Reconstructing the Thermal Sunyaev-Zel'dovich Effect in 3D

The 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 $\mathcal{C}_{\ell} (k)$ for individual 3D modes, defined by the radial and tangential wave numbers $(k;\ell)$, 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.Comment: 27 pages, 12 Figures. Published in MNRA

Impact of Numerical Relativity information on effective-one-body waveform models

We present a comprehensive comparison of the spin-aligned effective-one-body (EOB) waveform model of Nagar et al. [Phys. Rev. D93, 044046 (2016)], informed using 40 numerical-relativity (NR) datasets, against a set of 149, $\ell=m=2$, NR waveforms freely available through the Simulation Extreme Spacetime (SXS) catalog. We find that, without further calibration, these EOBNR waveforms have unfaithfulness (at design Advanced-LIGO sensitivity and evaluated with total mass $M$ varying as $10M_\odot\leq M \leq 200M_\odot$) always below $1\%$ against all NR waveforms except for three outliers, that still never exceed the $3\%$ level; with a minimal retuning of the (effective) next-to-next-to-next-to-leading-order spin-orbit coupling parameter for the non-equal-mass and non-equal-spin sector, that only needs three more NR waveforms, one is left with another two (though different) outliers, with maximal unfaithfulness of up to only $2\%$ for a total mass of $200M_\odot$. We show this is the effect of slight inaccuracies in the phenomenological description of the postmerger waveform of Del Pozzo and Nagar [arXiv:1606.03952] that was constructed by interpolating over only 40NR simulations. We argue that this is easily fixed by using either an alternative ringdown description (e.g., the superposition of quasi-normal-modes) or an improved version of the phenomenological representation. By analyzing a NR waveform with mass ratio $8$ and dimensionless spins $+0.85$ obtained with the BAM code, we conclude that the model would benefit from NR simulations specifically targeted at improving the postmerger-ringdown phenomenological fits for mass ratios $\gtrsim 8$ and spins $\gtrsim 0.8$.Comment: 24 pages, 20 figures, submitted to Phys. Rev.

Gravitational-Wave Asteroseismology with Fundamental Modes from Compact Binary Inspirals

The first detection of gravitational waves (GWs) from the binary neutron star (NS) inspiral GW170817 has opened a unique channel for probing the fundamental properties of matter at supra-nuclear densities inaccessible elsewhere in the Universe. This observation yielded the first constraints on the equation of state (EoS) of NS matter from the GW imprint of tidal interactions. Tidal signatures in the GW arise from the response of a matter object to the spacetime curvature sourced by its binary companion. They crucially depend on the EoS and are predominantly characterised by the tidal deformability parameters $\Lambda_{\ell}$, where $\ell=2,3$ denotes the quadrupole and octupole respectively. As the binary evolves towards merger, additional dynamical tidal effects become important when the orbital frequency approaches a resonance with the stars' internal oscillation modes. Among these modes, the fundamental ($f_\ell$-)modes have the strongest tidal coupling and can give rise to a cumulative imprint in the GW signal even if the resonance is not fully excited. Here we present the first direct constraints on fundamental oscillation mode frequencies for GW170817 using an inspiral GW phase model with an explicit dependence on the $f$-mode frequency and without assuming any relation between $f_\ell$ and $\Lambda_\ell$. We rule out anomalously small values of $f_\ell$ and, for the larger companion, determine a lower bound on the $f_2$-mode ($f_3$-mode) frequency of $\geq 1.39$ kHz ($\geq 1.86$ kHz) at the 90\% credible interval (CI). We then show that networks of future GW detectors will be able to measure $f$-mode frequencies to within tens of Hz from the inspiral alone. Such precision astroseismology will enable novel tests of fundamental physics and the nature of compact binaries.Comment: 8 pages, 5 figure

Assessing gravitational-wave binary black hole candidates with Bayesian odds

Gravitational waves from the coalescence of binary black holes can be distinguished from noise transients in a detector network through Bayesian model selection by exploiting the coherence of the signal across the network. We present a Bayesian framework for calculating the posterior probability that a signal is of astrophysical origin, agnostic to the specific search strategy, pipeline or search domain with which a candidate is identified. We apply this framework under \textit{identical} assumptions to all events reported in the LIGO-Virgo GWTC-1 catalog, GW190412 and numerous event candidates reported by independent search pipelines by other authors. With the exception of GW170818, we find that all GWTC-1 candidates, and GW190412, have odds overwhelmingly in favour of the astrophysical hypothesis, including GW170729, which was assigned significantly different astrophysical probabilities by the different search pipelines used in GWTC-1. GW170818 is de-facto a single detector trigger, and is therefore of no surprise that it is disfavoured as being produced by an astrophysical source in our framework. We find \textit{three} additional event candidates, GW170121, GW170425 and GW170727, that have significant support for the astrophysical hypothesis, with a probability that the signal is of astrophysical origin of 0.53, 0.74 and 0.64 respectively. We carry out a hierarchical population study which includes these three events in addition to those reported in GWTC-1, finding that the main astrophysical results are unaffected.Comment: 23 pages, 11 figures, comments and feedback welcome

A Multipolar Effective One Body Model for Non-Spinning Black Hole Binaries

We introduce \TEOBiResumSM{}, a nonspinning inspiral-merger-ringdown waveform model built within the effective one body (EOB) framework that includes gravitational waveform modes beyond the dominant quadrupole $(\ell,|m|) = (2,2)$. The model incorporates: (i) an improved Pad\'e resummation of the factorized waveform amplitudes $\rho_{\ell m}^{\rm orb}$ entering the EOB-resummed waveform where the 3PN, mass-ratio dependent, terms are hybridized with test-mass limit terms up to 6PN relative order for most of the multipoles up to $\ell=6$ included; (ii) an improved determination of the effective 5PN function $a_6^c(\nu)$ entering the EOB interaction potential done using the most recent, error-controlled, nonspinning numerical relativity (NR) waveforms from the Simulating eXtreme Spacetimes (SXS) collaboration; and (iii) a NR-informed phenomenological description of the multipolar ringdown. Such representation stems from 19 NR waveforms with mass ratios up to $m_1/m_2=18$ as well as test-mass waveform data, although it does not incorporate mode-mixing effects. The NR-completed higher modes through merger and ringdown considered here are: $(\ell,|m|) = \lbrace (2,1), (3,3), (3,2),(3,1),(4,4), (4,3),(4,2), (4,1),(5,5)\rbrace$. For simplicity, the other subdominant modes, up to $\ell=8$, are approximated by the corresponding, purely analytical, factorized and resummed EOB waveform. To attempt an estimate of (some of) the underlying analytic uncertainties of the model, we also contrast the effect of the 6PN-hybrid Pad\'e-resummed $\rho_{\ell m}$'s with the standard $3^{+2}$PN, Taylor-expanded, ones used in previous EOB works. The maximum unfaithfulness $\bar{F}$ against the SXS waveforms including all NR-completed modes up to $\ell=m=5$ is always $\lesssim 2\%$ for binaries with total mass $M$ as $50 M_{\odot} \leq M \lesssim 200 M_{\odot}$.Comment: 24 pages, 18 figures. Improved figures and presentation. Submitted to Phys. Rev.

Validity of common modelling approximations for precessing binary black holes with higher-order modes

The current paradigm for constructing waveforms from precessing compact binaries is to first construct a waveform in a non-inertial, co-precessing binary source frame followed by a time-dependent rotation to map back to the physical, inertial frame. A key insight in the construction of these models is that the co-precessing waveform can be effectively mapped to some equivalent aligned spin waveform. Secondly, the time-dependent rotation implicitly introduces $m$-mode mixing, necessitating an accurate description of higher-order modes in the co-precessing frame. We assess the efficacy of this modelling strategy in the strong field regime using Numerical Relativity simulations. We find that this framework allows for the highly accurate construction of $(2,\pm 2)$ modes in our data set, while for higher order modes, especially the $(2,|1|), (3,|2|)$ and $(4,|3|)$ modes, we find rather large mismatches. We also investigate a variant of the approximate map between co-precessing and aligned spin waveforms, where we only identify the slowly varying part of the time domain co-precessing waveforms with the aligned-spin one, but find no significant improvement. Our results indicate that the simple paradigm to construct precessing waveforms does not provide an accurate description of higher order modes in the strong-field regime, and demonstrate the necessity for modelling mode asymmetries and mode-mixing to significantly improve the description of precessing higher order modes.Comment: Improved version: correcting typos, adding acknowledgement and more reference

The perturbed universe: dynamics, statistics and phenomenology

Universe. 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

Gravitational-wave selection effects using neural-network classifiers

We present a novel machine-learning approach to estimate selection effects in gravitational-wave observations. Using techniques similar to those commonly employed in image classification and pattern recognition, we train a series of neural-network classifiers to predict the LIGO/Virgo detectability of gravitational-wave signals from compact-binary mergers. We include the effect of spin precession, higher-order modes, and multiple detectors and show that their omission, as it is common in large population studies, tends to overestimate the inferred merger rate in selected regions of the parameter space. Although here we train our classifiers using a simple signal-to-noise ratio threshold, our approach is ready to be used in conjunction with full pipeline injections, thus paving the way toward including actual distributions of astrophysical and noise triggers into gravitational-wave population analyses.Comment: 7 pages, 4 figures, 1 table. Published in PRD. Models and samples available at https://github.com/dgerosa/pdetclassifie