The simplest ΛCDM model provides a good fit to a large span of cosmological data but harbors large areas of phenomenology and ignorance. With the improvement of the number and the accuracy of observations, discrepancies among key cosmological parameters of the model have emerged. The most statistically significant tension is the 4σ to 6σ disagreement between predictions of the Hubble constant, H0, made by the early time probes in concert with the 'vanilla' ΛCDM cosmological model, and a number of late time, model-independent determinations of H0 from local measurements of distances and redshifts. The high precision and consistency of the data at both ends present strong challenges to the possible solution space and demands a hypothesis with enough rigor to explain multiple observations—whether these invoke new physics, unexpected large-scale structures or multiple, unrelated errors. A thorough review of the problem including a discussion of recent Hubble constant estimates and a summary of the proposed theoretical solutions is presented here. We include more than 1000 references, indicating that the interest in this area has grown considerably just during the last few years. We classify the many proposals to resolve the tension in these categories: early dark energy, late dark energy, dark energy models with 6 degrees of freedom and their extensions, models with extra relativistic degrees of freedom, models with extra interactions, unified cosmologies, modified gravity, inflationary models, modified recombination history, physics of the critical phenomena, and alternative proposals. Some are formally successful, improving the fit to the data in light of their additional degrees of freedom, restoring agreement within 1–2σ between Planck 2018, using the cosmic microwave background power spectra data, baryon acoustic oscillations, Pantheon SN data, and R20, the latest SH0ES Team Riess, et al (2021 Astrophys. J.908 L6) measurement of the Hubble constant (H0 = 73.2 ± 1.3 km s−1 Mpc−1 at 68% confidence level). However, there are many more unsuccessful models which leave the discrepancy well above the 3σ disagreement level. In many cases, reduced tension comes not simply from a change in the value of H0 but also due to an increase in its uncertainty due to degeneracy with additional physics, complicating the picture and pointing to the need for additional probes. While no specific proposal makes a strong case for being highly likely or far better than all others, solutions involving early or dynamical dark energy, neutrino interactions, interacting cosmologies, primordial magnetic fields, and modified gravity provide the best options until a better alternative comes along.
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Classical and Quantum Gravity is an established journal for physicists, mathematicians and cosmologists in the fields of gravitation and the theory of spacetime. The journal is now the acknowledged world leader in classical relativity and all areas of quantum gravity.
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Eleonora Di Valentino et al 2021 Class. Quantum Grav. 38 153001
Oliver James et al 2015 Class. Quantum Grav. 32 065001
Interstellar is the first Hollywood movie to attempt depicting a black hole as it would actually be seen by somebody nearby. For this, our team at Double Negative Visual Effects, in collaboration with physicist Kip Thorne, developed a code called Double Negative Gravitational Renderer (DNGR) to solve the equations for ray-bundle (light-beam) propagation through the curved spacetime of a spinning (Kerr) black hole, and to render IMAX-quality, rapidly changing images. Our ray-bundle techniques were crucial for achieving IMAX-quality smoothness without flickering; and they differ from physicists' image-generation techniques (which generally rely on individual light rays rather than ray bundles), and also differ from techniques previously used in the film industry's CGI community. This paper has four purposes: (i) to describe DNGR for physicists and CGI practitioners, who may find interesting and useful some of our unconventional techniques. (ii) To present the equations we use, when the camera is in arbitrary motion at an arbitrary location near a Kerr black hole, for mapping light sources to camera images via elliptical ray bundles. (iii) To describe new insights, from DNGR, into gravitational lensing when the camera is near the spinning black hole, rather than far away as in almost all prior studies; we focus on the shapes, sizes and influence of caustics and critical curves, the creation and annihilation of stellar images, the pattern of multiple images, and the influence of almost-trapped light rays, and we find similar results to the more familiar case of a camera far from the hole. (iv) To describe how the images of the black hole Gargantua and its accretion disk, in the movie Interstellar, were generated with DNGR—including, especially, the influences of (a) colour changes due to doppler and gravitational frequency shifts, (b) intensity changes due to the frequency shifts, (c) simulated camera lens flare, and (d) decisions that the film makers made about these influences and about the Gargantua's spin, with the goal of producing images understandable for a mass audience. There are no new astrophysical insights in this accretion-disk section of the paper, but disk novices may find it pedagogically interesting, and movie buffs may find its discussions of Interstellar interesting.
Germain Tobar and Fabio Costa 2020 Class. Quantum Grav. 37 205011
The theory of general relativity predicts the existence of closed time-like curves (CTCs), which theoretically would allow an observer to travel back in time and interact with their past self. This raises the question of whether this could create a grandfather paradox, in which the observer interacts in such a way to prevent their own time travel. Previous research has proposed a framework for deterministic, reversible, dynamics compatible with non-trivial time travel, where observers in distinct regions of spacetime can perform arbitrary local operations with no contradiction arising. However, only scenarios with up to three regions have been fully characterised, revealing only one type of process where the observers can verify to both be in the past and future of each other. Here we extend this characterisation to an arbitrary number of regions and find that there exist several inequivalent processes that can only arise due to non-trivial time travel. This supports the view that complex dynamics is possible in the presence of CTCs, compatible with free choice of local operations and free of inconsistencies.
Leonardo Abbrescia and Jared Speck 2023 Class. Quantum Grav. 40 243001
In this article, we provide notes that complement the lectures on the relativistic Euler equations and shocks that were given by the second author at the program Mathematical Perspectives of Gravitation Beyond the Vacuum Regime, which was hosted by the Erwin Schrödinger International Institute for Mathematics and Physics in Vienna in February 2022. We set the stage by introducing a standard first-order formulation of the relativistic Euler equations and providing a brief overview of local well-posedness in Sobolev spaces. Then, using Riemann invariants, we provide the first detailed construction of a localized subset of the maximal globally hyperbolic developments of an open set of initially smooth, shock-forming isentropic solutions in 1D, with a focus on describing the singular boundary and the Cauchy horizon that emerges from the singularity. Next, we provide an overview of the new second-order formulation of the 3D relativistic Euler equations derived in Disconzi and Speck (2019 Ann. Henri Poincare20 2173–270), its rich geometric and analytic structures, their implications for the mathematical theory of shock waves, and their connection to the setup we use in our 1D analysis of shocks. We then highlight some key prior results on the study of shock formation and related problems. Furthermore, we provide an overview of how the formulation of the flow derived in Disconzi and Speck (2019 Ann. Henri Poincare20 2173–270) can be used to study shock formation in multiple spatial dimensions. Finally, we discuss various open problems tied to shocks.
B P Abbott et al 2020 Class. Quantum Grav. 37 055002
The LIGO Scientific Collaboration and the Virgo Collaboration have cataloged eleven confidently detected gravitational-wave events during the first two observing runs of the advanced detector era. All eleven events were consistent with being from well-modeled mergers between compact stellar-mass objects: black holes or neutron stars. The data around the time of each of these events have been made publicly available through the gravitational-wave open science center. The entirety of the gravitational-wave strain data from the first and second observing runs have also now been made publicly available. There is considerable interest among the broad scientific community in understanding the data and methods used in the analyses. In this paper, we provide an overview of the detector noise properties and the data analysis techniques used to detect gravitational-wave signals and infer the source properties. We describe some of the checks that are performed to validate the analyses and results from the observations of gravitational-wave events. We also address concerns that have been raised about various properties of LIGO–Virgo detector noise and the correctness of our analyses as applied to the resulting data.
Andrzej Dragan et al 2023 Class. Quantum Grav. 40 025013
We develop an extension of special relativity in dimensional spacetime to account for superluminal inertial observers and show that such an extension rules out the conventional dynamics of mechanical point-like particles and forces one to use a field-theoretic framework. Therefore we show that field theory can be viewed as a direct consequence of extended special relativity.
Pedro G S Fernandes et al 2022 Class. Quantum Grav. 39 063001
We review the topic of 4D Einstein–Gauss–Bonnet (4DEGB) gravity, which has been the subject of considerable interest over the past two years. Our review begins with a general introduction to Lovelock's theorem, and the subject of Gauss–Bonnet terms in the action for gravity. These areas are of fundamental importance for understanding modified theories of gravity, and inform our subsequent discussion of recent attempts to include the effects of a Gauss–Bonnet term in four space–time dimensions by re-scaling the appropriate coupling parameter. We discuss the mathematical complexities involved in implementing this idea, and review recent attempts at constructing well-defined, self-consistent theories that enact it. We then move on to consider the gravitational physics that results from these theories, in the context of black holes, cosmology, and weak-field gravity. We show that 4DEGB gravity exhibits a number of interesting phenomena in each of these areas.
Lucas Lombriser 2023 Class. Quantum Grav. 40 155005
Theoretical and observational challenges to standard cosmology such as the cosmological constant problem and tensions between cosmological model parameters inferred from different observations motivate the development and search of new physics. A less radical approach to venturing beyond the standard model is the simple mathematical reformulation of our theoretical frameworks underlying it. While leaving physical measurements unaffected, this can offer a reinterpretation and even solutions of these problems. In this spirit, metric transformations are performed here that cast our Universe into different geometries. Of particular interest thereby is the formulation of cosmology in Minkowski space. Rather than an expansion of space, spatial curvature, and small-scale inhomogeneities and anisotropies, this frame exhibits a variation of mass, length and time scales across spacetime. Alternatively, this may be interpreted as an evolution of fundamental constants. As applications of this reframed cosmological picture, the naturalness of the cosmological constant is reinspected and promising candidates of geometric origin are explored for dark matter, dark energy, inflation and baryogenesis. An immediate observation thereby is the apparent absence of the cosmological constant problem in the Minkowski frame. The formalism is also applied to identify new observable signatures of conformal inhomogeneities, which have been proposed as simultaneous solution of the observational tensions in the Hubble constant, the amplitude of matter fluctuations, and the gravitational lensing amplitude of cosmic microwave background anisotropies. These are found to enhance redshifts to distant galaxy clusters and introduce a mass bias with cluster masses inferred from gravitational lensing exceeding those inferred kinematically or dynamically.
Martin Bojowald and Erick I Duque 2024 Class. Quantum Grav. 41 095008
A complete canonical formulation of general covariance makes it possible to construct new modified theories of gravity that are not of higher-curvature form, as shown here in a spherically symmetric setting. The usual uniqueness theorems are evaded by using a crucial and novel ingredient, allowing for fundamental fields of gravity distinct from an emergent space-time metric that provides a geometrical structure to all solutions. As specific examples, there are new expansion-shear couplings in cosmological models, a form of modified Newtonian dynamics can appear in a space-time covariant theory without introducing extra fields, and related effects help to make effective models of canonical quantum gravity fully consistent with general covariance.
Aaron Beyen et al 2024 Class. Quantum Grav. 41 095012
We revisit and improve the analytic study (Gregory et al 2018 Class. Quantum. Grav.35 155008) of spherically symmetric but dynamical black holes in Einstein's gravity coupled to a real scalar field. We introduce a series expansion in a small parameter ε that implements slow time dependence. At the leading order (LO), the generic solution is a quasi-stationary Schwarzschild–de Sitter (SdS) metric, i.e. one where time-dependence enters only through the mass and cosmological constant parameters of SdS. The two coupled ODEs describing the LO time dependence are solved up to quadrature for an arbitrary scalar potential. Higher order corrections can be consistently computed, as we show by explicitly solving the Einstein equations at the next to LO as well. We comment on how the quasi-stationary expansion we introduce here is equivalent to the non-relativistic expansion.
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A Bertocco et al 2024 Class. Quantum Grav. 41 117004
Seismic noise and local disturbances are dominant noise sources for ground-based gravitational waves detectors in the low frequency region (0.1–10 Hz) limiting their sensitivity and duty cycle. With the introduction of high-performance seismic isolation systems based on mechanical pendula, the 2nd generation laser interferometric detectors have reached the scientific goal of the first direct observation of GW signals thanks to the extension of the detection bandwidth down to 10 Hz. Now, the 3rd generation instrument era is approaching, and the Einstein telescope giant interferometer is becoming a reality with the possibility to install the detector in an underground site where seismic noise is 100 times smaller than on surface. Moreover, new available technologies as well as the experience acquired in operating advanced detectors are key points to further extend the detection bandwidth down to 2 Hz with the possibility to suspend cryogenic payload and then mitigating thermal noise too. Here, we present a preliminary study devoted to improving seismic attenuation performance of the advanced VIRGO superattenuator in the low frequency region of about five orders of magnitude. Particular care has been carried on in analyzing the possibility to improve the vertical attenuation performance with a multi-stage pendulum chain equipped with magnetic anti-springs that is hung to a double inverted pendulum in nested configuration. The feedback control requirements and possible strategies to be adopted for this last element will be presented.
Hideki Maeda and Jiří Podolský 2024 Class. Quantum Grav. 41 115012
We revisit the charged rotating Bañados–Teitelboim–Zanelli (BTZ) solution in the three-dimensional Einstein–Maxwell-Λ system. After the erroneous announcement of its discovery at the end of the original BTZ paper in 1992, the solution was first obtained by Clément in the paper published in 1996 by coordinate transformations from the charged non-rotating BTZ solution. While Clément's form of the solution is valid only for , we present a new form for a wider range of Λ by uniform scaling transformations and a reparametrization. We also introduce new coordinates corresponding to the Doran coordinates in the Kerr spacetime, in which the metric and also its inverse are regular at the Killing horizon, and described by elementary functions. Lastly, we show that (i) the algebraic Cotton type of the spacetime is type III on the Killing horizon and type I away from the horizon, and (ii) the energy-momentum tensor for the Maxwell field is of the Hawking–Ellis type I everywhere.
Dezhi Wang et al 2024 Class. Quantum Grav. 41 117003
Pointing-related displacement noises are crucial in space-based gravitational wave detectors, where point-ahead angle control of transmitted laser beams may contribute significantly. For TianQin that features a geocentric concept, the circular high orbit design with a nearly fixed constellation plane gives rise to small variations of the point-ahead angles within ±25 nrad in-plane and ±10 nrad off-plane, in addition to a static bias of 23 µrad predominantly within the constellation plane. Accordingly, TianQin may adopt fixed-value compensation for the point-ahead angles and absorb the small and slow variations into the pointing biases. To assess the in-principle feasibility, the far-field tilt-to-length (TTL) coupling effect is discussed, and preliminary requirements on far-field wavefront quality are derived, which have taken into account of TTL noise subtraction capability in post processing. The proposed strategy has benefits in simplifying the interferometry design, payload operation, and TTL noise mitigation for TianQin.
S K Maurya et al 2024 Class. Quantum Grav. 41 115009
In this paper, a significant leap forward in understanding compact stellar systems and the modified f(Q) gravity theory is achieved. The pivotal discovery lies in the successful derivation of an exact solution that fulfils the static geometry and spherical symmetry criteria, permitting the study of compact stellar configurations with an anisotropic fluid. The model is rigorously tested and satisfies the vital physical conditions within the stellar fluid, guaranteeing its viability. The numerical values of constant parameters have been calculated by using the observational data of the compact star, namely, Her X-1. The equi-mass contours highlight an impressive correlation between the f(Q) gravity parameters. Boosting α while keeping β fixed and concurrently boosting R leads to a significant global boost in mass distribution. This can be ascribed to the enhanced coupling arising from a higher α, which broadens the mass distribution. In addition, the larger object size arising from the rise in R allows for more mass accommodation. Therefore, raising both R and α leads to an exaggerated mass distribution, proving the combined influence of coupling strength and object size on total mass. Altogether, this investigation advances our knowledge of compact stellar systems and supports the evolution of the modified f(Q) theory of gravity, opening the way for more breakthroughs in this field.
Mehdi Assanioussi et al 2024 Class. Quantum Grav. 41 115007
In the present article, we review the classical covariant formulation of Yang–Mills theory and general relativity in the presence of spacetime boundaries, focusing mainly on the derivation of the presymplectic forms and their properties. We further revisit the introduction of the edge modes and the conditions which justify them, in the context where only field-independent gauge transformations are considered. We particularly show that the presence of edge modes is not justified by gauge invariance of the presymplectic form, but rather by the condition that the presymplectic form is degenerate on the initial field space, which allows to relate this presymplectic form to the symplectic form on the gauge reduced field space via pullback.
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Artur Alho et al 2024 Class. Quantum Grav. 41 073002
The purpose of this review it to present a renewed perspective of the problem of self-gravitating elastic bodies under spherical symmetry. It is also a companion to the papers (2022 Phys. Rev. D 105 044025, 2022 Phys. Rev. D 106 L041502) and (arXiv:2306.16584 [gr-qc]), where we introduced a new definition of spherically symmetric elastic bodies in general relativity, and applied it to investigate the existence and physical viability, including radial stability, of static self-gravitating elastic balls. We focus on elastic materials that generalize fluids with polytropic, linear, and affine equations of state, and discuss the symmetries of the energy density function, including homogeneity and the resulting scale invariance of the TOV equations. By introducing invariant characterizations of physically admissible initial data, we numerically construct mass-radius-compactness diagrams, and conjecture about the maximum compactness of stable physically admissible elastic balls.
Ellery Ames and Håkan Andréasson 2024 Class. Quantum Grav. 41 073001
The purpose of this work is to review the status about stationary solutions of the axially symmetric Einstein–Vlasov system with a focus on open problems of both analytical and numerical nature. For the latter we emphasize that the code used to construct stationary solutions in Ames et al (2016 Class. Quantum Grav.33 155008; 2019 Phys. Rev. D 99 024012) is open source, see Ames and Logg (2023 J. Open Source Softw.8 5979). In the analytical setting the open problems include establishing methods for proving existence of axisymmetric stationary solutions which are far from spherically symmetric, both in the general case and for certain special classes of solutions pointed out in the text. In the numerical setting there are intriguing properties of highly relativistic solutions that demand further attention, such as whether a sequence of such stationary solutions can approach a Kerr black hole, or if they necessarily approach the thin ring limit reminiscent of cosmic strings. The question of whether stationary solutions include states with thin-disk like morphologies as seen in many galaxies is also open. Finally, there are opportunities to extend this research to new settings such as the case of massless particles and coupled black hole-matter systems. We believe that some of the open problems highlighted here are of central importance for the understanding of nature.
Fabian Gittins 2024 Class. Quantum Grav. 41 043001
Rotating neutron stars that support long-lived, non-axisymmetric deformations known as mountains have long been considered potential sources of gravitational radiation. However, the amplitude from such a source is very weak and current gravitational-wave interferometers have yet to witness such a signal. The lack of detections has provided upper limits on the size of the involved deformations, which are continually being constrained. With expected improvements in detector sensitivities and analysis techniques, there is good reason to anticipate an observation in the future. This review concerns the current state of the theory of neutron-star mountains. These exotic objects host the extreme regimes of modern physics, which are related to how they sustain mountains. We summarise various mechanisms that may give rise to asymmetries, including crustal strains built up during the evolutionary history of the neutron star, the magnetic field distorting the star's shape and accretion episodes gradually constructing a mountain. Moving beyond the simple rotating model, we also discuss how precession affects the dynamics and modifies the gravitational-wave signal. We describe the prospects for detection and the challenges moving forward.
Chen-Te Ma 2024 Class. Quantum Grav. 41 023001
We review the various aspects of the 3D Einstein gravity theory with a negative cosmological constant and its boundary description. We also explore its connections to conformal field theories (CFTs), modular symmetry, and holography. It is worth noting that this particular theory is topological in nature, which means that all the physical degrees of freedom are located on the boundary. Additionally, we can derive the boundary description on a torus, which takes the form of a 2D Schwarzian theory. This observation suggests that the relevant degrees of freedom for the theory can be described using this 2D theory. Because of the renormalizability of the 3D gravity theory, one can probe the quantum regime. This suggests that it is possible to investigate quantum phenomena. Unlike the conventional CFTs, when considering the AdS3 background, the boundary theory loses modular symmetry. This represents a departure from the usual behavior of CFT and is quite intriguing. The Weyl transformation induces anomaly in CFTs, and we indicate that applying this transformation to the 2D Schwarzian theory leads to similar results. Summing over all geometries with the asymptotic AdS3 boundary condition is equivalent to summing over a modular group. The partition function is one-loop exact and therefore an analytical expression from the summation. This theory holds potential applications in Quantum Information and is a recurring theme in the study of holography, where gravitational theories are connected with CFTs.
Leonardo Abbrescia and Jared Speck 2023 Class. Quantum Grav. 40 243001
In this article, we provide notes that complement the lectures on the relativistic Euler equations and shocks that were given by the second author at the program Mathematical Perspectives of Gravitation Beyond the Vacuum Regime, which was hosted by the Erwin Schrödinger International Institute for Mathematics and Physics in Vienna in February 2022. We set the stage by introducing a standard first-order formulation of the relativistic Euler equations and providing a brief overview of local well-posedness in Sobolev spaces. Then, using Riemann invariants, we provide the first detailed construction of a localized subset of the maximal globally hyperbolic developments of an open set of initially smooth, shock-forming isentropic solutions in 1D, with a focus on describing the singular boundary and the Cauchy horizon that emerges from the singularity. Next, we provide an overview of the new second-order formulation of the 3D relativistic Euler equations derived in Disconzi and Speck (2019 Ann. Henri Poincare20 2173–270), its rich geometric and analytic structures, their implications for the mathematical theory of shock waves, and their connection to the setup we use in our 1D analysis of shocks. We then highlight some key prior results on the study of shock formation and related problems. Furthermore, we provide an overview of how the formulation of the flow derived in Disconzi and Speck (2019 Ann. Henri Poincare20 2173–270) can be used to study shock formation in multiple spatial dimensions. Finally, we discuss various open problems tied to shocks.
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Borissova
We investigate the requirement of suppressing spacetime geometries with a curvature singularity via destructive interference in the Lorentzian gravitational path integral as a constraint on the microscopic action for gravity. Based on simple examples of static spherically symmetric spacetimes, we demonstrate that complete singularity suppression in the path integral stipulates that the action for gravity be of infinite order in the curvature.
Mäkinen
We introduce a master constraint operator on the kinematical Hilbert space of loop quantum gravity representing a set of gauge conditions which classically fix the densitized triad to be diagonal. We argue that the master constraint approach provides a natural and systematic way of carrying out the quantum gauge-fixing procedure which underlies the model known as quantum-reduced loop gravity. The Hilbert space of quantum-reduced loop gravity is obtained as a particular space of solutions of the gauge-fixing master constraint operator. We give a concise summary of the fundamental structure of the quantum-reduced framework, and consider several possible extensions thereof, for which the master constraint formulation provides a convenient starting point. In particular, we propose a generalization of the standard Hilbert space of quantum-reduced loop gravity, which may be relevant in the application of the quantum-reduced model to physical situations in which the Ashtekar connection is not diagonal.
Yang
We propose a trick for calculating the surface gravity of the Killing horizon, especially for cases of rotating black holes. By choosing nice slices, the surface gravity and angular velocities can be directly read from relevant components of the inverse metric. We give several cases to show how to apply the trick step by step.
Aiello et al
Earth-based gravitational waves interferometric detectors are shot-noise limited in the high-frequency region of their sensitivity band. While enhancing the laser input power is the natural solution to improve on the shot noise limit, higher power also increases the optical aberration budget due to the laser absorption in the highly reflective coatings of mirrors, resulting in a drop of the sensitivity of the detector and in a limitation of its performance as well. Advanced Virgo exploits
Hartmann Wavefront Sensors to locally measure the absorption-induced aberrations by monitoring the optical path length change in the core optics. Despite the very high sensitivity featured by Hartmann sensors, environmental temperature fluctuations can cause a spurious curvature term to appear in the reconstructed wavefront due to the thermal expansion of the Hartmann plate, that could affect the accuracy of the aberration monitoring. We present the implementation and validation of a control loop to stabilize the Advanced Virgo Hartmann Wavefront Sensor temperature at the order of ΔT ≤ 0.01 K, keeping the spurious curvature within the detector's requirements on wavefront sensing accuracy.
Gerosa et al
Accurate modeling of selection effects is a key ingredient to the success of gravitational-wave astronomy. The detection probability plays a crucial role in both statistical population studies, where it enters the hierarchical Bayesian likelihood, and astrophysical modeling, where it is used to convert predictions from population-synthesis codes into observable distributions. We review the most commonly used approximations, extend them, and present some recipes for a straightforward implementation. These include a closed-form expression capturing both multiple detectors and noise realizations written in terms of the so-called Marcum $Q$-function and a ready-to-use mapping between signal-to-noise ratio thresholds and false-alarm rates from state-of-the-art detection pipelines. The bias introduced by approximating the matched filter signal-to-noise ratio with the optimal signal-to-noise ratio is not symmetric: sources that are nominally below threshold are more likely to be detected than sources above threshold are to be missed. Using both analytical considerations and software injections in detection pipelines, we confirm that including noise realizations when estimating the selection function introduces an average variation of a few %. This effect is most relevant for large catalogs and specific subpopulations of sources at the edge of detectability (e.g. high redshifts).
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A Bertocco et al 2024 Class. Quantum Grav. 41 117004
Seismic noise and local disturbances are dominant noise sources for ground-based gravitational waves detectors in the low frequency region (0.1–10 Hz) limiting their sensitivity and duty cycle. With the introduction of high-performance seismic isolation systems based on mechanical pendula, the 2nd generation laser interferometric detectors have reached the scientific goal of the first direct observation of GW signals thanks to the extension of the detection bandwidth down to 10 Hz. Now, the 3rd generation instrument era is approaching, and the Einstein telescope giant interferometer is becoming a reality with the possibility to install the detector in an underground site where seismic noise is 100 times smaller than on surface. Moreover, new available technologies as well as the experience acquired in operating advanced detectors are key points to further extend the detection bandwidth down to 2 Hz with the possibility to suspend cryogenic payload and then mitigating thermal noise too. Here, we present a preliminary study devoted to improving seismic attenuation performance of the advanced VIRGO superattenuator in the low frequency region of about five orders of magnitude. Particular care has been carried on in analyzing the possibility to improve the vertical attenuation performance with a multi-stage pendulum chain equipped with magnetic anti-springs that is hung to a double inverted pendulum in nested configuration. The feedback control requirements and possible strategies to be adopted for this last element will be presented.
Mehdi Assanioussi et al 2024 Class. Quantum Grav. 41 115007
In the present article, we review the classical covariant formulation of Yang–Mills theory and general relativity in the presence of spacetime boundaries, focusing mainly on the derivation of the presymplectic forms and their properties. We further revisit the introduction of the edge modes and the conditions which justify them, in the context where only field-independent gauge transformations are considered. We particularly show that the presence of edge modes is not justified by gauge invariance of the presymplectic form, but rather by the condition that the presymplectic form is degenerate on the initial field space, which allows to relate this presymplectic form to the symplectic form on the gauge reduced field space via pullback.
Matúš Papajčík and Jiří Podolský 2024 Class. Quantum Grav. 41 115008
We present a convenient method of algebraic classification of 2+1 spacetimes into the types I, II, D, III, N and O, without using any field equations. It is based on the 2+1 analogue of the Newman–Penrose curvature scalars of distinct boost weights, which are specific projections of the Cotton tensor onto a suitable null triad. The algebraic types are then simply determined by the gradual vanishing of such Cotton scalars, starting with those of the highest boost weight. This classification is directly related to the specific multiplicity of the Cotton-aligned null directions and to the corresponding Bel–Debever criteria. Using a bivector (that is 2-form) decomposition, we demonstrate that our method is fully equivalent to the usual Petrov-type classification of 2+1 spacetimes based on the eigenvalue problem and determining the respective canonical Jordan form of the Cotton–York tensor. We also derive a simple synoptic algorithm of algebraic classification based on the key polynomial curvature invariants. To show the practical usefulness of our approach, we perform the classification of several explicit examples, namely the general class of Robinson–Trautman spacetimes with an aligned electromagnetic field and a cosmological constant, and other metrics of various algebraic types.
Shun Yin Cheung et al 2024 Class. Quantum Grav. 41 115010
Gravitational-wave memory is a non-linear effect predicted by general relativity that remains undetected. We apply a Bayesian analysis framework to search for gravitational-wave memory using binary black hole mergers in LIGO-Virgo-KAGRA's third gravitational-wave transient catalogue. We obtain a Bayes factor of , in favour of the no-memory hypothesis, which implies that we are unable to measure memory with currently available data. This is consistent with previous work, suggesting that a catalogue of binary black hole mergers is needed to detect memory. We look for new physics by allowing the memory amplitude to deviate from the prediction of general relativity by a multiplicative factor A. We obtain an upper limit of A < 23 (95% credibility).
Alejandro Torres-Orjuela 2024 Class. Quantum Grav. 41 117001
The spherical modes of gravitational waves (GWs) have become a major focus of recent detection campaigns due to the additional information they can provide about different properties of the source. However, GW detection is restricted to only detecting one ray and hence it is not obvious how we can extract information about angular properties. In this note, we introduce a new gauge that makes visible GW detection does not only contain information on the second time derivative but also on the angular derivatives of the GW. In particular, we show that the angular derivatives are of the same order as the time derivatives of the wave thus allowing us to constrain the spherical modes. To further illustrate the detection of the spherical modes, we discuss how the evolution of the orbit of the source and thus the phase of the wave depends on them.
Indrajit Sen et al 2024 Class. Quantum Grav. 41 115005
Unitarity is a difficult concept to implement in canonical quantum gravity because of state non-normalisability and the problem of time. We take a realist approach based on pilot-wave theory to address this issue in the Ashtekar formulation of the Wheeler–DeWitt equation. We use the postulate of a definite configuration in the theory to define a global time for the gravitational-fermionic system recently discussed in Alexander et al (2022 Phys. Rev. D 106 106012), by parameterising a variation of a Weyl-spinor that depends on the Kodama state. The total Hamiltonian constraint yields a time-dependent Schrodinger equation, without semi-classical approximations, which we use to derive a local continuity equation over the configuration space. We implement the reality conditions at the level of the guidance equation, and obtain a real spin-connection, extrinsic curvature and triad along the system trajectory. We obtain quantum corrections to deSitter spacetime from the guidance equation. The non-normalisable Kodama state is naturally factored out of the full quantum state in the conserved current density, opening the possibility for quantum-mechanical unitarity. We also give a pilot-wave generalisation of the notion of unitarity applicable to non-normalisable states, and show the existence of equilibrium density for our system. Lastly, we find unitary states in mini-superspace by finding an approximate solution to the Hamiltonian constraint.
Ivan Booth et al 2024 Class. Quantum Grav. 41 115003
We consider an initial data set having a continuous symmetry and a marginally outer trapped surface (MOTS) that is not preserved by this symmetry. We show that such a MOTS is unstable except in an exceptional case. In non-rotating cases we provide a Courant-type lower bound on the number of unstable eigenvalues. These results are then used to prove the instability of a large class of exotic MOTSs that were recently observed in the Schwarzschild spacetime. We also discuss the implications for the apparent horizon in data sets with translational symmetry.
Fiorenzo Bastianelli and Mattia Damia Paciarini 2024 Class. Quantum Grav. 41 115002
We present an extension to arbitrary dimensions of a worldline path integral approach to one-loop quantum gravity, which was previously formulated in four spacetime dimensions. By utilizing this method, we recalculate gauge invariant coefficients related to the UV divergences of quantum gravity. These gauge invariant coefficients were previously obtained in arbitrary dimensions through two alternative techniques: the quantization of the spinning particle that propagates the graviton on Einstein spaces and the more conventional heat kernel approach. Our worldline path integrals are closer to the latter method and are employed to compute the trace of the heat kernel.
Paolo Gregori and Ricardo Schiappa 2024 Class. Quantum Grav. 41 115001
Two remarkable facts about Jackiw–Teitelboim (JT) two-dimensional dilaton-gravity have been recently uncovered: this theory is dual to an ensemble of quantum mechanical theories; and such ensembles are described by a random matrix model which itself may be regarded as a special (large matter-central-charge) limit of minimal string theory. This work addresses this limit, putting it in its broader matrix-model context; comparing results between multicritical models and minimal strings (i.e. changing in-between multicritical and conformal backgrounds); and in both cases making the limit of large matter-central-charge precise (as such limit can also be defined for the multicritical series). These analyses are first done via spectral geometry, at both perturbative and nonperturbative levels, addressing the resurgent large-order growth of perturbation theory, alongside a calculation of nonperturbative instanton-actions and corresponding Stokes data. This calculation requires an algorithm to reach large-order, which is valid for arbitrary two-dimensional topological gravity. String equations—as derived from the Gel'fand–Dikii construction of the resolvent—are analyzed in both multicritical and minimal string theoretic contexts, and studied both perturbatively and nonperturbatively (always matching against the earlier spectral-geometry computations). The resulting solutions, as described by resurgent transseries, are shown to be resonant. The large matter-central-charge limit is addressed—in the string-equation context—and, in particular, the string equation for JT gravity is obtained to next derivative-orders, beyond the known genus-zero case (its possible exact-form is also discussed). Finally, a discussion of gravitational perturbations to Schwarzschild-like black hole solutions in these minimal-string models, regarded as deformations of JT gravity, is included—alongside a brief discussion of quasinormal modes.
Ilkka Mäkinen 2024 Class. Quantum Grav.
We introduce a master constraint operator on the kinematical Hilbert space of loop quantum gravity representing a set of gauge conditions which classically fix the densitized triad to be diagonal. We argue that the master constraint approach provides a natural and systematic way of carrying out the quantum gauge-fixing procedure which underlies the model known as quantum-reduced loop gravity. The Hilbert space of quantum-reduced loop gravity is obtained as a particular space of solutions of the gauge-fixing master constraint operator. We give a concise summary of the fundamental structure of the quantum-reduced framework, and consider several possible extensions thereof, for which the master constraint formulation provides a convenient starting point. In particular, we propose a generalization of the standard Hilbert space of quantum-reduced loop gravity, which may be relevant in the application of the quantum-reduced model to physical situations in which the Ashtekar connection is not diagonal.