139 research outputs found
A Bayesian analysis of regularised source inversions in gravitational lensing
Strong gravitational lens systems with extended sources are of special
interest because they provide additional constraints on the models of the lens
systems. To use a gravitational lens system for measuring the Hubble constant,
one would need to determine the lens potential and the source intensity
distribution simultaneously. A linear inversion method to reconstruct a
pixellated source brightness distribution of a given lens potential model was
introduced by Warren & Dye. In the inversion process, a regularisation on the
source intensity is often needed to ensure a successful inversion with a
faithful resulting source. In this paper, we use Bayesian analysis to determine
the optimal regularisation constant (strength of regularisation) of a given
form of regularisation and to objectively choose the optimal form of
regularisation given a selection of regularisations. We consider and compare
quantitatively three different forms of regularisation previously described in
the literature for source inversions in gravitational lensing: zeroth-order,
gradient and curvature. We use simulated data with the exact lens potential to
demonstrate the method. We find that the preferred form of regularisation
depends on the nature of the source distribution.Comment: 18 pages, 10 figures; Revisions based on referee's comments after
initial submission to MNRA
Cosmological Applications of a Wavelet Analysis on the Sphere
The cosmic microwave background (CMB) is a relic radiation of the Big Bang and as such it contains a wealth of cosmological information. Statistical analyses of the CMB, in conjunction with other cosmological observables, represent some of the most powerful techniques available to cosmologists for placing strong constraints on the cosmological parameters that describe the origin, content and evolution of the Universe. The last decade has witnessed the introduction of wavelet analyses in cosmology and, in particular, their application to the CMB. We review here spherical wavelet analyses of the CMB that test the standard cosmological concordance model. The assumption that the temperature anisotropies of the CMB are a realisation of a statistically isotropic Gaussian random field on the sphere is questioned. Deviations from both statistical isotropy and Gaussianity are detected in the reviewed works, suggesting more exotic cosmological models may be required to explain our Universe. We also review spherical wavelet analyses that independently provide evidence for dark energy, an exotic component of our Universe of which we know very little currently. The effectiveness of accounting correctly for the geometry of the sphere in the wavelet analysis of full-sky CMB data is demonstrated by the highly significant detections of physical processes and effects that are made in these reviewed work
The Emission of Electromagnetic Radiation from Charges Accelerated by Gravitational Waves and its Astrophysical Implications
We provide calculations and theoretical arguments supporting the emission of
electromagnetic radiation from charged particles accelerated by gravitational
waves (GWs). These waves have significant indirect evidence to support their
existence, yet they interact weakly with ordinary matter. We show that the
induced oscillations of charged particles interacting with a GW, which lead to
the emission of electromagnetic radiation, will also result in wave
attenuation. These ideas are supported by a small body of literature, as well
as additional arguments for particle acceleration based on GW memory effects.
We derive order of magnitude power calculations for various initial charge
distributions accelerated by GWs. The resulting power emission is extremely
small for all but very strong GWs interacting with large quantities of charge.
If the results here are confirmed and supplemented, significant consequences
such as attenuation of early universe GWs could result. Additionally, this
effect could extend GW detection techniques into the electromagnetic regime.
These explorations are worthy of study to determine the presence of such
radiation, as it is extremely important to refine our theoretical framework in
an era of active GW astrophysics.Comment: Appears in Gravitational Wave Astrophysics, Editor C.F. Sopuerta,
Astrophysics and Space Science Proceedings, Volume 40. ISBN
978-3-319-10487-4. Springer International Publishing Switzerland, 2015, p.
30
Model selection applied to reconstruction of the Primordial Power Spectrum
The preferred shape for the primordial spectrum of curvature perturbations is
determined by performing a Bayesian model selection analysis of cosmological
observations. We first reconstruct the spectrum modelled as piecewise linear in
\log k between nodes in k-space whose amplitudes and positions are allowed to
vary. The number of nodes together with their positions are chosen by the
Bayesian evidence, so that we can both determine the complexity supported by
the data and locate any features present in the spectrum. In addition to the
node-based reconstruction, we consider a set of parameterised models for the
primordial spectrum: the standard power-law parameterisation, the spectrum
produced from the Lasenby & Doran (LD) model and a simple variant
parameterisation. By comparing the Bayesian evidence for different classes of
spectra, we find the power-law parameterisation is significantly disfavoured by
current cosmological observations, which show a preference for the LD model.Comment: Minor changes to match version accepted by JCA
Area Invariance of Apparent Horizons under Arbitrary Boosts
It is a well known analytic result in general relativity that the
2-dimensional area of the apparent horizon of a black hole remains invariant
regardless of the motion of the observer, and in fact is independent of the slice, which can be quite arbitrary in general relativity.
Nonetheless the explicit computation of horizon area is often substantially
more difficult in some frames (complicated by the coordinate form of the
metric), than in other frames. Here we give an explicit demonstration for very
restricted metric forms of (Schwarzschild and Kerr) vacuum black holes. In the
Kerr-Schild coordinate expression for these spacetimes they have an explicit
Lorentz-invariant form. We consider {\it boosted} versions with the black hole
moving through the coordinate system. Since these are stationary black hole
spacetimes, the apparent horizons are two dimensional cross sections of their
event horizons, so we compute the areas of apparent horizons in the boosted
space with (boosted) , and obtain the same result as in the
unboosted case. Note that while the invariance of area is generic, we deal only
with black holes in the Kerr-Schild form, and consider only one particularly
simple change of slicing which amounts to a boost. Even with these restrictions
we find that the results illuminate the physics of the horizon as a null
surface and provide a useful pedagogical tool. As far as we can determine, this
is the first explicit calculation of this type demonstrating the area
invariance of horizons. Further, these calculations are directly relevant to
transformations that arise in computational representation of moving black
holes. We present an application of this result to initial data for boosted
black holes.Comment: 19 pages, 3 figures. Added a new section and 2 plots along with a
coautho
Cosmological parameter estimation using Very Small Array data out to â= 1500
We estimate cosmological parameters using data obtained by the Very Small Array (VSA) in its extended configuration, in conjunction with a variety of other cosmic microwave background (CMB) data and external priors. Within the flat Î cold dark matter (ÎCDM) model, we find that the inclusion of high-resolution data from the VSA modifies the limits on the cosmological parameters as compared to those suggested by the Wilkinson Microwave Anisotropy Probe (WMAP) alone, while still remaining compatible with their estimates. We find that Ωbh2= 0.0234+0.0012â0.0014, Ωdmh2= 0.111+0.014â0.016, h= 0.73+0.09â0.05, nS= 0.97+0.06â0.03, 1010AS= 23+7â3 and Ï= 0.14+0.14â0.07 for WMAP and VSA when no external prior is included. On extending the model to include a running spectral index of density fluctuations, we find that the inclusion of VSA data leads to a negative running at a level of more than 95 per cent confidence ( nrun=â0.069 ± 0.032 ), something that is not significantly changed by the inclusion of a stringent prior on the Hubble constant. Inclusion of prior information from the 2dF galaxy redshift survey reduces the significance of the result by constraining the value of Ωm. We discuss the veracity of this result in the context of various systematic effects and also a broken spectral index model. We also constrain the fraction of neutrinos and find that fÎœ < 0.087 at 95 per cent confidence, which corresponds to mÎœ < 0.32 eV when all neutrino masses are equal. Finally, we consider the global best fit within a general cosmological model with 12 parameters and find consistency with other analyses available in the literature. The evidence for nrun < 0 is only marginal within this model
Particle motion in the field of a five-dimensional charged black hole
In this paper, we have investigated the geodesics of neutral particles near a
five-dimensional charged black hole using a comparative approach. The effective
potential method is used to determine the location of the horizons and to study
radial and circular trajectories. This also helps us to analyze the stability
of radial and circular orbits. The radius of the innermost stable circular
orbits have also been determined. Contrary to the case of massive particles for
which, the circular orbits may have up to eight possible values of specific
radius, we find that the photons will only have two distinct values for the
specific radii of circular trajectories. Finally we have used the dynamical
systems analysis to determine the critical points and the nature of the
trajectories for the timelike and null geodesics.Comment: 15 pages, accepted for publication in Astrophysics and Space Scienc
Reconstruction of the Dark Energy equation of state
One of the main challenges of modern cosmology is to investigate the nature
of dark energy in our Universe. The properties of such a component are normally
summarised as a perfect fluid with a (potentially) time-dependent
equation-of-state parameter . We investigate the evolution of this
parameter with redshift by performing a Bayesian analysis of current
cosmological observations. We model the temporal evolution as piecewise linear
in redshift between `nodes', whose -values and redshifts are allowed to
vary. The optimal number of nodes is chosen by the Bayesian evidence. In this
way, we can both determine the complexity supported by current data and locate
any features present in . We compare this node-based reconstruction with
some previously well-studied parameterisations: the Chevallier-Polarski-Linder
(CPL), the Jassal-Bagla-Padmanabhan (JBP) and the Felice-Nesseris-Tsujikawa
(FNT). By comparing the Bayesian evidence for all of these models we find an
indication towards possible time-dependence in the dark energy
equation-of-state. It is also worth noting that the CPL and JBP models are
strongly disfavoured, whilst the FNT is just significantly disfavoured, when
compared to a simple cosmological constant . We find that our node-based
reconstruction model is slightly disfavoured with respect to the CDM
model.Comment: 17 pages, 5 figures, minor correction
Foreground removal from CMB temperature maps using an MLP neural network
One of the main obstacles in extracting the Cosmic Microwave Background (CMB)
signal from observations in the mm-submm range is the foreground contamination
by emission from galactic components: mainly synchrotron, free-free and thermal
dust emission. Due to the statistical nature of the intrinsic CMB signal it is
essential to minimize the systematic errors in the CMB temperature
determinations. Following the available knowledge of the spectral behavior of
the galactic foregrounds simple, power law-like spectra have been assumed. The
feasibility of using a simple neural network for extracting the CMB temperature
signal from the combined CMB and foreground signals has been investigated. As a
specific example, we have analysed simulated data, like that expected from the
ESA Planck Surveyor mission. A simple multilayer perceptron neural network with
2 hidden layers can provide temperature estimates, over more than 80 percent of
the sky, that are to a high degree uncorrelated with the foreground signals. A
single network will be able to cover the dynamic range of the Planck noise
level over the entire sky.Comment: Accepted for publication in Astrophysics and Space Scienc
Bayesian joint estimation of non-Gaussianity and the power spectrum
We propose a rigorous, non-perturbative, Bayesian framework which enables one
jointly to test Gaussianity and estimate the power spectrum of CMB
anisotropies. It makes use of the Hilbert space of an harmonic oscillator to
set up an exact likelihood function, dependent on the power spectrum and on a
set of parameters , which are zero for Gaussian processes. The latter
can be expressed as series of cumulants; indeed they perturbatively reduce to
cumulants. However they have the advantage that their variation is essentially
unconstrained. Any truncation(i.e.: finite set of ) therefore still
produces a proper distribution - something which cannot be said of the only
other such tool on offer, the Edgeworth expansion. We apply our method to Very
Small Array (VSA) simulations based on signal Gaussianity, showing that our
algorithm is indeed not biased.Comment: 11pages, 4 figures, submitted to MNRA
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