `dust', this
approach gives the correct results for scales much smaller than the
cosmological horizon, but for scenarios in which the fluid has pressure this is
no longer the case. In this article, we present the correspondence of
perturbations in Newtonian and cosmological perturbation theory, showing exact
mathematical equivalence for pressureless matter, and giving the relativistic
corrections for matter with pressure. As an example, we study the case of
scalar field dark matter which features non-zero pressure perturbations. We
discuss some problems which may arise when evolving the perturbations in this
model with Newtonian numerical simulations and with CMB Boltzmann codes.Comment: 5 pages; v2: typos corrected and refs added, submitted version; v3:
version to appear in JCA
Vector and tensor contributions to the curvature perturbation at second order
We derive the evolution equation for the second order curvature perturbation
using standard techniques of cosmological perturbation theory. We do this for
different definitions of the gauge invariant curvature perturbation, arising
from different splits of the spatial metric, and compare the expressions. The
results are valid at all scales and include all contributions from scalar,
vector and tensor perturbations, as well as anisotropic stress, with all our
results written purely in terms of gauge invariant quantities. Taking the
large-scale approximation, we find that a conserved quantity exists only if, in
addition to the non-adiabatic pressure, the transverse traceless part of the
anisotropic stress tensor is also negligible. We also find that the version of
the gauge invariant curvature perturbation which is exactly conserved is the
one defined with the determinant of the spatial part of the inverse metric.Comment: 21 pages. Appendix added and conclusions extended. Updated to match
version published in JCA
Consistent perturbations in an imperfect fluid
We present a new prescription for analysing cosmological perturbations in a
more-general class of scalar-field dark-energy models where the energy-momentum
tensor has an imperfect-fluid form. This class includes Brans-Dicke models,
f(R) gravity, theories with kinetic gravity braiding and generalised galileons.
We employ the intuitive language of fluids, allowing us to explicitly maintain
a dependence on physical and potentially measurable properties. We demonstrate
that hydrodynamics is not always a valid description for describing
cosmological perturbations in general scalar-field theories and present a
consistent alternative that nonetheless utilises the fluid language. We apply
this approach explicitly to a worked example: k-essence non-minimally coupled
to gravity. This is the simplest case which captures the essential new features
of these imperfect-fluid models. We demonstrate the generic existence of a new
scale separating regimes where the fluid is perfect and imperfect. We obtain
the equations for the evolution of dark-energy density perturbations in both
these regimes. The model also features two other known scales: the Compton
scale related to the breaking of shift symmetry and the Jeans scale which we
show is determined by the speed of propagation of small scalar-field
perturbations, i.e. causality, as opposed to the frequently used definition of
the ratio of the pressure and energy-density perturbations.Comment: 40 pages plus appendices. v2 reflects version accepted for
publication in JCAP (new summary of notation, extra commentary on choice of
gauge and frame, extra references to literature
Averaging Robertson-Walker Cosmologies
The cosmological backreaction arises when one directly averages the Einstein
equations to recover an effective Robertson-Walker cosmology, rather than
assuming a background a priori. While usually discussed in the context of dark
energy, strictly speaking any cosmological model should be recovered from such
a procedure. We apply the Buchert averaging formalism to linear
Robertson-Walker universes containing matter, radiation and dark energy and
evaluate numerically the discrepancies between the assumed and the averaged
behaviour, finding the largest deviations for an Einstein-de Sitter universe,
increasing rapidly with Hubble rate to a 0.01% effect for h=0.701. For the LCDM
concordance model, the backreaction is of the order of Omega_eff~4x10^-6, with
those for dark energy models being within a factor of two or three. The impacts
at recombination are of the order of 10^-8 and those in deep radiation
domination asymptote to a constant value. While the effective equations of
state of the backreactions in Einstein-de Sitter, concordance and quintessence
models are generally dust-like, a backreaction with an equation of state
w_eff<-1/3 can be found for strongly phantom models.Comment: 18 pages, 11 figures, ReVTeX. Updated to version accepted by JCA
Pure kinetic k-essence as the cosmic speed-up
In this paper, we consider three types of k-essence. These k-essence models
were presented in the parametric forms. The exact analytical solutions of the
corresponding equations of motion are found. It is shown that these k-essence
models for the presented solutions can give rise to cosmic acceleration.Comment: 10 pages, typos corrected, main results remain the same, minor
changes to match IJTP accepted versio
Gauge Issues in Extended Gravity and f(R) Cosmology
We consider issues related to the conformal mapping between the Einstein and
Jordan frames in f(R) cosmology. We consider the impact of the conformal
transformation on the gauge of a perturbed system and show that unless the
system is written in a restricted set of gauges the mapping could produce an
inconsistent result in the target frame. Newtonian gauge lies within the
restricted group but synchronous gauge does not. If this is not treated
carefully it could in principle contaminate numerical calculations.Comment: 12 pages, REVTeX4. Replaced with version accepted by JCAP. Citations
added and some clarification
Weak lensing generated by vector perturbations and detectability of cosmic strings
We study the observational signature of vector metric perturbations through
the effect of weak gravitational lensing. In the presence of vector
perturbations, the non-vanishing signals for B-mode cosmic shear and curl-mode
deflection angle, which have never appeared in the case of scalar metric
perturbations, naturally arise. Solving the geodesic and geodesic deviation
equations, we drive the full-sky formulas for angular power spectra of weak
lensing signals, and give the explicit expressions for E-/B-mode cosmic shear
and gradient-/curl-mode deflection angle. As a possible source for seeding
vector perturbations, we then consider a cosmic string network, and discuss its
detectability from upcoming weak lensing and CMB measurements. Based on the
formulas and a simple model for cosmic string network, we calculate the angular
power spectra and expected signal-to-noise ratios for the B-mode cosmic shear
and curl-mode deflection angle. We find that the weak lensing signals are
enhanced for a smaller intercommuting probability of the string network, ,
and they are potentially detectable from the upcoming cosmic shear and CMB
lensing observations. For , the minimum detectable tension of
the cosmic string will be down to . With a
theoretically inferred smallest value , we could even detect the
string with .Comment: 39 pages, 5 figures, v2: references added, minor corrections, v3:
matches version published in JCA
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