Master Thesis Proposals: Particles and Gravitation

The holographic correspondence AdS/CFT is a powerful duality that connects a theory of gravity in anti-de Sitter space with a (quantum) conformal field theory that lives on the boundary of the spacetime. In this context, the Ryu-Takayanagi formula allows to compute entanglement entropies of CFTs by computing the area of an extremal surface that extends from the boundary into the bulk of AdS. In this project we will use this formula and apply it to the case of black hole solutions, which represent thermal states. This will allow us to study the dependence of holographic entanglement entropy on the temperature. Furthermore, we will consider modifications of Einstein gravity in the bulk, which also lead to modifications of the Ryu-Takayanagi formula. Using this generalized formula, we will then study the expansion of the holographic entanglement entropy for small temperatures and investigate the possible universal character of the coefficients of this expansion. These results will also be interpreted in the context of the first law of entanglement entropy. The analysis could also be extended by studying the effect of a chemical potential on the entanglement entropy. 

When the densest stars in the universe (neutron star or neutron star-black hole pairs) orbit each other, they get closer due to emitted gravitational radiation. Neutron stars have a solid exterior crust that may shatter in this extreme encounters. In this project, you will explore whether the star can shatter like a glass does when a singer hits its resonant note. This depends on the properties of dense matter and, in particular, on the symmetry energy parameter that is predicted from nuclear physics. Furthermore, if detectors can see gamma rays from such a shattering process just before measuring the gravitational waves emission from the merger, we may find the resonant frequency at which the crust shatters. This could potentially help constrain the properties of the crust and nuclei, bridging the gap between 20 orders of magnitude in spatial extent. 

The LHCb detector is one of the main experiments at the LHC at CERN, specialized on the study of CP breaking and rare decays of b hadrons. Semileptonic transitions of a b quark to an s quark and two leptons (b -> sll) have been intensively studied during the last decade, with some hints of potential new physics effects. The analogous transitions with a d quark in the final state (b -> dll) are more suppressed in the Standard Model and thus highly sensitive to potential new physics effects, at even higher scales. There transitions are however largely unexplored due to the experimental challenges they involve. Only two b -> dll decays with muons and none with electrons in the final state have been observed to date. The large data sample collected by the LHCb experiment should enable the observation of these decays, provided a powerful discriminating power with respect other transitions is achieved in the event selection. The goal of this project is to search for the b -> de+e- transition B -> pi e+e-, using the data from the LHCb experiment and applying machine learning techniques to suppress the large background affecting this final state. This is the first step towards measuring the properties b -> dll transitions, most notably lepton flavour universality ratios, which provide a stringent test of the Standard Model.

The Standard Model of Cosmology, the so-called ΛCDM model [1], is afflicted by
several discrepancies with observations that might be calling for new physics. The Hubble tension between the local measurement of H0 by SH0ES and Planck’s CMB-inferred value already reaches the ~5σ C.L. Others attain the 2-3σ C.L., as the tension between the growth of large-scale structures measured with weak lensing and galaxy clustering probes and Planck. Both have been there for already a decade. See the review [2] and references therein for details. The growth rate tension is usually quantified in terms of the parameter σ8, which is the root-mean-square mass fluctuations at a scale of R8=8h-1Mpc, with h=H0/(100km/s/Mpc) the reduced Hubble parameter. It has been recently argued that the use of σ8 might introduce a bias in cosmological analyses of models with a value of H0 quite different from the one preferred by ΛCDM (h~0.67) [3]. This has been proved to be true in the context of early dark energy models [4] and modified theories of gravity [5].

In this thesis the student will quantify the bias introduced by the use of σ8 in fitting analyses of several dynamical dark energy models. This bias could be playing a crucial role in the assessment of the aforesaid cosmological tensions, and could also be of utmost importance to understand their interplay. The student will derive the most relevant cosmological equations at the background and linear perturbation levels for the various models and familiarize with the Einstein-Boltzmann code CLASS [6], the use of Monte Carlo techniques and samplers, and basic concepts of Bayesian statistics [7], This analysis is expected to shed light on the discussion of the cosmological tensions and give rise to a publication in a high-impact journal in the field.

The solution of quantum field theories is one of the most challenging topics in modern theoretical physics. Recently, promising advances have relied on the use of variational approaches that exploit machine learning techniques [1]. These approaches encode the gauge symmetries in the architecture of neural networks [2], which provides advantages with respect to other sampling techniques [3]. Variational solutions to quantum field theories can be then exploited to find numerical solutions to these problems [4].  

In this project, you will employ machine learning techniques to address a simplified quantum field theories, and solve it variationally. The results you will obtain will be  benchmarked with other methods, including lattice field theory. You will study and analyze the quality of the variational ansatz depending on different architectures. You will look into the efficiency of these new variational techniques, as well as different sampling and optimization strategies.

Traditionally, the determination of two-particle momentum correlations in relativistic heavy ion collisions has been viewed as a tool to explore the space-time evolution of the emitting. However nowadays the precise experimental data and new theoretical techniques, the so called femtoscopy, allow the possibility to go further and to extract information about the interaction between these two particles. In this project we will perform theoretical simulations in the framework of chiral models with unitarization imposed in coupled channels, and we will concentrate on the influence of coupled-channel effects on the two-particle momentum correlation function [1]. As a first step we will study systems like pp or K+p, which are ideal for testing and applying the femtoscopic techniques, because there is only a single S -wave state where strong correlations are expected to occur for low momenta and the thresholds of other channels are far away from the energy region of interest [1].

The quark-gluon plasma is a new state of matter that can be formed by colliding heavy ions at ultrarelativistic velocities. From all the particles formed in these collisions, heavy quarkonium is one of the most promosing probes to obtain information about this new state of matter. One of the most succesful approaches to the study of the evolution of quarkonium in a medium is to model it as a Markovian open quantum system. Recently, it has been found using this approach that regeneration is crucial to reproduce experimental data on quarkonium excited states. However, it has been observed that after including regeneration the number of detected Upsilon(2S) states over Upsilon (1S) increases but the ratio of Upsilon(3S) over Upsilon(2S) decreases. This result is unintuitive because s-wave quarkonium states are ordered in size and, therefore, we expect larger states to be more suppressed by the medium. We propose to find the reason of this behaviour by studying the evolution of quarkonium with a recently proposed numerical method, the Jumptime unravelling. References:N. Brambilla, M.A. Escobedo, J. Soto and A. Vairo, Quarkonium suppression in heavy-ion collisions: an open quantum system approach, Phys. Rev. D \textbf{96} (2017) no.3, 034021 [arXiv:1612.07248 [hep-ph]].

Dark matter is a mysterious constituent of the universe, 5 times more abundant than ordinary (or visible) matter. The characterisation of its properties remains one of the most pressing problems of particle physics. In particular, dark matter could be in a degenerate quantum state in some galaxies, with novel phenomenological consequences. The proposed work would consist in studying a toy model of fermions with attractive long range interaction to mimic the peculiar properties of these galaxies, which can be done using state-of-the-art tensor network techniques. The student is expected to investigate the ground state (and thermal) properties of this quantum model, and understand which new properties may appear in the final virialized states ('halos') from quantum degeneracy pressure as compared to their classical counterpart. Because of its interdisciplinary nature, this work would be done in co-supervision with Prof. Diego Blas from Universitat Autònoma de Barcelona, and Prof. Mari Carmen Bañuls from Max Planck Institute for Quantum Optics (Garching, Germany). The student would moreover have the opportunity to visit the MPQ to work closely with Prof. Bañuls for a period of one to a few weeks (all expenses covered).

Localization is a technique to compute functional integrals exactly. The location technique applied to the calculation of exact physical observables is one of the most spectacular recent results in non-abelian gauge theories.
This led to the calculation of the exact partition function, Wilson loop operators in supersymmetric theories, including all perturbative and non-perturbative contributions, with an exact account on all instanton effects. This master thesis will investigate several open problems in relation to four-dimensional non-abelian gauge theories by means of supersymmetric localization of path integrals.

Superstring theory in anti de Sitter space is dual to superconformal field theories, that is, to field theories invariant under scale symmetries and supersymmetries. In the last 20 years, this AdS/CFT duality has led to multiple applications, including classical and quantum gravitational physics, condensed matter, integrability and several aspects of superstring theory, representing the main trending topic in theoretical physics. This master thesis will study conformal field theories in spaces which are direct product of anti de sitter spaces and spheres, with the aim of understanding boundary anomalies and their AdS/CFT counterpart.

The fusion of two black holes — a signature phenomenon of General Relativity — is usually regarded as a process so complex that nothing short of a supercomputer simulation can accurately capture it. But no -- not always. In this work the student will see how the event horizon of the merger can be found in a simple way in the limit where one of the black holes is much smaller than the other, which is a situation that does occur in nature. Remarkably, the ideas and techniques involved are elementary: the equivalence principle, null geodesics in the Schwarzschild or Kerr solutions, and the notion of event horizon itself. The student will get a deeper appreciation of these notions, as well as develop some skills with Mathematica in the numerical solution of (simple) differential equations and in the graphic presentation of a realistic phenomenon that is happening right now in our Universe.

Based on quark and lepton masses, as well as on the CKM mixing pattern, the couplings of Higgs with fermions ( seem to be highly hierarchic. That hierarchy is expected to be due to the severe breaking of an underlying flavour symmetry group.

New improved results on the size of the flavour changing neutral processes collected at LHC are helpful in building New Physics models which encompass the observed since of CP violation and of the hierarchy among various species of quarks and leptons. Most significantly recent LHCb results on b -> s mu mu suggest some tensions with respect to the Standard Model (SM).

Moreover, models which explain these tensions can be handle Dark matter candidates.

The gauge/gravity duality, or holography, is a versatile tool to study the strongly coupled dynamics of gauge theory matter. One of areas were the holographic principle shows its strengths is in the computation of the phase diagram of quantum field theories with known gravity duals. For certain realisations of the duality, the field theory enjoys non-trivial phase diagrams, including phase transitions of different degrees. The goal of this project is to determine the effective action of a particular class of models and to relate this effective action to their known phase structure.

We will study non-relativistic holography using non-relativistic strings and non-relativistic gravities.

We will study the symmetries of M theory and the connection free Lie superalgebras.

Dark energy (DE) is believed to be the physical cause that produces the measured accelerated expansion of the universe. Within the standard model of cosmology (i.e. the current paradigm) the DE is identified with a strict cosmological constant. However, the plain simplicity of this idea lies at the root of its unconvincing theoretical status. In addition, phenomenologically, the standard model is also disputable at present. Tensions of various sorts and of different degrees are known to be present among existing datasets within such framework. For example, the recently measured local value of the Hubble parameter, H0, is significantly higher than the one inferred from the measurements of the anisotropies in the cosmic microwave background (CMB) by the Planck satellite. Also, the current paradigm predicts exceeding structure formation power as compared to the observations etc. The possibility that these facts are actually pointing to serious 'cracks' in the current cosmological paradigm is slowly but strongly setting in.

In this work, the student will have the opportunity to explore the nature of these cosmological problems as well as some theoretical models of dynamical DE capable to alleviate them. Among these models, the dynamical vacuum models are well-motivated from the theoretical point of view (e.g. within quantum field theory in curved spacetime). Interestingly, they also predict a possible time variation of the fundamental "constants" of Nature, including the masses and couplings of the elementary particles, what could act as an additional signature of physics beyond the standard models both of particle physics and cosmology.

Despite the vacuum energy and in general the dark energy (DE) is postulated as being the physical cause that produces the measured accelerated expansion of the universe, the usual prediction in quantum field theory (QFT) is much too large as compared to the critical density of the Universe. The mismatch is ultimately responsible for the "Cosmological Constant Problem", which is the biggest conundrum of fundamental physics ever. The main problem stems from the usually proposed renormalization procedures of the energy-momentum tensor in QFT, which lead to contributions proportional to the quartic powers of the mass of the quantum fields (i.e. proportional to $m^4$). However, if one considers an appropriate variant of the adiabatic regularization and renormalization of quantum fields in a FLRW background it is possible to provide a well defined result which can elude the $m^4$ terms and ultimately provides a dynamical vacuum energy density $\rho_{vac}(H)$ evolving as powers of the Hubble rate, H, and its derivatives, therefore sufficiently small.

In this work, the student will have the opportunity to perform such a QFT calculation in an appropriate context, in which matter is represented by a scalar field non-minimally coupled to curvature. He/she will verify that $\rho_{vac}(H)$ evolves as a constant term (representing the cosmological constant part of the final result) plus some dynamical components of order $H^2$ and $H^4$. The higher powers are relevant for the early universe only, where they can trigger fast inflation through effective string-theory effects generating those terms. These are induced by the presence of anomalous Chern-Simon couplings involving the Kalb-Ramond field of the gravitational multiplet. At present, $\rho_{vac}(H)$ is dominated by the additive constant term accompanied by a tiny dynamical component of order $H^2$. This result tells us that the vacuum energy density is not just constant but evolves with time. Its current variation is small enough, but still potentially measurable. At the phenomenological level, it looks as a kind of effective quintessence behavior. In point of fact, however, there is not a real quintessence field but an underlying QFT vacuum changing ('running') very mildly with the cosmic expansion.

The so called final state interacions or rescattering effects give rise to large uncertainties in the cross sections of hadronic collisions. They are due to the fact that the hadrons produced in a collision may suffer non-negligible interactions between themselves before reaching the detector. A recently proposed effective theory [1] may be instrumental to systematically address this problem. We propose to initially explore this issue in the scattering of scalar particles, and eventually in the relevant case of the Chiral Lagrangian [2].

The plethora of charmonium (and some bottomonium) resonances discovered during the last decade, the so called XYZ states [1], challenge our current understanding of QCD. An important ingredient to describe those states is the interaction of heavy quarkonia with heavy-light meson pairs. We propose to include a realistic estimate of this interaction in the calculation of the heavy quarkonium spectrum. The estimate should be first obtained by fitting lattice QCD data on the string breaking phenomena of refs. [2,3], and extrapolating them to realistic values of the light quark masses [4]. The outcome should be then incorporated in a coupled-channel Schrödinger equation and the spectrum calculated numerically.

Primordial Inflation is a very early stage of expansion of the Universe at very high energy, which is thought to explain many observed properties of our Universe. We aim to study the connection with Particle Physics of such models, in particular the presence of photons and other gauge fields during inflation, in order to compute observable consequences of this possible connection. We also look for models which can produce detectable gravitational wave signals.

The QCD Axion is one of the best motivated extra particles, beyond the the Standard Model of Particle Physics, which may also explain the dark matter problem. We propose to study its production in the Early Universe in several different scenarios and forecast its detectability in the near future.

The LHCb experiment is due to be upgraded in 2018. The full detector will be able to take data from LHC collisions at 40MHz rate taking full advantage of the collider bunch crossing rate. The calorimeter electronics has been re-designed for the upgrade. One of the key ingredients of the new calorimeter upgrade is the ICECAL chip from the Barcelona group. The ASIC passed the Electronics Design Reviewof the LHCb collaboration and Production . Now the full electronics, where the ASIC is integrated into the PCB boards, connected to the remaining elements of the new LHCB CALO must be tested and comissioned, before it will start operation in early 2021. Together with the group of the LAL-Orsay, a mini-DAQ has to be tested and debugged to make sure the final installation will be capable to readout the CALO data at a 40 MHz rate

After 2025 the LHC collider will enter the High Luminosity regime (HL-LHC), where the instantaneous luminosity will be enhanced an order of magnitud with respect to present 4 x 10^33 /cm^2 /s . The Upgraded (2021) LHCb detector will have to run after 2025 with the LHC beam slightly defocused (using again the lumi leverage method to get a constant lumi in LHCb) so that its detectors and DAQ system can cope with the a inelastic interaction rate per bunch crossing rate similar to that before the HL-LHC. An R&D program within the experimental heavy flavour community has started to make possible with a second LHCb Upgrade to take advantage of the full potential of the HL-LHC also in LHCb. The scheduled calendar aims to installing some prove-of-concept sub-detectors in 2025 at LHCb, in those areas that will be most affected the ageing of the current detectors. With that experience, a major refurbishing of the LHCb detector, aka LHCb Upgrade II, is foreseen in 2030 to be able to take as much data as available from the LHC and collected a total of 300/fb of pp-collision data by the end of the operation of the LHC (circa 2036). The ICCUB has started an R&D program to build a new CALO for LHCb with increased granularity (to cope with the increased multiplicity of the HL-LHC regime), increased radiation hardness and an ultrafast RO electronics capable to provide a time stamp of the data collected with a resolution below 100ps to provide time separation between the different inelastic proton-proton collisions that will take place in each LHC bunch crossing (aprox. 40). The TFM proposed will address the test of different combination of sensors (scintillating crystals), photo-sensor (SiPM, PMTs, SPADS, etc..), readout electronics (FastIC, MusIC, etc...) to consider a possible solution for an upgraded LHCb CALO for the HL-LHC..

The LHCb detector at the LHC has observed a number of small deviations with respect to the Standard Model predictions in b -> sll transitions, most notably in tests of Lepton Universality comparing the couplings to muons and electrons. While a pattern is emerging, it is of uttermost importance to confirm if these deviations are present in the whole family of b -> sll decays. A first measurement of Lepton Universality with Lambda_b decays was performed by LHCb with a fraction of the collected data, with results consistent with the deviations observed in the meson sector but also with the SM predictions. It is thus critical to update this measurement with the full dataset. In particular, optimisation of the event selection and a study of the pK spectrum will enable improvements beyond the pure statistical gain from the size of the analysed data sample.

The propagation of gravitational waves (GW) in an expanding universe, whose composition is dominated by dark energy and dark matter, is usually treated by simply introducing the cosmological red-shift in the frequency. While this is enough for many applications, we have proven that there are other effects that need to be included, in particular a careful treatment of the difference in the reference frames where the waves are produced and detected. This analysis potentially leads to a way of measuring the cosmological constant and other cosmological parameters. In this work we propose to study this in detail. Detection of GW in Pulsar Timing Arrays (PTA) is a possibility and the influence of these effects on the current bounds on the graviton mass is another venue of investigation.

The Higgs particle is one of the cornerstones of the Standard Model of particle physics. Yet, we are not sure whether this particle is truly elementary or, on the contrary, is a composite state, the lightest resonance in a strongly interacting extended electroweak symmetry breaking sector perhaps. In this case, other resonances with various quantum numbers must exist and indeed they are predicted when requirements of unitarization and causality are demanded on this extended sector. In this work we propose to consider various possible alternatives for the Higgs and investigate proposal to experimentally reveal whether these alternatives may be the one chosen by Nature.

General Relativity encompasses a huge variety of physical phenomena, from the collision of astrophysical black holes, to the dynamics (via holography) of strongly-coupled plasmas and the spontaneous symmetry-breaking in superconductors. Black holes play a central role in all this. However, their equations are exceedingly hard to solve. The apparent lack of a generic tunable parameter that allows to solve the theory perturbatively (like the electric coupling constant in electrodynamics, or the rank of the gauge group in large-NYang-Mills theory) is arguably the single most important obstacle for generic efficient approaches to the physics of strong gravity and black holes. In General Relativity, one natural parameter suggests itself: the number of dimensions D. Recently we have demonstrated that the limit of large D is optimally tailored for the investigation of black holes, classical and potentially also quantum. We have derived a simple set of nonlinear equations that describe the dynamical evolution of black holes, strings and branes that efficiently capture a surprisingly large amount of black hole physics.

It is well known that using Einstein’s equations one can prove a set of laws of “black hole thermodynamics” where the horizon area plays the role of entropy. In 1995 Jacobson showed that it is possible to reverse this logic and derive the Einstein equations by assuming that dynamical spacetime satisfies a first law of thermodynamics. More recently, in a related but different set up, the Einstein equations have been derived from a hypothesis about vacuum entanglement.

The study of the dark energy is a central subject in cosmology and fundamental physics. Despite the many efforts, our theoretical understanding of the ultimate nature of the dark energy component of the universe still lags well behind the astounding experimental evidence achieved from the increasingly sophisticated observational tools at our disposal. While the canonical possibility is a strict cosmological constant, the exceeding simplicity of this possibility lies also at the root of its unconvincing theoretical status. In this work the student will have the opportunity to explore the cosmological implications of the dynamical models of the vacuum energy. Some of these models are actually well-motivated from the theoretical point of view (e.g. within quantum field theory in curved spacetime) and may provide a rich phenomenology that could be explored in future observations. In particular, the dynamics of vacuum can affect the Hubble expansion and the details of structure formation, as collected e.g. from the data on type Ia supernovae, the Cosmic Microwave Background and the Baryonic Acoustic Oscillations. In this study the cosmology of some these models will be solved and confronted with the data. At the same time the relation of these vacuum models on possible evidence of dynamical dark energy recently pointed out in the literature will also be addressed.

A new effective field theory has been proposed which describes physical phenomena dominated by on-shell degrees of freedom. It has been recently applied to study the high temperature limit of the photon polarisation tensor of QED for soft external momenta, as it is known that it is dominated by the contribution of the on-shell fermions and antifermions of the plasma. It is possible to generalise the on-shell effective field theory for a non-vanishing value of a chemical potential and chiral chemical potential, and check that also these techniques allow one to study a set of variety of phenomena in these cases. In particular, we will concentrate in the study of chiral anomalous effects at finite density. The student is supposed to learn the basics of the real time formalism of thermal field theory, which generalises QFT from the vacuum to a thermal state, and be able to carry out one-loop calculations with it.

We will study BMS symmetries as canonical symmetries of quantum field theories, and the relation with other realizations.

Presently LHC has observed a state which is compatible with the Standard Model Higgs Scalar responsible for electroweak symmetry breaking (EWSM) . On the other hand no direct signature of new physics staes has been observed.

This allows to parametrize the possible effects of NP in the electroweak symmetry breaking sector in terms of an effective lagrangian containing higher dimension operators. Recently we have performed an analysis of the existing data in order to constraint the coefficients of these operators. The proyect will review this subject and will evaluate the maximum allowed deviations from the SM predictions in the Higgs related signatures at the future high precision runs of the LHC.

During the last 15 years neutrino oscillation experiments have produced results which show that neutrinos are massive and oscillate in flavour. One of the most recent results come from the Daya-Bay experiment which measures the disappearance of reactor antineutrinos at distances of the order of km. This experiment was the first one to provide with statistical significance a measurement of the last mixing angle of the leptonic mixing matrix, theta_13 based on the observation of a deficit in the observed over expected number of events. This summer Daya-Bay has released their data on the energy spectrum of their events which can provide additional information. The project proposes to review the formalism of neutrino oscillations and to proceed wiht the relevant computations to make an statistical analysis of the observed energy spectrum.

We will use the equivalence between strongly coupled gauge theories and gravity in Anti de Sitter space to study various aspects of gauge theories.

If dark matter particles are very heavy, they may form bound states mediated by the interaction with Standard Model particles. Direct detection experiments may be sensitive to break-up events. We propose to build an effective field theory in which dark matter particles are non-relativistic, and explore the possible existence of bound states, both in the case that the SU_L(2) x U_Y(1) symmetry is linearly realized and in the case that it is non-linearly realized (composite Higgs).

Generalized geometry is a new framework for geometric structures, which, in particular, regards complex and symplectic structures as two particular cases of the same structure: a generalized complex structure. This, and other features (like the appearance of B-fields as generalized diffeomorphisms), made generalized geometry become a very suitable language for some aspects of string theory, like mirror symmetry and M-theory.

This main goal of this project is acquiring a basic but strong conceptual understanding of generalized geometry, which would allow the student to deal with mathematical and physical literature in the future as well as making independent use of the main concepts involved in generalized geometry.

The student is expected to review the basics of the theory from the viewpoint of her/his interests with the close supervision of the tutor. Moreover, and in a more independent way, the student should approach and discuss some uses of generalized geometry in Theoretical Physics from a mathematical point of view.

This project requires a good mathematical background.

The Jefferson Laboratory in Virginia hosts two experiments (GlueX and CLAS12) dedicated to the study of meson interaction. These experiments are searching for exotic mesons produced by photons on a hydrogen target. The most promising signal of an exotic meson, in this case a state composed of a q qbar together with an extra gluon, has been observed in the P-wave of the eta+pi0 final state. However the confirmation of this discovery requires a comparison between theoretical predictions and experimental observables.
The project consists in studying the reaction gamma + p --> eta + pi0 + p at high energies and developing a model for the production of exotic meson in this reaction (to be compared with GlueX preliminary data)

Gravitational waves are constantly passing us. However, even the strongest waves that come from merging black holes have a tiny effect on the arms of the gravitational wave detectors on Earth. They stretch and squeeze them by a thousand of the width of a proton.

You will search for gravitational waves in LIGO-Virgo data to find short unknown signals. You will demonstrate the potential of the maximum entropy method to determine the properties of exotic, unknown signals. This technique recovers coherent signals from a network of gravitational wave detectors. It assumes that signal behaves differently from noise, i.e., that the signal is correlated at different detectors in the network, while the noise is uncorrelated. You will learn numerical methods, noise modelling, some of the mathematics behind the data analysis, and practice on real detector data. You will start by reconstructing very short events of possible exotic origin like GW190521.

Requirements: linear algebra, python, complex analysis

Just like light waves, gravitational waves are most generally characterized by their propagation direction and time-dependent waveform in each of two independent polarization states. These properties of incident gravitational plane waves can be inferred from observations made in a properly oriented network of detectors. You will learn to characterize the wave polarization via its (frequency dependent) Stokes parameters to infer important, general properties of the wave's source: e.g., point sources of circularly polarized radiation must be non-axisymmetric and radiating angular momentum, while point sources of linearly polarized waves must be either axisymmetric or oriented so that the direction of angular momentum loss is orthogonal to the observer line-of-sight. This is particularly interesting for more exotic sources, e.g., black hole binaries with high spin or high eccentricity. You will find the regions of the gravitational wave sky where the LIGO-Virgo network is sensitive to both gravitational wave polarizations, and estimate the number of sources.

The first event where both polarizations were detected is GW170814. You will start by computing the Stokes parameters for this event.

After the discovery of gravitational waves (GWs, Abbott et al. 2017), the LIGO-Virgo gravitational wave (GW) interferometers have detected dozens of binary black hole (BBH) mergers. Various models exist to successfully explain the merger rate and evolution and properties of black hole binaries: they may originate from massive star binaries, or from dynamical interactions in dense stellar environments, such as globular clusters (GCs). Although model predictions differ, the data does not yet allow us to discriminate between formation channels. There is so far no clear dominant formation channel. The relative contribution of each of these channels could be anywhere between 20-90%.

A unique prediction of the dynamical channel is the existence of BBH with measurable eccentricity (i.e., at the LIGO-Virgo frequencies). In this project you will make predictions for the properties of eccentric mergers that occur in GCs as the result of GW capture. You will use the model predictions for the evolution of GCs and their BHs (Antonini & Gieles 2020a,b), and combine these with recipes for mergers following GW capture in single-single and single-binary encounters (Samsing et al. 2020). The goal of this project is to quantify where these eccentric BBH mergers lie in the mass-eccentric diagram.