Science (Faculty of)

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Amended Model of Large Scale Dark Matter Structure
(University of Waterloo, 2020-09-03) Chen, Alice; Afshordi, Niayesh
Dark matter makes up around a quarter of the total energy density in the universe, but its identity remains elusive. Current ways of studying dark matter have centered around its macroscopic properties, such as density distribution and large scale structure formation. The halo model of large scale structure is an important tool that cosmologists use to study the phenomenological behaviour and nonlinear evolution of structure in the universe. However, it is well known that there is no simple way to impose conservation laws in the halo model. This can severely impair the predictions on large scales for observables such as weak lensing or the kinematic Sunyaev-Zel’dovich effect, which should satisfy mass and momentum conservation, respectively. For example, the standard halo model overpredicts weak lensing power spectrum by > 8% on scales > 20 degrees. To address this problem, we present an Amended Halo Model, explicitly separating the linear perturbations from compensated halo profiles. This is guaranteed to respect conservation laws, as well as linear theory predictions on large scales. We also provide a simple fitting function for the compensated halo profiles, and discuss the modified predictions for 1- halo and 2-halo terms, as well as other cosmological observations such as weak lensing power spectrum. Similar to previous and recent works centered around the halo model, this work is physically motivated and matches simulation data to a greater degree of accuracy than the standard halo model currently does. We compare our results to previous work, and argue that the amended halo model provides a more efficient and accurate framework to capture physical effects that happen in the process of large scale cosmological structure formation.
Aspects of Nonlocality: from Particles to Black Holes
(University of Waterloo, 2016-05-06) Saravani, Mehdi; Afshordi, Niayesh; Sorkin, Rafael
This dissertation is a collection of works on different aspects of the following subjects: causal set--continuum correspondence, wave propagation on causal sets, nonlocal quantum field theory, potential connection between dark matter and quantum gravity and causal structure of black holes in Lorentz violating gravitational theories. We present two results which concern certain aspects of the question: when is a causal set well approximated by a Lorentzian manifold? The first result is a theorem which shows that the number-volume correspondence, if required to hold even for arbitrarily small regions, is best realized via Poisson sprinkling. The second result concerns a family of lattices in 1+1 dimensional Minkowski space, known as Lorentzian lattices, which we show provide a much better number-volume correspondence than Poisson sprinkling for large volumes. We argue, however, that this feature should not persist in higher dimensions and conclude by conjecturing a form of the aforementioned theorem that holds under weaker assumptions, namely that Poisson sprinkling provides the best number-volume correspondence in 3+1 dimensions for spacetime regions with macroscopically large volumes. We then study wave propagation on a background causal set. We introduce a family of generalized d'Alembertian operators in D-dimensional Minkowski spacetimes which are manifestly Lorentz-invariant, retarded, and non-local. The prototypes of these operators arose in earlier work as averages of matrix operators meant to describe the propagation of a scalar field in a causal set. We generalize the original definitions to produce an infinite family of ''Generalized Causet Box (GCB) operators'' parametrized by certain coefficients, and we derive the conditions on the latter needed for the usual d'Alembertian to be recovered in the infrared limit. The continuum average of a GCB operator is an integral operator in Minkowski, and it is these continuum operators that we mainly study. To that end, we compute their action on plane waves, or equivalently their Fourier transforms g(p) [p being the momentum-vector]. For timelike p, g(p) has an imaginary part whose sign depends on whether p is past or future-directed. For small p, g(p) is necessarily proportional to p.p, but for large p it becomes a constant, raising the possibility of a genuinely Lorentzian perturbative regulator for quantum field theory in Minkowski. We also address the question of whether or not the evolution defined by the GCB operators is stable, finding evidence that the original 4D causal set d'Alembertian is unstable, while its 2D counterpart is stable. Following our earlier work on wave propagation on a causal set, we study the quantum theory of a massless scalar field whose evolution is given not by the the d'Alembertian, but by an operator which is Lorentz invariant, reduces to d'Alembertian at low energies, and defines an explicitly retarded evolution. This modification results in the existence of a continuum of massive particles, in addition to the usual massless ones, in the free theory. When interactions are introduced, these massive or off-shell quanta can be produced by the scattering of massless particles, but once produced, they no longer interact, which makes them a natural candidate for dark matter which we dub off-shell dark matter (OfDM). Finally, we generalize this idea to massive scalar fields too. We then consider phenomenological predictions of OfDM model in the context of cosmology. OfDM particles rate of production is suppressed by the scale of nonlocality (e.g. Planck length). As a result, we show that OfDM is only produced in the first moments of big bang, and then effectively decouples (except through its gravitational interactions). We examine the observational predictions of this model: In the context of cosmic inflation, we show that this proposal relates the reheating temperature to the inflaton mass, which narrows down the uncertainty in the number of e-foldings of specific inflationary scenarios. We also demonstrate that OfDM is indeed cold, and discuss potentially observable signatures on small scale matter power spectrum. Finally, we explore the validity of Cosmic Censorship conjecture in Lorentz violating theories of gravity. Is Cosmic Censorship special to General Relativity, or can it survive a violation of local Lorentz invariance? Studies have shown that singularities in Lorentz violating Einstein-Aether (or Horava-Lifshitz) theories can lie behind a universal horizon in simple black hole spacetimes. Even infinitely fast signals cannot escape these universal horizons. We review this result and extend it, for an incompressible aether, to 3+1D dynamical or spinning spacetimes which possess inner Killing horizons, and show that a universal horizon always forms in between the outer and (would-be) inner horizons. This finding suggests a notion of Cosmic Censorship, given that geometry in these theories never evolves beyond the universal horizon (avoiding potentially singular inner Killing horizons). A surprising result is that there are 3 distinct possible stationary universal horizons for a spinning black hole, only one of which matches the dynamical spherical solution. This motivates dynamical studies of collapse in Einstein-Aether theories beyond spherical symmetry, which may reveal instabilities around the spherical solution.
Aspects of Quantum Gravity: From Black Hole Thermodynamics to Holography
(University of Waterloo, 2024-09-16) Yang, Jiayue; Mann, Robert; Afshordi, Niayesh
Understanding the nature of quantum gravity remains one of the cutting-edge challenges in modern theoretical physics. Despite widespread interest and extensive research, the formulation of a complete theory of quantum gravity remains an unsolved problem. This thesis aims to explore quantum gravity from two primary perspectives: black hole thermodynamics and holography. Black hole chemistry extends black hole thermodynamics by incorporating the cosmological constant, treating the black hole mass as enthalpy rather than energy, and interpreting the cosmological constant and its conjugate variable as pressure and volume, respectively. Holographic complexity investigates the duality between gravitational quantities in the bulk and quantum complexity on the boundary. This includes various proposals such as complexity=volume (CV), complexity=spacetime volume (CV2.0), complexity=action (CA), and complexity=anything proposals. In our exploration of black hole thermodynamics, we investigate phase transitions near quadruple points, where four distinct black hole phases coexist. Utilizing the free-energy landscape technique within the framework of four-dimensional Einstein gravity coupled with nonlinear electrodynamics (NLE), we undertake the first investigation into the dynamics of recently discovered multicriticality in black holes. By treating off-shell Gibbs free energy as a potential and solving the Smoluchowski equation numerically, we capture the evolution of the state probability distributions during black hole phase transitions. Our study reveals how off-shell Gibbs free energy, shaped by ensemble temperatures, influences these transitions and highlights intricate behaviours such as weak and strong oscillations. In our investigation of holography, we analyze the complexity of conformal field theories (CFTs) compactified on a circle with a Wilson line, corresponding to magnetized solitons in four-dimensional and five-dimensional Anti-de Sitter space (AdS). We explore three distinct proposals for holographic complexity. Our study reveals that these proposals exhibit a confinement-deconfinement phase transition driven by variations in the Wilson line, with the complexity of formation acting as the order parameter for this transition. We find that the proposed volume and action complexity functionals obey a scaling relation with the radius of the circle. We show that this scaling law is applicable to a broad family of potential complexity functionals and conjecture that the scaling law applies to the complexity of conformal field theories on a circle in more general circumstances.
Black holes in cosmological spacetimes and alternative theories of gravity
(University of Waterloo, 2023-08-09) corman, maxence; East, William E.; Afshordi, Niayesh
This thesis is dedicated to the study of spacetimes surrounding black holes within the context of cosmology, high energy physics and modified theories of gravity. We do this by applying and adapting modern numerical relativity techniques to probe the inhomogeneous and strong field regime in a number of different scenarios. The first application we consider is the nonlinear evolution of unstable flux compactifi- cations in a low-energy limit of string theory. Going beyond stationary solutions and their perturbations, we find rich dynamics, in some cases finding that the evolution from an unstable homogeneous state to a stable warped compactification can serve as a toy-model for slow-roll inflation, while in other cases finding solutions that eventually evolve to a singular state. We then apply the methods for numerically evolving scalar fields coupled to the Ein- stein field equations to address several problems in early universe cosmological scenarios. We study the conditions under which inflation can arise from very inhomogeneous initial conditions. To do so, we introduce and compare several different ways of constucting ini- tial data with large inhomogeneities in both the scalar field and time derivative profiles, by solving for the coupled Einstein constraint equations. We then study the evolution of various classes of initial conditions in both single- and two-field inflationary models. In some of the cases studied, the initial gradient and kinetic energy are much larger than the inflationary energy scale such that black holes can form. Taken together, our results suggest inflation can arise from highly inhomogeneous conditions. Using the same numerical techniques, we study the nonlinear classical dynamics and evo- lutions of black holes in a particular nonsingular bouncing cosmology. We find that for sufficiently large black holes the black hole apparent horizon can disappear during the contraction phase. Despite this, we show that most of the local cosmological evolution remains largely unaffected by the presence of the black hole. For all the cases explored, the black hole’s event horizon persists throughout the bounce, suggesting the nonsingular bouncing model under study is fairly robust to large perturbations. Finally, we use and further develop a novel formulation of the Einstein field equations for evolving a large class of modified theories of gravity. We use this formulation to study the nonlinear dynamics of binary black hole mergers in a specific class of theories, where the black holes acquire a scalar charge. We consider quasi-circular inspirals with different mass-ratios, varying the coupling parameter introducing deviations from General Relativity and quantifying the impact on the emitted scalar and gravitational waveforms. We also compare our numerical results to analytic post-Newtonian calculations of the radiation emitted during the inspiral.
Charged Black Hole Solutions in Alternative Theories of Gravity
(University of Waterloo, 2016-09-06) Meiers, Michael; Mann, Robert; Afshordi, Niayesh
In my thesis, I examine charged black holes in two contexts. The first part covers the formation of something analogous to event horizons for a class of Lorentz-Violating theories which allow for signals to travel faster than light. In particular, the focus is put on the construction of horizons for the limiting case where the signal travels infinitely fast called a universal horizon. An explicit construction for a metric containing a massive collapsing charged shell is presented followed by an extension into rotating systems using a geometric argument. The latter context is Randall Sundrum model of gravity applied to higher dimensions. The research begins with a general ansatz and restricts parameter space using the equations of motion and junction conditions created by brane on which some charge is trapped. Some examination of the available solutions follows, and an analysis of the entropy relations for large and small black hole solutions concludes the results.
Cosmological beam plasma instabilities
(University of Waterloo, 2017-08-24) Shalaby, Mohamad; Broderick, Avery; Afshordi, Niayesh
Blazars are the main source of extragalactic very high energy gamma-rays. These gamma rays annihilate on the extragalactic background light, producing electron-positron pair beams with TeV energies. The pair beams are very dilute, with beam-IGM density ratio of $\alpha \sim 10^{-15}$, ultra-relativistic, $\gamma \sim 10^6$, and energetically subdominant ($\gamma \alpha \sim 10^{-9}$). Such pair beams suffer from prevailing cosmological scale, linear beam-plasma instabilities. The associated instability growth rates suggest that at least initially these overwhelmingly dominate inverse Compton cooling, currently the only alternative mechanism by which the pair beams lose energy. Therefore, the full non-linear evolution of the instabilities is key to determining the mechanism by which these pair-beams lose their energy. Kinetic numerical simulations are the only method by which we can currently study the full non-linear evolution of the blazar-induced beam-plasma instabilities. However, the extreme parameters of the pair beams make direct simulations via existing particle-in-cell (PIC) codes infeasible. To address this, we developed a new Spatially Higher-order Accurate, Relativistic PIC algorithm (SHARP). A one dimensional implementation of the SHARP algorithm (SHARP-1D) is given in detail. We show explicitly that SHARP-1D can overcome a number of the limitations of existing PIC algorithms. Using SHARP-1D, we demonstrate a number of points that are important to correctly simulate the full evolution of beam-plasma instabilities. We show that convergence for PIC algorithms requires increasing both spatial resolution and the number of particles per cell concurrently. For a beam-plasma system, we show that the spectral resolution is another important resolution criteria and under-resolved simulations can lead to erroneous physical conclusions. We quantify the required box sizes to faithfully resolve the spectral support of the instabilities. When the background plasmas contain structure, we show that a significant fraction of beam energy (similar to that in uniform plasma simulations; $\sim 20$\%) is, still, lost during the linear evolution of the electrostatic unstable modes. Compared to uniform plasma growth rates, we find lower growth rates, however, the non-uniform systems stay longer in the linear regime. Therefore, the IGM inhomogeneities are unlikely to affect the efficiency of beam-plasma instabilities to cool the blazar-induced pair beams.
Cosmological Tests of Causal Set Phenomenology
(University of Waterloo, 2017-09-20) Zwane, Nosiphiwo Tivelele; Sorkin, Rafael; Afshordi, Niayesh
Causal Set Theory is an approach to Quantum Gravity that postulates that the fundamental structure of a spacetime manifold is a Lorentz Invariant discrete structure endowed with a causal order from which the geometry and topology of the spacetime can be recovered. The continuum emerges as an approximation at macroscopic scales. Lorentz Invariant discreteness can have consequences that can be observed at low energies. In this work, we search for signatures of causal set predictions. Causal Set Theory predicts that the cosmological constant $\Lambda$ is Everpresent and fluctuates between positive and negative values. This Cosmological model, a stochastic function of cosmic time that varies from one realization to another, generates a space of histories of dark energy. Via Monte Carlo Markov chains we search the space of histories of dark energy to find the best fit to Cosmic Microwave Background (CMB) data, Big Bang Nucleosynthesis (BBN) data and Baryon acoustic oscillations (BAO) data. The model fits the current cosmological observations well and eases the tension that standard $\Lambda$CDM has at high redshift. Causal Set Theory also predicts that a particle propagating on a causal set will undergo diffusion in momentum space. For massive particles, the diffusion process has only one parameter, the diffusion constant. For massless particles this process has two parameters $-$ the diffusion constant and the drift parameter. These parameters depend on the non-locality scale of the theory. Simulations were run to find the relation between these parameters and the non-locality scale. There by using bounds on the diffusion constant, we set bounds on the non-locality scale.
Dark Matter and Neutrinos in the Foggy Universe
(University of Waterloo, 2019-01-07) Okoli, Chiamaka; Afshordi, Niayesh; Taylor, James
Dark matter is predicted to be the main contribution to the matter content in the universe, in addition to ordinary baryonic matter such as protons and neutrons. However, we are limited in our knowledge of the nature of this main content of matter and some of its characteristics, hence the term "the Foggy Universe". The majority of the work included in this thesis is related to dark matter. It includes an investigation of the characteristics of dark matter haloes -- structures expected to hold the galaxies/clusters -- and a proposal to effectively search for dark matter particles through dark matter annihilation products such as gamma rays. In the last part of the thesis, we include a novel large-scale effect of cosmological neutrinos on haloes in the universe that is dependent on the neutrino mass. In more detail, this thesis is a collection of the contributions we made to cosmological research regarding the nature of dark matter. Motivated by the non-existence of halo concentrations for small mass haloes due to the poor mass resolution of N-body simulations, we propose and verify the agreement of an analytical mass-concentration model using the ellipsoidal collapse theory and assuming the conservation of total energy. Thereafter, and guided by the success of this prediction, we use this model to make analytical calculations that may be relevant for the indirect detection of dark matter particles using gamma-rays as by-products of dark matter annihilation. We consider noise estimates to include the expected gamma rays due to the formation of stars in the galaxies hosted by these haloes and the presence of the isotropic gamma-ray background to predict a signal-to-noise ratio as a function of halo mass in a bid to pinpoint the most interesting halo masses that should be good targets for this detection. Given that neutrinos are the second most abundant particle in the universe after the photons, we finish off by quantifying the effect of dynamical friction from primordial neutrinos that may slow down haloes and presented how this effect may be extracted from galaxy surveys using different galaxy species in redshift space. Although independent of the number density of galaxies in the survey, the confidence level of this proposed detection is dependent on the survey properties -- such as the number of galaxies, mean redshift of the survey -- and the neutrino properties such as the mass and hierarchy of the species and could be greater than $3 \sigma$ using an optimal survey.
Entanglement Entropy of Scalar Fields in Causal Set Theory
(University of Waterloo, 2017-08-15) Kouchekzadeh Yazdi, Yasaman; Afshordi, Niayesh; Sorkin, Rafael
Entanglement entropy is now widely accepted as having deep connections with quantum gravity. It is therefore desirable to understand it in the context of causal sets, especially since they provide the UV cutoff needed to render entanglement entropy finite in a natural and covariant manner. Defining entropy in a causal set is not straightforward because the type of canonical hypersurface-data on which definitions of entanglement typically rely is not available in a causal set. Instead, we appeal to a more global expression given in [1] which, for a gaussian scalar field, expresses the entropy of a spacetime region in terms of the field’s correlation function within that region. We first consider this spacetime entropy for a 1+1-dimensional "causal diamond" in a flat continuous spacetime immersed in the vacuum within a larger causal diamond (our choice of vacuum being the Sorkin-Johnston vacuum described more fully in Chapter 2). The spacetime entropy of the smaller diamond in this case measures (when interpreted spatially) the entanglement between a line-segment and its complement within a larger line-segment. In this situation we carry out the computation numerically for a massless scalar field. The required ultraviolet cutoff is implemented as a truncation on spacetime mode sums, and we find excellent agreement with the expected form of the entropy (i.e. an area law) from conformal field theory. Carrying this formula over to a causal set, one obtains an entanglement entropy which is finite with a natural UV cutoff and Lorentz invariant. Herein we evaluate this entropy for causal sets sprinkled into a 1+1-dimensional causal diamond in flat spacetime, and specifically for a smaller order-interval (causal diamond) within a larger concentric one. We find in the first instance an entropy that obeys a (spacetime) volume law instead of the expected (spatial) area law. We find, however, that one can obtain the expected area law by following a prescription for truncating the eigenvalues of a certain "Pauli-Jordan" operator and the projections of their eigenfunctions on the Wightman function that enters into the entropy formula. We also study the "entropy of coarse-graining" generated by thinning out the causal set, and we compare it with what one obtains by similarly thinning out a chain of harmonic oscillators, finding the same "universal" behaviour in both cases.
Neutron Stars, the Exotica - From Modifying General Relativity to Strong Magnetic Fields
(University of Waterloo, 2015-12-22) Kamiab, Farbod; Afshordi, Niayesh
The gravitational aether theory is a modification of General Relativity that decouples vacuum energy from gravity, and thus can potentially address the cosmological constant problem. The classical theory is distinguishable from General Relativity only in the presence of relativistic pressure (or vorticity). Since the interior of neutron stars has high pressure and as their mass and radius can be measured observationally, they are the perfect laboratory for testing the validity of the aether theory. In this thesis, we first solve the hydrostatic equations of stellar structure for the gravitational aether theory and find the predicted mass-radius relation of nonrotating neutron stars using two different realistic proposals for the equation of state of nuclear matter. We find that the maximum neutron-star mass predicted by the aether theory is 12%-16% less than the maximum mass predicted by general relativity assuming these two equations of state. We then study the dynamics of a neutron star in the aether theory and establish that a Cauchy problem can be defined. We derive the dynamical equations, and through analyzing them, we find two modes, one of which is well-posed (expansion of matter in the aether frame) and the other is not well-posed (collapse of matter in the aether frame). Starting from a hydrostatic neutron star configuration that we perturb by adding extrinsic curvature (and radial velocity), we numerically evolve the Einstein field equations for the aether theory in the well-posed mode and find that it evolves towards the not well-posed regime. This feature may pose a serious challenge to our initial value formulation of the aether theory. Whether an alternative formulation can handle the collapsing neutron stars is a question of utmost importance for the viability of the aether theory. It has been clear for some time now that super-critical surface magnetic fields, exceeding 4 × 10^13 G, exist on a subset of neutron stars. These magnetars may harbor interior fields many orders of magnitude larger, potentially reaching equipartition values. However, the impact of these strong fields on stellar structure has been largely ignored, potentially complicating attempts to infer the high density nuclear equation of state. In this thesis, we assess the effect of these strong magnetic fields on the mass-radius relationship of neutron stars. We employ an effective field theory model for the nuclear equation of state that includes the impact of hyperons, anomalous magnetic moments, and the physics of the crust. We consider two magnetic field geometries, bounding the likely magnitude of the impact of magnetic fields: a statistically isotropic, tangled field and a force-free configuration. In both cases even equipartition fields have at most a 30% impact on the maximum mass. However, the direction of the effect of the magnetic field depends on the geometry employed - force-free fields leading to reductions in the maximum neutron star mass and radius while tangled fields increase both - challenging the common intuition in the literature on the impact of magnetic fields.
New Views on the Cosmological Big Bang
(University of Waterloo, 2017-09-20) Gould, Elizabeth; Afshordi, Niayesh
This dissertation is a collection of four different proposals to describe the early universe. Each will draw from insights of different areas of physics to suggest a description which differs from the standard inflationary paradigm. First we start with holographic cosmology in which cosmological predictions of the very early Universe are expressed in terms of the observables of a three dimensional quantum field theory (QFT). This framework includes conventional slow-roll inflation, which is described in terms of a strongly coupled QFT, but it also allows for qualitatively new models for the very early Universe, where the dual QFT may be weakly coupled. The new models describe a universe which is non-geometric at early times. While standard slow-roll inflation leads to a (near-)power-law primordial power spectrum, perturbative superrenormalizable QFT’s yield a new holographic spectral shape. Here, we compare the two predictions against cosmological observations. We use CosmoMC to determine the best fit parameters, and MultiNest for Bayesian Evidence, comparing the likelihoods. We find that the dual QFT should be non-perturbative at the very low multipoles (l ≲ 30), while for higher multipoles (l ≳ 30) the new holographic model, based on perturbative QFT, fits the data just as well as the standard power-law spectrum assumed in ΛCDM cosmology. This finding opens the door to applications of non-perturbative QFT techniques, such as lattice simulations, to observational cosmology on gigaparsec scales and beyond. We then turn to the suggestion that the universe repeats in cycles, with an infinite series of similar cycles in the past and the future. Here, we instead propose that the cosmic history repeats itself exactly, constructing a universe on a periodic temporal history, which we call periodic time cosmology. In particular, the primordial power spectrum, convolved with the transfer function throughout the cosmic history, would form the next cycle’s primordial power spectrum. By matching the big bang to the infinite future using a conformal rescaling (a la Penrose), we uniquely determine the primordial power spectrum, in terms of the transfer function up to two free parameters. While nearly scale invariant with a red tilt, using Planck and Baryonic Acoustic Oscillation observations, we find the minimal model is disfavoured compared to a power-law power spectrum at 5.1σ. However, extensions of ΛCDM cosmic history change the large scale transfer function and can provide better relative fits to the data. For example, the best fit seven parameter model for our Periodic Time Cosmology, with w = −1.024 for dark energy equation of state, is only disfavoured relative to a power-law power spectrum at 1.8σ level. Therefore, consistency between cosmic history and initial conditions provides a viable description of cosmological observations in the context of Periodic Time Cosmology. Next, we discuss the 5D holographic big bang model, a novel model for the emergence of the early universe out of a 5D collapsing star (an apparent white hole), in the context of Dvali-Gabadadze-Porrati (DGP) cosmology. The model does not have a big bang singularity, and yet can address cosmological puzzles that are traditionally solved within inflationary cosmology. We compute the exact power spectrum of cosmological curvature perturbations due to the effect of a thin atmosphere accreting into our 3-brane. The spectrum is scale-invariant on small scales and red on intermediate scales, but becomes blue on scales larger than the height of the atmosphere. While this behaviour is broadly consistent with the non-parametric measurements of the primordial scalar power spectrum, it is marginally disfavoured relative to a simple power law (at 2.7σ level). Furthermore, we find that the best fit nucleation temperature of our 3-brane is at least 3 orders of magnitude larger than the 5D Planck mass, suggesting an origin in a 5D quantum gravity phase. Finally, we turn to the status of locality in quantum mechanics. Motivations for violations of the notion of relativistic locality include the Bell’s inequalities for hidden variable theories, the cosmological horizon problem, and Lorentz-violating approaches to quantum geometrodynamics, such as Horava-Lifshitz gravity. We explore a proposal for a “real ensemble” non-local description of quantum mechanics, in which “particles” can copy each others’ observable values AND phases, independent of their spatial separation. We first specify the exact theory, ensuring that it is consistent and has (ordinary) quantum mechanics as a fixed point, where all particles with the same values for a given observable have the same phases. We then study the stability of this fixed point numerically, and analytically, for simple models. We provide evidence that most systems (in our study) are locally stable to small deviations from quantum mechanics, and furthermore, the phase variance per value of the observable, as well as systematic deviations from quantum mechanics, decay as ∼ (Energy×Time)^(−2n) , where n ≥ 1. Interestingly, this convergence is controlled by the absolute value of energy (and not energy difference), suggesting a possible connection to gravitational physics. Finally, we discuss different issues related to this theory, as well as potential novel applications for the spectrum of primordial cosmological perturbations and the cosmological constant problem.
On the Initial Boundary Value Problem in Numerical Relativity
(University of Waterloo, 2025-01-23) Dailey, Conner; Afshordi, Niayesh; Schnetter, Erik
The principal goal of this thesis is to properly understand, characterize, and numerically implement initial boundary value problems in numerical relativity. Throughout the history of solving Einstein's field equations on computers, boundaries have been mostly dealt with in an approximate way. For example, boundaries might be placed far away from strongly gravitating sources, where approximations like linearized gravity are valid. It has become necessary however to place boundaries in the strong gravity regime of a dynamical spacetime to model complicated and interesting physics, which necessitates a complete understanding of the initial boundary value problem of Einstein's field equations. One motivation for this comes from a need to simulate black hole echoes. In classical general relativity, black holes are perfectly absorbing objects, where the mass of radially incoming wavepackets of matter or gravitational waves is absorbed by the black hole. Thus conclusive evidence of modifications to general relativity, such as quantum gravity, could include partial reflections of radially incoming wavepackets, called black hole echoes. To properly understand the modifications this would bring to detectable gravitational wave signals, we require simulations where reflecting boundary conditions are imposed close to the horizon of a black hole. Another motivation comes from recent advances in Cauchy characteristic matching, which combines state of the art numerical techniques to obtain physically accurate gravitational waveforms from simulations. This can allow numerical relativists to dramatically save on the computational cost of black hole merger simulations, but only if boundaries can be placed in the strong gravity regime. This thesis presents advances in simulating initial boundary value problems in numerical relativity. Starting with spherical symmetry, a framework for reflecting a scalar field in a fully dynamical spacetime is developed and implemented numerically using the Einstein-Christoffel formulation. The evolution of a wave packet and its numerical convergence, including when the location of a reflecting boundary is very close to the horizon of a black hole, is studied. Next, this approach is generalized to spacetimes with no symmetries and implemented numerically using the generalized harmonic formulation. The evolution equations are cast into a summation by parts scheme, which seats the numerical method closer to a class of provably numerically stable systems. State of the art numerical methods are demonstrated, including an embedded boundary numerical method that allows for arbitrarily shaped domains on a rectangular grid and even boundaries that evolve and move across the grid. As a demonstration of these frameworks, the evolution of gravitational wave scattering off of a boundary either inside or just outside the horizon of a black hole, is studied. Finally, a boundary condition framework designed to control quasi-local energy flux is proposed motivated by examples from electromagnetism.
Probing Dark Matter from the Galaxy to the Cosmic Web
(University of Waterloo, 2020-01-23) Yang, Tianyi; Hudson, Michael; Afshordi, Niayesh
Dark matter, although invisible, accounts for the majority of matter of the universe. How this invisible component affects cosmic structure formation is one of the primary lines of inquiry in physical cosmology, and the key to understanding its nature. In this thesis, we present two methods to probe dark matter from the Milky Way to the filaments of the cosmic web. In the first part of this thesis, we demonstrate how to use stellar clustering in action space to probe the underlying gravitational potential of the Milky Way's dark matter halo. Provided that the correct potential is used for the system, integrals of motion such as action variables of small structures (for instance the tidal streams surrounding the galaxy) are conserved during galaxy formation and evolution. If the incorrect potential is applied, action variables will not be conserved, weakening the small-scale clustering in the action space. Conversely, the correct potential is expected to maximize small-scale clustering in action space. After justifying the viability of this idea using simulations, we apply this method to the 2nd data release from Gaia mission, and use it to measure the fraction that the halo contributes to the total centrifugal force at solar position, f_h, and logarithmic slope, α, of a power-law dark matter halo profile. We use stars within 9-11 kpc and 11.5-15 kpc from Galactic centre, and find the power-law potential, which is parametrized by f_h and α, is (f_h, α)= (0.391±0.009, 1.835±0.092) and (0.351± 0.012,1.687± 0.079) respectively. We then use the best-fit potential to compute the total circular velocity of the Milky Way within R = 9-15 kpc. The resulting circular velocity curve is consistent with past measurements (although it is ~ 5-10% lower than previous methods based on masers or globular clusters). To our knowledge, this is the first study that applies this methodology to real data. Furthermore, by constraining the Milky Way potential, our result indirectly shows the existence of dark matter halo around Milky Way. On cosmological scales, massive dark matter halos are expected to be connected by bridges, known as filaments. Like other large scale structures in our universe, filaments are expected to be dominated by dark matter, making them hard to detect. But are these filaments any darker than other structures, such as voids, clusters and galaxies? In the second part of this thesis, we investigate how ``bright'' these dark filaments are, which can be characterized by their mass-to-light, or M/L ratios. We first estimate the mass of these dark filaments via weak gravitational lensing: stacking and analyzing the weak lensing signals between Luminous Red Galaxy (LRG) pairs selected from SDSS III BOSS survey. Using the CFHTLens shape measurements, we measure the mass of filaments at a significance level of 4.5σ. To isolate the filament signal, a catalogue of non-physical projected pairs is constructed. Then, we investigate the average luminosity level of filaments by subtracting the stacked non-physical pairs from the stacked LRG pairs selected from the BOSS survey. We fit a Schechter function over the observed excess galaxy number in filaments, and so, compute the total luminosity in SDSS r and g band. Then, we calculate the mass-to-light ratio, M/L, and the colour (g-r). To investigate the redshift dependence of these parameters, the above analyses are conducted in two independent redshift samples (LOWZ and CMASS as divided by BOSS survey). We find M/L = 309±94, (g-r) = 0.59±0.24 for LOWZ sample, and M/L = 435±189, (g-r) = 0.38±0.45 for CMASS sample. If we combine both samples, we find M/L = 351±87, (g-r) = 0.51±0.22. Due to the uncertainties, we find no significant redshift dependence of these parameters. Our study provides the first measurement of the mass-to-light ratios of filaments of the cosmic web, showing that they are comparable to the cosmic mean value.
Probing the dark universe with gravitational lensing
(University of Waterloo, 2018-09-17) Karami, Mansour; Afshordi, Niayesh; Broderick, Avery
Since its early success as an experimental test of the theory of general relativity in 1919, gravitational lensing has come a long way and is firmly established as an indispensable element for many astrophysical applications. In this thesis, we explore novel applications of gravitational lensing that further our understanding of the dark sectors of the cosmos and other astrophysical objects, namely dark matter nanostructure, black holes and the Galactic disk. We pay particular attention to developing concrete and optimal statistical methodologies and numerical implemen- tations for these novel probes. We start by developing a statistical framework to measure the dark matter power spectrum in the deep nonlinear regime, using transient weak lensing, and simultaneously measure the time delays for strongly lensed quasars. We then outline how observations of microlensing in optical and radio can unravel the structure, dynamics, and content of the Galactic disk, and in particular, be used to detect stellar mass black holes. Lastly, using the shadow images of the super-massive black holes caused by extreme lensing effect, we can learn about the structure of space-time, accretion flows and astrophysical jets. We present a Bayesian framework for analyzing the data from the Event Horizon Telescope Collaboration.
The quantum and the gravity: Newtonian and Cosmological applications
(University of Waterloo, 2018-07-18) Altamirano, Natacha; Mann, Robert; Afshordi, Niayesh
The gravitational decoherence field studies the suppression of coherence in quantum systems caused by effects rooted in the gravitational interaction. This models are not just important to yield interesting ideas about the search, in regimes others than the Planck scale, for the interplay between quantum mechanics and general relativity, but also from a theoretical point of view. The fact that the gravitational field can not be shielded opens the question of how strong will the gravitational ‘environment’ decohere a quantum system? and if this decoherence can somehow explain the absence of macroscopical super- positions? This thesis studies in depth the ‘Classical Channel Gravity’ (CCG) model, a recent proposal of gravitational decoherence that assumes that the gravitational interac- tion is always accompanied with an intrinsic decoherence mechanism which ensures that there is no transmission of quantum information between the parties involved. This model can be understood a series of weak continuous quantum measurements accompanied with a feedback term produced by some underlying hidden gravitational degrees of freedom. We first study all the possible emergent dynamics from collisional Markovian dynamics; these ones range from exact unitary to arbitrary fast decoherence (Zeno effect). The second part of the thesis is devoted to study the Newtonian and post Newtonian limits of the CCG model, with particular focus on the testability features of CCG. In particular, we apply this model to coupled clocks and find that the amount of decoherence predicted by CCG is the same as the decoherence that an ‘environment of clocks’ will imprint in a single clock in the context of unitary evolution. On the other hand, we find that this effect is far from being detectable with the current achieved time accuracy. However, CCG as a model for multi partite systems and two systems with very different masses seems to yield an amount of decoherence that is not only able to be detectable with current experiments but also seems to indicate that this model is ruled out. Nevertheless, we also mention potential caveats with our assumptions and discuss other physically motivated directions to further study this result. Finally, we also explore the extension of CCG for the cosmological scenario. In this context the scale factor is being decohered by test particles ‘sitting’ on spacetime. We find that this decoherence will be seen by an observer unaware of the CCG fundamental mechanism as an emergent form of dark energy filling the universe.
Quantum Aspects of Black Holes: From Microstates to Echoes and Somewhere In-Between
(University of Waterloo, 2023-05-23) Saraswat, Krishan; Afshordi, Niayesh
In this thesis we explore quantum aspects of black holes from a variety of perspectives. In part I of this thesis we are motivated by the black hole information paradox to explore the idea of gravitational wave echoes from the perspective of black hole microstate statistics. We adopt the idea that a UV complete description of a black hole should involve exp(S) microstates in a thermal ensemble, where S = A/4G , is the Bekenstein Hawking entropy of the black hole. Furthermore, we take the stance that issues about the existence of echoes and black hole microstructure might be understood in terms of thermal correlators in the ensemble of microstates. We make use of the spectral form factor as a proxy for a thermal 2-point correlator calculation. We study how spacing statistics between microstates affects the thermalization behaviour of the black hole at late and early times. We find “echoes” in cases where there is substantial eigenvalue repulsion between individual microstates or if there are regularly spaced clusters of microstates. In part II of the thesis we analyze the process of information recovery and unitarity in black hole/gravity systems coupled to non-gravitational baths. In the first work of part II we study how the evaporation rate of a black hole changes when radiation is extracted near the horizon and apply our results to study how long it takes to recover information thrown into a black hole after the Page time. In the last work of part II we study entanglement wedge nesting in 3D AdS spacetimes cut off by an end-of-the-world brane. Finally, in part III we summarize the main results of the research works.
Quantum Black Holes in the Sky
(University of Waterloo, 2020-09-30) Wang, Qingwen; Afshordi, Niayesh
Black Holes are possibly the most enigmatic objects in our Universe. From their detection in gravitational waves upon their mergers, to their snapshot eating at the centres of galaxies, black hole astrophysics has undergone an observational renaissance in the past 4 years. Nevertheless, they remain active playgrounds for strong gravity and quantum effects, where novel aspects of the elusive theory of quantum gravity may be hard at work. In this thesis, we provide an overview of the strong motivations for why ''Quantum Black Holes'' may be radically different from their classical counterparts in Einstein’s General Relativity. We then discuss the observational signatures of quantum black holes, focusing on gravitational wave echoes as smoking guns for quantum horizons (or exotic compact objects), which have led to significant recent excitement and activity. We review the theoretical underpinning of gravitational wave echoes and build up realistic templates for further data analysis. Finally, we discuss the future theoretical and observational landscape for unraveling the ''Quantum Black Holes in the Sky''.
Quantum Information across Spacetime: From Gravitational Waves to Spinning Black Holes
(University of Waterloo, 2021-08-20) Robbins, Matthew; Mann, Robert; Afshordi, Niayesh
This thesis is split into two parts. In the first part, we investigate Bose-Einstein condensates (BECs) as a means to detect gravitational waves. For the detection of continuous gravitational waves, we study its sensitivity with initially-squeezed phonons by optimizing the properties of the condensate and the measurement duration. We show that this method of detecting gravitational waves in the kilohertz regime is limited by current experimental techniques in squeezing BEC phonons. Without focusing on a specific detector setup, our study shows that substantive future improvements in technology (e.g., increasing the squeezing of BEC states or their physical size) will be necessary for such a detector to be competitive in measuring gravitational waves of astrophysical and/or cosmological origin. We then consider a modulating speed of sound of the BEC trap, whose frequency matches that of an incoming continuous gravitational wave. The trap modulation induces parametric resonance in the BEC, which in turn enhances sensitivity of the BEC to gravitational waves. We find that such a BEC detector could potentially be used to detect gravitational waves across several orders of magnitude in frequency, with the sensitivity depending on the speed of sound, size of the condensate, and frequency of the phonons. We estimate the sensitivity such an experiment would have to gravitational waves and discuss the current technological limitations. We also comment on the potential noise sources as well as what is necessary for such a detector to become feasible. In the second part of this thesis, we turn our attention to Unruh-DeWitt detectors (a two-level quantum system) and rotating Bañados-Teitelboim-Zanelli (BTZ) black holes. In both flat and curved spacetimes, there are weak and strong versions of the anti-Unruh/anti-Hawking effects, relating the detector response, Kubo-Martin-Schwinger (KMS) temperature of the background scalar field, and the temperature given by the Excitation to De-excitation Ratio (EDR) of the detector. We first investigate the effect of rotation on the weak and strong anti-Hawking effects for an Unruh-DeWitt detector orbiting a BTZ black hole in the co-rotating frame. We will show that rotation amplifies the strength of the weak anti-Hawking effect while simultaneously being boundary condition dependent for whether it amplifies or reduces the strength of the strong anti-Hawking effect. There is also a non-monotonic relationship for the strong anti-Hawking effect between the EDR temperature and the angular momentum of the black hole. In addition, we note that the weak anti-Hawking effect is independent of a changing anti-de Sitter (AdS) length, while a longer AdS length increases the temperature range of the strong anti-Hawking effect. We then consider two detectors orbiting a BTZ black hole and show that such correlations – vacuum entanglement – in the environment of near-extremal black holes is significantly amplified (up to 10-fold) relative to their slowly rotating counterparts. We demonstrate this effect by calculating the entanglement between the detectors through the concurrence extracted from the vacuum. The effect is manifest at intermediate distances from the horizon, and is most pronounced for near-extremal small mass black holes. The effect is also robust, holding for all boundary conditions of the field and at large spacelike detector separations. Smaller amplification occurs near the horizon, where we find that the entanglement shadow – a region near the black hole from which entanglement cannot be extracted – is diminished in size as the black hole’s angular momentum increases.
Studying the largest scales in the Universe with the kinetic Sunyaev-Zel'dovich effect
(University of Waterloo, 2022-01-19) Cayuso, Juan; Johnson, Matthew; Afshordi, Niayesh
As we progress further into the era of precision cosmology, new avenues to test our fundamental models of the Universe are opening up. This Ph.D. thesis is concerned with the development and understanding of a technique known as kinetic Sunyaev-Zel'dovich (kSZ) velocity reconstruction, which aims to extract information about the Universe on the largest accessible scales using measurements of the Cosmic Microwave Background (CMB) anisotropies sourced by the kSZ effect and data from galaxy redshift surveys. kSZ velocity reconstruction estimates the remote CMB dipole, i.e. the l=1 multipole moment of the observed CMB sky as seen by observers on our past lightcone. This observable probes cosmological perturbations on scales of several Gpc, and thus has the potential to be a valuable source of information on the fundamental early Universe phenomena that leaves imprints on such scales. Preliminary forecasts from the foundational literature on kSZ velocity reconstruction indicate that high signal to noise reconstructions of the remote dipole will be possible in the context of next generation CMB experiments and galaxy surveys. The goal of this thesis is to further develop the technical details of the technique and provide motivation for its use as a tool to probe physics on ultra-large scales. Chapter 1 elaborates on the motivation behind this thesis and provides a review of the key material necessary to understand kSZ velocity reconstruction. Chapter 2 presents an extended formalism for kSZ velocity reconstruction, which describes new sources of noise and bias and incorporates more realistic experimental conditions. Forecasts for the reconstruction of the remote dipole are presented in the same chapter, and these show that high signal to noise is still achievable using the new estimators. Chapter 3 presents the first suite of N-body simulations of remote dipole reconstruction on our past lightcone, which implement a novel methodology to treat the wide range of scales involved in kSZ velocity reconstruction (tens of Mpc to tens of Gpc). These simulations were used to test the robustness of the reconstruction technique against the effects of gravitational non-linearities, redshift space distortions, and CMB lensing. Additionally, these simulations were used to demonstrate the relevance of large scale contributions to the remote dipole that are not captured by other approaches to kSZ velocity reconstruction. Chapter 4 presents an analysis of parameter constraints on CMB anomalies models, aimed to demonstrate that the reconstructed remote CMB dipole and the reconstructed remote CMB quadrupole (obtained using a similar technique to kSZ velocity reconstruction) can help us go beyond the constraints achievable with traditional probes of the anomalies like the primary CMB temperature, primary CMB polarization, and large-scale galaxy distribution.
Unifying Thermal Big Bang and Black Holes
(University of Waterloo, 2020-09-30) Hergott, Samantha; Afshordi, Niayesh
Theories that stand the test of constant bombardment of new (and old) ideas, observations and unexplained phenomena are hard to come by. Despite countless attempts over many years of trying, cosmology and gravitational theories are of those lacking in a full unified description. A tachyacoustic model of the thermal big bang has been proposed which has a remarkable prediction for the scalar index parameter of primordial fluctuations. In this work we provide a brief review of the motivations leading up to this tachyacoustice big bang model as well as review problems with dark energy and quantum black holes and proposed solutions. In this thesis, we tie these ideas together by finding black hole solutions of the underlying tachyacoustic theory. This also leads to an explanation for current cosmic acceleration, resulting in a three-in-one unified potential model of big bang, black holes, and dark energy.

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