109 research outputs found
Ever more accurate effective-one-body waveforms for gravitational-wave astrophysics
No full textDiese Dissertation konzentriert sich auf die Entwicklung akkurater und effizienter Modelle für die Gravitationsstrahlung, die von verschmelzenden binären Schwarzen Löchern emittiert wird -- mit besonderem Fokus auf die Konstruktion, die Kalibrierung und die Anwendung von sogenannten ``effective-one-body'' Wellenformmodellen. Im Zentrum der Arbeit stehen die Entwicklung des SEOBNRv5HM-Wellenformmodells sowie des Open-Source-Frameworks pySEOBNR, das die Entwicklung, Kalibrierung und Validierung der nächsten Generation von effective-one-body Modellen unterstützt. Das Modell zeichnet sich auch durch eine deutlich gesteigerte Präzision und Recheneffizienz aus. Parallel dazu integrieren wir post-Minkowskische Resultate in den effective-one-body Formalismus, um die konservative Dynamik gebundener Systeme mittels Ergebnissen der Streutheorie zu verbessern. Dies kulminiert in dem SEOBNR-PM-Modell. Die entwickelten Modelle werden zur Bestimmung der Eigenschaften von binären schwarzen Löchern eingesetzt, wobei sowohl synthetische als auch reale Gravitationswellendaten studiert werden. Um Unsicherheiten durch die Kalibrierung zu numerischer Relativität zu berücksichtigen, führen wir eine neue probabilistische Methode ein, bei der über Wellenformunsicherheiten marginalisiert wird und so die Robustheit der Parameterbestimmung verbessert wird. Abschließend erweitern wir die SEOBNRv5-Modelle, um potenzielle Abweichungen von der Allgemeinen Relativitätstheorie zu untersuchen. Theorie-spezifisch konstruieren wir Inspiral-Merger-Ringdown-Wellenformen in der Einstein-scalar-Gauss-Bonnet-Gravitation. Theorie-agnostisch erweitern wir das parametrisierte pSEOBNR-Framework auf präzessierende Binärsysteme, mit Fokus auf die Spektroskopie Schwarzer Löcher, bei der die Quasinormalmoden eines neu entstandenen schwarzen Lochs studiert werden.This thesis focuses on the development of accurate and efficient models for the gravitational radiation emitted by coalescing binary black holes, with particular emphasis on the construction, calibration, and application of effective-one-body waveform models. Central to this work is the development of the SEOBNRv5HM waveform model and the open-source pySEOBNR framework, which supports the development, calibration, and validation of the next generation of effective-one-body waveform models. It achieves significantly improved accuracy and higher computational efficiency compared to its predecessor. In parallel, we present progress toward incorporating post-Minkowskian results into the effective-one-body formalism, allowing us to inform the conservative dynamics of bound systems from scattering calculations. This culminates in the development of the SEOBNR-PM model. The waveform models developed are applied to infer the source properties of binary black hole mergers, using both synthetic and real gravitational-wave data. To account for modeling uncertainties arising from numerical-relativity calibration, we introduce a novel probabilistic approach that marginalizes over waveform uncertainties, thereby improving the robustness of parameter inference. Finally, we extend the SEOBNRv5 models to explore potential deviations from general relativity. In the theory-specific direction, we construct inspiral-merger-ringdown waveforms in Einstein-scalar-Gauss-Bonnet gravity, an extension of general relativity predicting distinctive signatures in black hole coalescences. In the theory-agnostic direction, we extend the parameterized pSEOBNR framework to the spin-precessing binaries, focusing on black hole spectroscopy, which tests general relativity by analyzing the quasinormal modes of the remnant black holes
The perturbed universe: dynamics, statistics and phenomenology
No full textUniverse. By studying the perturbations to cosmological spacetimes, and the subsequent growth of large scale structure, we find that we can link both fundamentally and astrophysically interesting physics to cosmological observables. We use a healthy mix of statistical, analytical and numerical techniques throughout this thesis.
In Chapter 2 we introduce and summarise the statistics of random fields, as these are fundamental
objects used to model cosmological observables. We introduce the spherical Fourier-Bessel
expansion as a tool to perform genuine 3-dimensional studies of cosmological random fields. In
Chapter 3 we introduce the theory of inflation and discuss the basic machinery that allows us to
calculate the statistical properties of the quantum mechanical flucatuations that seed large scale
structure. What we see is that different fundamental physics in the early Universe leads to different
statistical properties that we may test. The second half of Chapter 3 introduces the large scale
structure of the Universe that describes the clustering of galaxies on cosmological scales. We discuss
the growth and evolution of structure under gravitational collapse and the core observables
that are predicted, such as the power spectrum, variance and skewness.
Chapter 4 introduces the Minkowski functionals. These are a set of topological statistics that
probe the morphological properties of random fields. In particular they may be used to quantify
deviations from Gaussianity in the large scale structure of galaxies. The deviations from Gaussianity
can be generated by two primary mechanisms: 1) The gravitational collapse of perturbations
is a non-linear process. Even if we have Gaussian initial conditions, gravitational collapse will
induce non-Gaussianity. 2) Different theories for the early Universe will imprint different non-
Gaussian features in the primordial perturbations that seed large scale structure, i.e. we have
non-Gaussian initial conditions. We can connect the amplitude and momentum dependence of
the non-Gaussianity to different fundamental interactions. We introduce a topological statistic
based on the Minkowski functionals that retains the momentum dependence giving us greater
distinguishing power between different contributions to non-Gaussianity.
In Chapter 5 we introduce the Baryon Acoustic Oscillations (BAOs) as described in the spherical
Fourier-Bessel formalism. The BAOs are a solid prediction in cosmology and should help us to
constrain cosmological parameters. We implement a full 3-dimensional study and study how
redshift space distortions, induced by the motion of galaxies, and non-linearities, induced by
gravitational collapse, impact the characteristics of these BAOs.
Chapter 6 extends the spherical Fourier-Bessel theme by introducing the thermal Sunyaev-
Zel’dovich (tSZ) effect and cosmological weak lensing (WL). It is thought that weak lensing will
provide an unbiased probe of the dark Universe and that the tSZ effect will probe the thermal
history of the Universe. Unfortunately, the tSZ effect loses redshift information as it is a line of sight
projection. We study the cross-correlation of the tSZ effect with WL in order to reconstruct the
tSZ effect in a full 3-dimensional study in an attmept to recover the lost distance information. We
use the halo model, spectroscopic redshift surveys and suvery effects to understand how detailed
modelling effects the tSZ-WL cross correlation.
Chapter 7 marks a real change in theme and introduces the subject of relativistic cosmology. Inparticular we introduce the 1+3, 1+1+2 and 2+2 formalisms as tools to study cosmological perturbations. We provide rather self-contained introductions and provide some minor corrections
to the literature in the 1+1+2 formalism as well as introducing new results.
In Chapter 8 we apply the 1+1+2 and 2+2 approaches to the Schwarzschild spacetime. Here
we outline the full system of equations in both approaches and how they are related, setting up a
correspondence between the two. Our aim is to construct closed, covariant, gauge-invariant and
frame-invariant wave equations that govern the gravitational perturbations of the Schwarzschild
spacetime. We correct a result in the literature and derive two new equations. The first governs
axial gravitational perturbations and is related to the magnetic Weyl scalar. The second is valid
for both polar and axial perturbations and is given by a combination of the magnetic and electric
Weyl 2-tensors. We discuss their relation to the literature at large.
Finally, in Chapter 9 we apply the 1+1+2 and 2+2 approaches the LTB spacetime. This
inhomogeneous but spherically symmetric spacetime is the first stepping stone into genuinely
inhomogeneous cosmological spacetimes. We seek a closed, covariant master equation for the
gravitational perturbations of the LTB spacetime. We present an equation governing axial gravitational
perturbations and a preliminary equation, valid for both the polar and axial sectors, that is
constructed from the electric and magneticWeyl 2-tensors but is coupled to the energy-momentum
content of the LTB spacetime. We discuss how auxilliary equations may be introduced in order to
close the master equation for polar and axial perturbations. This last result leads to the identification
of H as a master variable for axial perturbations of all vacuum LRS-II spacetimes and the
LTB spacetime. It is thought that these results can be extended to non-vacuum LRS-II spacetimes.
Likewise, the master variable constructed from Weyl variables constitutes a master variable for all
vacuum LRS-II spacetimes and it is thought that this will extend to the non-vacuum case
Impact of post-Born lensing on the CMB
No full textLensing of the CMB is affected by post-Born lensing, producing corrections to
the convergence power spectrum and introducing field rotation. We show
numerically that the lensing convergence power spectrum is affected at the
level on accessible scales, and that this correction and the
field rotation are negligible for observations with arcminute beam and noise
levels . The field rotation
generates of the total lensing B-mode polarization amplitude
( in power on small scales), but has a blue spectrum on large scales,
making it highly subdominant to the convergence B modes on scales where they
are a source of confusion for the signal from primordial gravitational waves.
Since the post-Born signal is non-linear, it also generates a bispectrum with
the convergence. We show that the post-Born contributions to the bispectrum
substantially change the shape predicted from large-scale structure
non-linearities alone, and hence must be included to estimate the expected
total signal and impact of bispectrum biases on CMB lensing reconstruction
quadratic estimators and other observables. The field-rotation power spectrum
only becomes potentially detectable for noise levels , but its bispectrum with the convergence may be
observable at with Stage IV observations. Rotation-induced and
convergence-induced B modes are slightly correlated by the bispectrum, and the
bispectrum also produces additional contributions to the lensed BB power
spectrum.Comment: 26 pages, 11 figures, 1 table. Sign change in Eq 5.2 corrects sign of
correlation bispectrum in Eq 5.7 & Fig. 11. Footnote on page 15 justifying
the treatment of polarization rotation, based on the recent analysis in
arXiv:1706.02673. Footnote for Table I page 14 stating Lmax used was 4000.
Footnote pg. 10 added. Fixed sign in Eq 2.
Covariant perturbations of f(R) black holes: the Weyl terms
No full textIn this paper we revisit non-spherical perturbations of the Schwarzschild black hole in the context of f(R) gravity. Previous studies were able to demonstrate the stability of the f(R) Schwarzschild black hole against gravitational perturbations in both the even and odd parity sectors. In particular, it was seen that the Regge-Wheeler and Zerilli equations in f(R) gravity obey the same equations as their General Relativity counterparts. More recently, the 1+1+2 semi-tetrad formalism has been used to derive a set of two wave equations: one for transverse, trace-free (tensor) perturbations and one for the additional scalar modes that characterise fourth-order theories of gravitation. The master variable governing tensor perturbations was shown to be a modified Regge-Wheeler tensor obeying the same equation as in General Relativity. However, it is well known that there is a non-uniqueness in the definition of the master variable. In this paper we derive a set of two perturbation variables and their concomitant wave equations that describe gravitational perturbations in a covariant and gauge invariant manner. These variables can be related to the Newman-Penrose (NP) Weyl scalars as well as the master variables from the 2+2 formalism
Reconstructing the Thermal Sunyaev-Zel’dovich Effect in 3D
No full textThe thermal Sunyaev-Zel’dovich (tSZ) effect measures the line-of-sight projection of the thermal pressure of free electrons and lacks any redshift information. By cross-correlating the tSZ effect with an external cosmological tracer we can recover a good fraction of this lost information. Weak lensing (WL) is thought to provide an unbiased probe of the dark Universe, with many WL surveys having sky coverage that overlaps with tSZ surveys. Generalising the tomographic approach, we advocate the use of the spherical Fourier-Bessel (sFB) expansion to perform an analysis of the cross-correlation between the projected (2D) tSZ Compton y-parameter maps and 3D weak lensing convergence maps. We use redshift dependent linear biasing and the halo model as a tool to investigate the tSZ-WL cross-correlations in 3D. We use the Press-Schechter (PS) and the Sheth-Tormen (ST) mass-functions in our calculations, finding that the results are quite sensitive to detailed modelling. We provide detailed analysis of surveys with photometric and spectroscopic redshifts. The signal-to-noise (S/N) of the cross-spectra C`(k) for individual 3D modes, defined by the radial and tangential wave numbers (k; `), remains comparable to, but below, unity though optimal binning is expected to improve this. The results presented can be generalised to analyse other CMB secondaries, such as the kinetic Sunyaev-Zel’dovich (kSZ) effect
Covariant perturbations of f(R) black holes: the Weyl terms
No full textIn this paper we revisit non-spherical perturbations of the Schwarzschild black hole in the context of f(R) gravity. Previous studies were able to demonstrate the stability of the f(R) Schwarzschild black hole against gravitational perturbations in both the even and odd parity sectors. In particular, it was seen that the Regge-Wheeler and Zerilli equations in f(R) gravity obey the same equations as their General Relativity counterparts. More recently, the 1+1+2 semi-tetrad formalism has been used to derive a set of two wave equations: one for transverse, trace-free (tensor) perturbations and one for the additional scalar modes that characterise fourth-order theories of gravitation. The master variable governing tensor perturbations was shown to be a modified Regge-Wheeler tensor obeying the same equation as in General Relativity. However, it is well known that there is a non-uniqueness in the definition of the master variable. In this paper we derive a set of two perturbation variables and their concomitant wave equations that describe gravitational perturbations in a covariant and gauge invariant manner. These variables can be related to the Newman-Penrose (NP) Weyl scalars as well as the master variables from the 2+2 formalism
The most powerful astrophysical events: Gravitational-wave peak luminosity of binary black holes as predicted by numerical relativity
No full textFor a brief moment, a binary black hole (BBH) merger can be the most powerful astrophysical event
in the visible Universe. Here we present a model fit for this gravitational-wave peak luminosity of
nonprecessing quasicircular BBH systems as a function of the masses and spins of the component black
holes, based on numerical relativity (NR) simulations and the hierarchical fitting approach introduced
by X. Jiménez-Forteza et al. [Phys. Rev. D 95, 064024 (2017).]. This fit improves over previous results in
accuracy and parameter-space coverage and can be used to infer posterior distributions for the peak
luminosity of future astrophysical signals like GW150914 and GW151226. The model is calibrated to the
l ≤ 6 modes of 378 nonprecessing NR simulations up to mass ratios of 18 and dimensionless spin
magnitudes up to 0.995, and includes unequal-spin effects. We also constrain the fit to perturbative
numerical results for large mass ratios. Studies of key contributions to the uncertainty in NR peak
luminosities, such as (i) mode selection, (ii) finite resolution, (iii) finite extraction radius, and (iv) different
methods for converting NR waveforms to luminosity, allow us to use NR simulations from four different
codes as a homogeneous calibration set. This study of systematic fits to combined NR and large-mass-ratio
data, including higher modes, also paves the way for improved inspiral-merger-ringdown waveform
models
Cosmology with the Laser Interferometer Space Antenna
No full textThe Laser Interferometer Space Antenna (LISA) has two scientific objectives of cosmological focus: to probe the expansion rate of the universe, and to understand stochastic gravitational-wave backgrounds and their implications for early universe and particle physics, from the MeV to the Planck scale. However, the range of potential cosmological applications of gravitational-wave observations extends well beyond these two objectives. This publication presents a summary of the state of the art in LISA cosmology, theory and methods, and identifies new opportunities to use gravitational-wave observations by LISA to probe the universe
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