338 research outputs found

### Brane-world cosmological perturbations: a covariant approach

The standard cosmological model, based on general relativity with an
inflationary era, is very effective in accounting for a broad range of observed
features of the universe. However, the ongoing puzzles about the nature of dark
matter and dark energy, together with the problem of a fundamental theoretical
framework for inflation, indicate that cosmology may be probing the limits of
validity of general relativity. The early universe provides a testing ground
for theories of gravity, since gravitational dynamics can lead to
characteristic imprints on the CMB and other cosmological observations.
Precision cosmology is in principle a means to constrain and possibly falsify
candidate quantum gravity theories like M theory. Generalized Randall-Sundrum
brane-worlds provide a phenomenological means to test aspects of M theory. I
outline the 1+3-covariant approach to cosmological perturbations in these
brane-worlds, and its application to CMB anisotropies.Comment: Based on a talk at the Brane-world Gravity Workshop, Yukawa
Institute, Jan 2002. 17 pages, 4 figure

### Brane-world gravity

The observable universe could be a 1+3-surface (the "brane") embedded in a
1+3+d-dimensional spacetime (the "bulk"), with standard-model particles and
fields trapped on the brane while gravity is free to access the bulk. At least
one of the d extra spatial dimensions could be very large relative to the
Planck scale, which lowers the fundamental gravity scale, possibly even down to
the electroweak (~ TeV) level. This revolutionary picture arises in the
framework of recent developments in M theory. The 1+10-dimensional M theory
encompasses the known 1+9-dimensional superstring theories, and is widely
considered to be a promising potential route to quantum gravity. General
relativity cannot describe gravity at high enough energies and must be replaced
by a quantum gravity theory, picking up significant corrections as the
fundamental energy scale is approached. At low energies, gravity is localized
at the brane and general relativity is recovered, but at high energies gravity
"leaks" into the bulk, behaving in a truly 1+3+d-dimensional way. This
introduces significant changes to gravitational dynamics and perturbations,
with interesting testable implications for high-energy astrophysics, black
holes and cosmology. Brane-world models offer a phenomenological way to test
some of the novel predictions and corrections to general relativity that are
implied by M theory. This review discusses the geometry, dynamics and
perturbations of simple brane-world models for cosmology and astrophysics,
mainly focusing on warped 5-dimensional brane-worlds based on the
Randall-Sundrum models.Comment: Corrections, improvements, new references; to appear in Living
Reviews of Relativity; 58 pages, revtex4, 13 fig

### Is the Universe homogeneous?

The standard model of cosmology is based on the existence of homogeneous
surfaces as the background arena for structure formation. Homogeneity underpins
both general relativistic and modified gravity models and is central to the way
in which we interpret observations of the CMB and the galaxy distribution.
However, homogeneity cannot be directly observed in the galaxy distribution or
CMB, even with perfect observations, since we observe on the past lightcone and
not on spatial surfaces. We can directly observe and test for isotropy, but to
link this to homogeneity, we need to assume the Copernican Principle. First, we
discuss the link between isotropic observations on the past lightcone and
isotropic spacetime geometry: what observations do we need to be isotropic in
order to deduce spacetime isotropy? Second, we discuss what we can say with the
Copernican assumption. The most powerful result is based on the CMB: the
vanishing of the dipole, quadrupole and octupole of the CMB is sufficient to
impose homogeneity. Real observations lead to near-isotropy on large scales -
does this lead to near-homogeneity? There are important partial results, and we
discuss why this remains a difficult open question. Thus we are currently
unable to prove homogeneity of the Universe on large-scales, even with the
Copernican Principle. However we can use observations of the CMB, galaxies and
clusters to test homogeneity itself.Comment: Based on an invited talk at a Theo Murphy Meeting "Testing general
relativity with cosmology". Minor corrections, references updated. To appear
Phil. Trans. R. Soc.

### Geometry and dynamics of the brane-world

Recent developments in string theory have led to 5-dimensional warped
spacetime models in which standard-model fields are confined to a 3-brane (the
observed universe), while gravity can propagate in the fifth dimension. Gravity
is localized near the brane at low energies, even if the extra dimension is
noncompact. A review is given of the classical geometry and dynamics of these
brane-world models. The field equations on the brane modify the general
relativity equations in two ways: local 5-D effects are imprinted on the brane
as a result of its embedding, and are significant at high energies; nonlocal
effects arise from the 5-D Weyl tensor. The Weyl tensor transmits tidal
(Coulomb), gravitomagnetic and gravitational wave effects to the brane from the
5-D nonlocal gravitational field. Local high-energy effects modify the dynamics
of inflation, and increase the amplitude of scalar and tensor perturbations
generated by inflation. Nonlocal effects introduce new features in cosmological
perturbations. They induce a non-adiabatic mode in scalar perturbations and
massive modes in vector and tensor perturbations, and they can support vector
perturbations even in the absence of matter vorticity. In astrophysics, local
and nonlocal effects introduce fundamental changes to gravitational collapse
and black hole solutions.Comment: Minor corrections to Eqs. 14, 42, 64, and reference update

### Covariant velocity and density perturbations in quasi-Newtonian cosmologies

Recently a covariant approach to cold matter universes in the zero-shear
hypersurfaces (or longitudinal) gauge has been developed. This approach reveals
the existence of an integrability condition, which does not appear in standard
non-covariant treatments. A simple derivation and generalization of the
integrability condition is given, based on showing that the quasi-Newtonian
models are a sub-class of the linearized `silent' models. The solution of the
integrability condition implies a propagation equation for the acceleration. It
is shown how the velocity and density perturbations are then obtained via this
propagation equation. The density perturbations acquire a small
relative-velocity correction on all scales, arising from the fully covariant
general relativistic analysis.Comment: 11 pages Revtex; to appear Phys. Rev.

### Asymmetric brane-worlds with induced gravity

The Randall-Sundrum scenario, with a 1+3-dimensional brane in a 5-dimensional
bulk spacetime, can be generalized in various ways. We consider the case where
the Z2-symmetry at the brane is relaxed, and in addition the gravitational
action is generalized to include an induced gravity term on the brane. We
derive the complete set of equations governing the gravitational dynamics for a
general brane and bulk, and identify how the asymmetry and the induced gravity
act as effective source terms in the projected field equations on the brane.
For a Friedmann brane in an anti de Sitter bulk, the solution of the Friedmann
equation is given by the solution of a quartic equation. We find the
perturbative solutions for small asymmetry, which has an effect at late times.Comment: references added; version to appear Phys Rev

### Cosmological perturbations in Horava-Lifshitz theory without detailed balance

In the Horava-Lifshitz theory of quantum gravity, two conditions -- detailed
balance and projectability -- are usually assumed. The breaking of
projectability simplifies the theory, but it leads to serious problems with the
theory. The breaking of detailed balance leads to a more complicated form of
the theory, but it appears to resolve some of the problems. Sotiriou, Visser
and Weinfurtner formulated the most general theory of Horava-Lifshitz type
without detailed balance. We compute the linear scalar perturbations of the FRW
model in this form of HL theory. We show that the higher-order curvature terms
in the action lead to a gravitational effective anisotropic stress on small
scales. Specializing to a Minkowski background, we study the spin-0 scalar mode
of the graviton, using a gauge-invariant analysis, and find that it is stable
in both the infrared and ultraviolet regimes for $0 \le \xi \le 2/3$. However,
in this parameter range the scalar mode is a ghost.Comment: Some typos were corrected. Verison appeared in Phys. Rev. D81, 024009
(2010

### Inhomogeneity and the foundations of concordance cosmology

The apparent accelerating expansion of the Universe is forcing us to examine
the foundational aspects of the standard model of cosmology -- in particular,
the fact that dark energy is a direct consequence of the homogeneity
assumption. We discuss the foundations of the assumption of spatial
homogeneity, in the case when the Copernican Principle is adopted. We present
results that show how (almost-) homogeneity follows from (almost-) isotropy of
various observables. The analysis requires the fully nonlinear field equations
-- i.e., it is not possible to use second- or higher-order perturbation theory,
since one cannot assume a homogeneous and isotropic background. Then we
consider what happens if the Copernican Principle is abandoned in our Hubble
volume. The simplest models are inhomogeneous but spherically symmetric
universes which do not require dark energy to fit the distance modulus. Key
problems in these models are to compute the CMB anisotropies and the features
of large-scale structure. We review how to construct perturbation theory on a
non-homogeneous cosmological background, and discuss the complexities that
arise in using this to determine the growth of large-scale structure.Comment: 26 pages and 1 figure. Invited review article for the CQG special
issue on nonlinear cosmological perturbations. v2 has additional refs and
comments, minor errors corrected, version in CQ

### Acoustic oscillations and viscosity

Using a simple thermo-hydrodynamic model that respects relativistic
causality, we revisit the analysis of qualitative features of acoustic
oscillations in the photon-baryon fluid. The growing photon mean free path
introduces transient effects that can be modelled by the causal generalization
of relativistic Navier-Stokes-Fourier theory. Causal thermodynamics provides a
more satisfactory hydrodynamic approximation to kinetic theory than the
quasi-stationary (and non-causal) approximations arising from standard
thermodynamics or from expanding the photon distribution to first order in the
Thomson scattering time. The causal approach introduces small corrections to
the dispersion relation obtained in quasi-stationary treatments. A dissipative
contribution to the speed of sound slightly increases the frequency of the
oscillations. The diffusion damping scale is slightly increased by the causal
corrections. Thus quasi-stationary approximations tend to over-estimate the
spacing and under-estimate the damping of acoustic peaks. In our simple model,
the fractional corrections at decoupling are $\gtrsim 10^{-3}$.Comment: Improved version with new quantitative estimates and some
corrections. We show how quasi-stationary approximations based on expanding
the photon distribution to first order in the Thomson time tend to
under-estimate the frequency and damping of acoustic oscillation

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