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.
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.
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.
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.
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.
V K Oikonomou 2024 Class. Quantum Grav. 41 085008
In this work we consider an axionic scalar-tensor theory of gravity and its effects on static neutron stars (NSs). The axionic theory is considered in the regime in which the axion oscillates around its potential minimum, which cosmologically occurs post-inflationary, when the Hubble rate is of the same order as the axion mass. We construct the Tolman–Oppenheimer–Volkoff equations for this axionic theory and for a spherically symmetric static spacetime and we solve these numerically using a quite robust double shooting LSODA based python integration method. Regarding the equations of state, we used nine mainstream and quite popular ones, namely, the WFF1, the SLy, the APR, the MS1, the AP3, the AP4, the ENG, the MPA1 and the MS1b, using the piecewise polytropic description for each. From the extracted data we calculate the Jordan frame masses and radii, and we confront the resulting phenomenology with five well-known NS constraints. As we demonstrate, the AP3, the ENG and the MPA1 equations of state yield phenomenologically viable results which are compatible with the constraints, with the MPA1 equation of state enjoying an elevated role among the three. The reason is that the MPA1 fits well the phenomenological constraints. A mentionable feature is the fact that all the viable phenomenologically equations of state produce maximum masses which are in the mass-gap region with , but lower that the causal 3 solar masses limit. We also compare the NS phenomenology produced by the axionic scalar-tensor theory with the phenomenology produced by inflationary attractors scalar-tensor theories.
Otto C W Kong 2024 Class. Quantum Grav. 41 085013
We present an exact quantum observable analog of the weak equivalence principle for a 'relativistic' quantum particle. The quantum geodesic equations are obtained from Heisenberg equations of motion as an exact analog of a fully covariant classical Hamiltonian evolution picture, with the proper identification of the canonical momentum variables as pµ, rather than pµ. We discuss the meaning of the equations in relation to projective measurements as well as equations with solution curves as ones in the noncommutative geometric picture of spacetime, and a plausible approach to quantum gravity as a theory about quantum observables as physical quantities including the notion of quantum coordinate transformation.
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Jared Fuchs et al 2024 Class. Quantum Grav. 41 095013
Warp drives are exotic solutions of general relativity that offer novel means of transportation. In this study, we present a solution for a constant-velocity subluminal warp drive that satisfies all of the energy conditions. The solution involves combining a stable matter shell with a shift vector distribution that closely matches well-known warp drive solutions such as the Alcubierre metric. We generate the spacetime metric numerically, evaluate the energy conditions, and confirm that the shift vector distribution cannot be reduced to a coordinate transformation. This study demonstrates that classic warp drive spacetimes can be made to satisfy the energy conditions by adding a regular matter shell with a positive ADM mass.
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.
G Abellán et al 2024 Class. Quantum Grav. 41 105011
In the present work, we study the consequences of including the lapse function as an additional degree of freedom for a general spherical warp-based geometry. By allowing a non-uniform lapse function to evolve, we find that it is possible to accommodate a fluid that includes heat flow. This broadens the range of fluid types that have been studied in these systems and is consistent with the spherical warp metric. Having added the lapse function, we solved the system of equations using an anisotropic fluid with heat flow. In this way, we can examine the different characteristics of the variables of the system. Next, we study the energy conditions and establish how these are modified by including heat flux for an appropriate generic observer in a locally flat spacetime. Finally, we explore all energy conditions using the numerical solutions and verify the regions where they are satisfied.
Giulio Favaro et al 2024 Class. Quantum Grav. 41 105009
This study explores the impact of crystalline fraction on the mechanical losses of amorphous tantalum oxide (tantala, Ta2O5) thin films intended for gravitational wave detectors. We use ion beam sputtering technique to prepare a series of samples, which are then subjected to controlled thermal annealing to achieve varying degrees of crystallized fraction. The microscopic structure of the annealed samples is characterized by combining different analytical techniques. Our investigation reveals that the amorphous films comprise randomly distributed crystalline grains, whose density and average size depends on the duration of thermal treatment. To assess mechanical losses of the coatings, a gentle nodal suspension system is applied. Remarkably, a substantial reduction of approximately 20% in the coating's mechanical loss angle with respect to annealed amorphous coatings is observed for samples exhibiting a crystalline fraction of around 5%. This improvement may lead to the definition of alternative thermal treatments to improve the mechanical performances of coatings for gravitational wave detectors or other highly sensitive optical experiments. However the reduction in mechanical losses comes at the expense of an increase in optical scattering. The possibility of reducing the optical losses to the level required by gravitational interferometers by modifying the grain size distribution via appropriate annealing treatments is discussed.
Massimo Giovannini 2024 Class. Quantum Grav. 41 105010
We observe that the energy and the enthalpy densities can be smeared by two fudge factors that are constrained by the contracted Bianchi identities. Depending on the analytic properties of the smearing functions the underlying cosmological solutions belong to two physically different classes, namely the bounces of the scale factor and the curvature bounces. While the curvature bounces are naturally compatible with a stage of accelerated expansion, the bounces of the scale factor demand an early phase of accelerated contraction even if a short inflationary stage may arise prior to the decelerated regime. Despite the regularity of the underlying solutions, gradient instabilities and singularities do occasionally appear in the evolution of curvature inhomogeneities. After deducing the specific criteria behind these occurrences, the background-independent conclusions are corroborated by a series of concrete examples associated with different forms of the smearing functions. The evolution of the curvature inhomogeneities restricts the ranges of the solutions that turn out to be unsuitable even for a limited description of the pre-inflationary initial data. The same observation holds in the case of the gauge-invariant evolution of the matter density contrast. It is however not excluded that a class of scenarios (mainly associated with the curvature bounces) could indeed avoid the potential instabilities. All in all the present analysis explore a general approach whose results are relevant in all the contexts where bouncing solutions are invoked either as complementary or as alternative to the conventional inflationary scenarios.
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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.
Open all abstracts, in this tab
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).
Giambo et al
We examine a spherically-symmetric class of spacetimes carrying vacuum energy, while considering the influence of an external dark energy environment represented by a non-dynamical quintessence field. Our investigation focuses on a specific set of solutions affected by this field, leading to distinct kinds of spacetime deformations, resulting in regular, singular, and wormhole solutions. We thoroughly discuss the underlying physics associated with each case and demonstrate that more complex deformations are prone to instability. Ultimately, we find that our results lead to isotropic de Sitter-like solution that behaves as a quintessence fluid. To achieve this, we investigate the nature of the corresponding fluid, showing that it cannot provide the sound speed equal to a constant equation of state near the center. Consequently, we reinterpret the fluid as a slow-roll quintessence by investigating its behavior in asymptotic regimes. Further, we explore the potential implications of violating the isotropy condition on the pressures and we finally compare our findings with the de Sitter and Hayward solutions, highlighting both the advantages and disadvantages of our scenarios.
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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.
Lorenzo Aiello et al 2024 Class. Quantum Grav.
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.
Davide Gerosa and Malvina Bellotti 2024 Class. Quantum Grav.
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).
Roberto Giambo and Orlando Luongo 2024 Class. Quantum Grav.
We examine a spherically-symmetric class of spacetimes carrying vacuum energy, while considering the influence of an external dark energy environment represented by a non-dynamical quintessence field. Our investigation focuses on a specific set of solutions affected by this field, leading to distinct kinds of spacetime deformations, resulting in regular, singular, and wormhole solutions. We thoroughly discuss the underlying physics associated with each case and demonstrate that more complex deformations are prone to instability. Ultimately, we find that our results lead to isotropic de Sitter-like solution that behaves as a quintessence fluid. To achieve this, we investigate the nature of the corresponding fluid, showing that it cannot provide the sound speed equal to a constant equation of state near the center. Consequently, we reinterpret the fluid as a slow-roll quintessence by investigating its behavior in asymptotic regimes. Further, we explore the potential implications of violating the isotropy condition on the pressures and we finally compare our findings with the de Sitter and Hayward solutions, highlighting both the advantages and disadvantages of our scenarios.
Giulio Favaro et al 2024 Class. Quantum Grav. 41 105009
This study explores the impact of crystalline fraction on the mechanical losses of amorphous tantalum oxide (tantala, Ta2O5) thin films intended for gravitational wave detectors. We use ion beam sputtering technique to prepare a series of samples, which are then subjected to controlled thermal annealing to achieve varying degrees of crystallized fraction. The microscopic structure of the annealed samples is characterized by combining different analytical techniques. Our investigation reveals that the amorphous films comprise randomly distributed crystalline grains, whose density and average size depends on the duration of thermal treatment. To assess mechanical losses of the coatings, a gentle nodal suspension system is applied. Remarkably, a substantial reduction of approximately 20% in the coating's mechanical loss angle with respect to annealed amorphous coatings is observed for samples exhibiting a crystalline fraction of around 5%. This improvement may lead to the definition of alternative thermal treatments to improve the mechanical performances of coatings for gravitational wave detectors or other highly sensitive optical experiments. However the reduction in mechanical losses comes at the expense of an increase in optical scattering. The possibility of reducing the optical losses to the level required by gravitational interferometers by modifying the grain size distribution via appropriate annealing treatments is discussed.
Massimo Giovannini 2024 Class. Quantum Grav. 41 105010
We observe that the energy and the enthalpy densities can be smeared by two fudge factors that are constrained by the contracted Bianchi identities. Depending on the analytic properties of the smearing functions the underlying cosmological solutions belong to two physically different classes, namely the bounces of the scale factor and the curvature bounces. While the curvature bounces are naturally compatible with a stage of accelerated expansion, the bounces of the scale factor demand an early phase of accelerated contraction even if a short inflationary stage may arise prior to the decelerated regime. Despite the regularity of the underlying solutions, gradient instabilities and singularities do occasionally appear in the evolution of curvature inhomogeneities. After deducing the specific criteria behind these occurrences, the background-independent conclusions are corroborated by a series of concrete examples associated with different forms of the smearing functions. The evolution of the curvature inhomogeneities restricts the ranges of the solutions that turn out to be unsuitable even for a limited description of the pre-inflationary initial data. The same observation holds in the case of the gauge-invariant evolution of the matter density contrast. It is however not excluded that a class of scenarios (mainly associated with the curvature bounces) could indeed avoid the potential instabilities. All in all the present analysis explore a general approach whose results are relevant in all the contexts where bouncing solutions are invoked either as complementary or as alternative to the conventional inflationary scenarios.
Hsin-Yu Chen et al 2024 Class. Quantum Grav.
Advancements in cosmology through next-generation ground-based gravitational wave observatories will bring in a paradigm shift. We explore the pivotal role that gravitational-wave standard sirens will play in inferring cosmological parameters with next-generation observatories, not only achieving exquisite precision but also opening up unprecedented redshifts. We examine the merits and the systematic biases involved in gravitational-wave standard sirens utilizing binary black holes, binary neutron stars, and neutron star-black hole mergers. Further, we estimate the precision of bright sirens, golden dark sirens, and spectral sirens for these binary coalescences and compare the abilities of various next-generation observatories (\asharp, Cosmic Explorer, Einstein Telescope, and their possible networks). When combining different sirens, we find sub-percent precision over more than 10 billion years of cosmic evolution for the Hubble expansion rate $H(z)$. 
 This work presents a broad view of opportunities to precisely measure the cosmic expansion rate, decipher the elusive dark energy and dark matter, and potentially discover new physics in the uncharted Universe with next-generation gravitational-wave detectors.
Alexander F Jercher and Sebastian Steinhaus 2024 Class. Quantum Grav. 41 105008
We develop a model of spatially flat, homogeneous and isotropic cosmology in Lorentzian Regge calculus, employing four-dimensional Lorentzian frusta as building blocks. By examining the causal structure of the discrete spacetimes obtained by gluing such four-frusta in spatial and temporal direction, we find causality violations if the sub-cells connecting spatial slices are spacelike. A Wick rotation to the Euclidean theory can be defined globally by a complexification of the variables and an analytic continuation of the action. Introducing a discrete free massless scalar field, we study its equations of motion and show that it evolves monotonically. Furthermore, in a continuum limit, we obtain the equations of a homogeneous scalar field on a spatially flat Friedmann background. Vacuum solutions to the causally regular Regge equations are static and flat and show a restoration of time reparametrisation invariance. In the presence of a scalar field, the height of a frustum is a dynamical variable that has a solution if causality violations are absent and if an inequality relating geometric and matter boundary data is satisfied. Edge lengths of cubes evolve monotonically, yielding a contracting or an expanding branch of the Universe. In a small deficit angle expansion, the system can be deparametrised via the scalar field and a continuum limit of the discrete theory can be defined which we show to yield the relational Friedmann equation. These properties are obstructed if higher orders of the deficit angle are taken into account. Our results suggest that the inclusion of timelike sub-cells is necessary for a causally regular classical evolution in this symmetry restricted setting. Ultimately, this works serves as a basis for forthcoming investigations on the cosmological path integral within the framework of effective spin foams.
Orlando Luongo and Tommaso Mengoni 2024 Class. Quantum Grav. 41 105006
We here explore a generalized K-essence model which exhibits characteristics akin to ordinary matter. The inflationary framework proposed aims to unify old with chaotic inflation into a single scheme and it considers minimally and non-minimally coupled scenarios, adopting three classes of potentials, in both Jordan and Einstein frames. We show that, to obtain a suitable amount of particles obtained from vacuum energy conversion during inflation, mitigating the classical cosmological constant problem, large-field inflation and, particularly, the Starobinsky-like class of solutions appears the most suitable one.