Classical and Quantum Gravity

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.

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.

The TianQin-1 satellite (TQ-1), which is the first technology demonstration satellite for the TianQin project, was launched on 20 December 2019. The first round of experiment had been carried out from 21 December 2019 until 1 April 2020. The residual acceleration of the satellite is found to be about 1 × 10 ⁻¹⁰ m/s ²/Hz ^1/2 at 0.1 Hz and about 5 × 10 ⁻¹¹ m/s ²/Hz ^1/2 at 0.05 Hz, measured by an inertial sensor with a sensitivity of 5 × 10 ⁻¹² m/s ²/Hz ^1/2 at 0.1 Hz. The micro-Newton thrusters has demonstrated a thrust resolution of 0.1  μN and a thrust noise of 0.3  μN/Hz ^1/2 at 0.1 Hz. The residual noise of the satellite with drag-free control is 3 × 10 ⁻⁹ m/s ²/Hz ^1/2 at 0.1 Hz. The noise level of the optical readout system is about 30 pm/Hz ^1/2 at 0.1 Hz. The temperature stability at temperature monitoring position is controlled to be about ±3 mK per orbit, and the mismatch between the center-of-mass of the satellite and that of the test mass is measured with a precision of better than 0.1 mm.

On 14 September 2015, a gravitational wave signal from a coalescing black hole binary system was observed by the Advanced LIGO detectors. This paper describes the transient noise backgrounds used to determine the significance of the event (designated GW150914) and presents the results of investigations into potential correlated or uncorrelated sources of transient noise in the detectors around the time of the event. The detectors were operating nominally at the time of GW150914. We have ruled out environmental influences and non-Gaussian instrument noise at either LIGO detector as the cause of the observed gravitational wave signal.

The Gravity Probe B mission provided two new quantitative tests of Einstein’s theory of gravity, general relativity (GR), by cryogenic gyroscopes in Earth’s orbit. Data from four gyroscopes gave a geodetic drift-rate of −6601.8 ± 18.3 marc-s yr ⁻¹ and a frame-dragging of −37.2 ± 7.2 marc-s yr ⁻¹, to be compared with GR predictions of −6606.1 and −39.2 marc-s yr ⁻¹ (1 marc-s = 4.848 × 10 ⁻⁹ radians). The present paper introduces the science, engineering, data analysis, and heritage of Gravity Probe B, detailed in the accompanying 20 CQG papers.

This paper addresses a simple question: how small can one make a gravitational source mass and still detect its gravitational coupling to a nearby test mass? We describe an experimental scheme based on micromechanical sensing to observe gravity between milligram-scale source masses, thereby improving the current smallest source mass values by three orders of magnitude and possibly even more. We also discuss the implications of such measurements both for improved precision measurements of Newton’s constant and for a new generation of experiments at the interface between quantum physics and gravity.

There are several common conventions in use by the gravitational-wave community to describe the amplitude of sources and the sensitivity of detectors. These are frequently confused. We outline the merits of and differences between the various quantities used for parameterizing noise curves and characterizing gravitational-wave amplitudes. We conclude by producing plots that consistently compare different detectors. Similar figures can be generated on-line for general use at http://rhcole.com/apps/GWplotter.

GW170817 is the very first observation of gravitational waves originating from the coalescence of two compact objects in the mass range of neutron stars, accompanied by electromagnetic counterparts, and offers an opportunity to directly probe the internal structure of neutron stars. We perform Bayesian model selection on a wide range of theoretical predictions for the neutron star equation of state. For the binary neutron star hypothesis, we find that we cannot rule out the majority of theoretical models considered. In addition, the gravitational-wave data alone does not rule out the possibility that one or both objects were low-mass black holes. We discuss the possible outcomes in the case of a binary neutron star merger, finding that all scenarios from prompt collapse to long-lived or even stable remnants are possible. For long-lived remnants, we place an upper limit of 1.9 kHz on the rotation rate. If a black hole was formed any time after merger and the coalescing stars were slowly rotating, then the maximum baryonic mass of non-rotating neutron stars is at most , and three equations of state considered here can be ruled out. We obtain a tighter limit of for the case that the merger results in a hypermassive neutron star.

The regular black hole solution arising as a spherically symmetric vacuum solution of Born–Infeld gravity possesses an asymptotic interior structure which is very well described by a four-dimensional generalization of the non-rotating BTZ metric. According to this picture no singularity exists, and instead, infalling observers experience a constant curvature manifold as they travel towards future null infinity. This is characterized by the BTZ event horizon. The exterior structure of the black hole is also studied, and it is shown that it corresponds to the Schwarzschild solution provided the black hole mass is not too small. In this way, the regular black hole state can be seen as a spacetime which connects two constant curvature asymptotic spaces, namely, the flat Minkowski spacetime in the outside region, and the locally AdS constant negative curvature one characterizing the BTZ-like asymptotic interior.

We present an analytic computation of an explicit renormalisation group flow for cosmological states in loop quantum gravity. A key ingredient in our analysis are Perelomov coherent states for the Lie group SU(1, 1) whose representation spaces are embedded into the standard loop quantum cosmology (LQC) Hilbert space. The SU(1, 1) group structure enters our analysis by considering a classical set of phase space functions that generates the Lie algebra . We implement this Poisson algebra as operators on the LQC Hilbert space in a non-anomalous way. This task requires a rather involved ordering choice, whose existence is one of the main results of the paper. As a consequence, we can transfer recently established results on coarse graining cosmological states from direct quantisations of the above Poisson algebra to the standard LQC Hilbert space and full theory embeddings thereof. We explicitly discuss how the representation spaces used in this latter approach are embedded into the LQC Hilbert space and how the representation label sets a lower cut-off for the loop quantum gravity spins (=U(1) representation labels in LQC). Our results provide an explicit example of a non-trivial renormalisation group flow with a scale set by the representation label and interpreted as the minimally resolved geometric scale.

The grand challenges of contemporary fundamental physics—dark matter, dark energy, vacuum energy, inflation and early universe cosmology, singularities and the hierarchy problem—all involve gravity as a key component. And of all gravitational phenomena, black holes stand out in their elegant simplicity, while harbouring some of the most remarkable predictions of General Relativity: event horizons, singularities and ergoregions.

The hitherto invisible landscape of the gravitational Universe is being unveiled before our eyes: the historical direct detection of gravitational waves by the LIGO-Virgo collaboration marks the dawn of a new era of scientific exploration. Gravitational-wave astronomy will allow us to test models of black hole formation, growth and evolution, as well as models of gravitational-wave generation and propagation. It will provide evidence for event horizons and ergoregions, test the theory of General Relativity itself, and may reveal the existence of new fundamental fields. The synthesis of these results has the potential to radically reshape our understanding of the cosmos and of the laws of Nature.

The purpose of this work is to present a concise, yet comprehensive overview of the state of the art in the relevant fields of research, summarize important open problems, and lay out a roadmap for future progress. This write-up is an initiative taken within the framework of the European Action on ‘Black holes, Gravitational waves and Fundamental Physics’.

The Laser Interferometer Space Antenna (LISA) will open the mHz band of the gravitational wave spectrum for exploration. Sensitivity curves are a useful tool for surveying the types of sources that can be detected by the LISA mission. Here we describe how the sensitivity curve is constructed, and how it can be used to compute the signal-to-noise ratio for a wide range of binary systems. We adopt the 2018 LISA mission performance requirement design parameters. We consider both sky-averaged sensitivities, and the sensitivity to sources at particular sky locations. The calculations are included in a publicly available Python notebook.

We consider single-field inflation in light of string-motivated ‘swampland’ conjectures suggesting that effective scalar field theories with a consistent UV completion must have field excursion , in combination with a sufficiently steep potential, . Here, we show that the swampland conjectures are inconsistent with existing observational constraints on single-field inflation. Focusing on the observationally favoured class of concave potentials, we map the allowed swampland region onto the n _S - r ‘zoo plot’ of inflationary models, and find that consistency with the Planck satellite and BICEP2/Keck Array requires and , in strong tension with swampland conjectures. Extension to non-canonical models such as DBI Inflation does not significantly weaken the bound.

Teleparallel gravity and its popular generalization gravity can be formulated as fully invariant (under both coordinate transformations and local Lorentz transformations) theories of gravity. Several misconceptions about teleparallel gravity and its generalizations can be found in the literature, especially regarding their local Lorentz invariance. We describe how these misunderstandings may have arisen and attempt to clarify the situation. In particular, the central point of confusion in the literature appears to be related to the inertial spin connection in teleparallel gravity models. While inertial spin connections are commonplace in special relativity, and not something inherent to teleparallel gravity, the role of the inertial spin connection in removing the spurious inertial effects within a given frame of reference is emphasized here. The careful consideration of the inertial spin connection leads to the construction of a fully invariant theory of teleparallel gravity and its generalizations. Indeed, it is the nature of the spin connection that differentiates the relationship between what have been called good tetrads and bad tetrads and clearly shows that, in principle, any tetrad can be utilized. The field equations for the fully invariant formulation of teleparallel gravity and its generalizations are presented and a number of examples using different assumptions on the frame and spin connection are displayed to illustrate the covariant procedure. Various modified teleparallel gravity models are also briefly reviewed.

Accurate models of gravitational waves from merging black holes are necessary for detectors to observe as many events as possible while extracting the maximum science. Near the time of merger, the gravitational waves from merging black holes can be computed only using numerical relativity. In this paper, we present a major update of the Simulating eXtreme Spacetimes (SXS) Collaboration catalog of numerical simulations for merging black holes. The catalog contains 2018 distinct configurations (a factor of 11 increase compared to the 2013 SXS catalog), including 1426 spin-precessing configurations, with mass ratios between 1 and 10, and spin magnitudes up to 0.998. The median length of a waveform in the catalog is 39 cycles of the dominant gravitational-wave mode, with the shortest waveform containing 7.0 cycles and the longest 351.3 cycles. We discuss improvements such as correcting for moving centers of mass and extended coverage of the parameter space. We also present a thorough analysis of numerical errors, finding typical truncation errors corresponding to a waveform mismatch of  ∼10 ⁻⁴. The simulations provide remnant masses and spins with uncertainties of 0.03% and 0.1% (90th percentile), about an order of magnitude better than analytical models for remnant properties. The full catalog is publicly available at www.black-holes.org/waveforms.

We show that the Lorentzian Snyder models, together with their Galilei and Carroll limiting cases, can be rigorously constructed through the projective geometry description of Lorentzian, Galilean and Carrollian spaces with nonvanishing constant curvature. The projective coordinates of such curved spaces take the role of momenta, while translation generators over the same spaces are identified with noncommutative spacetime coordinates. In this way, one obtains a deformed phase space algebra, which fully characterizes the Snyder model and is invariant under boosts and rotations of the relevant kinematical symmetries. While the momentum space of the Lorentzian Snyder models is given by certain projective coordinates on (anti-)de Sitter spaces, we discover that the momentum space of the Galilean (Carrollian) Snyder models is given by certain projective coordinates on curved Carroll (Newton–Hooke) spaces. This exchange between the Galilei and Carroll limits emerging in the transition from the geometric picture to the phase space picture is traced back to an interchange of the role of coordinates and translation operators. As a physically relevant feature, we find that in Galilean Snyder spacetimes the time coordinate does not commute with space coordinates, in contrast with previous proposals for non-relativistic Snyder models, which assume that time and space decouple in the non-relativistic limit c → ∞. This remnant mixing between space and time in the non-relativistic limit is a quite general Planck-scale effect found in several quantum spacetime models.

The cancellation of noise from terrestrial gravity fluctuations, also known as Newtonian noise (NN), in gravitational-wave detectors is a formidable challenge. Gravity fluctuations result from density perturbations associated with environmental fields, e.g., seismic and acoustic fields, which are characterized by complex spatial correlations. Measurements of these fields necessarily provide incomplete information, and the question is how to make optimal use of available information for the design of a noise-cancellation system. In this paper, we present a machine-learning approach to calculate a surrogate model of a Wiener filter. The model is used to calculate optimal configurations of seismometer arrays for a varying number of sensors, which is the missing keystone for the design of NN cancellation systems. The optimization results indicate that efficient noise cancellation can be achieved even for complex seismic fields with relatively few seismometers provided that they are deployed in optimal configurations. In the form presented here, the optimization method can be applied to all current and future gravitational-wave detectors located at the surface and with minor modifications also to future underground detectors.

A manifestly diffeomorphism invariant exact renormalization group requires extra diffeomorphism invariant ultraviolet regularisation at some effective cutoff scale Λ. This motivates construction of a ‘Parisi-Sourlas’ supergravity, in analogy with the gauge theory case, where the superpartner fields have the wrong spin-statistics such that they can become Pauli–Villars regulator fields after spontaneous symmetry breaking. We show that in contrast to gauge theory, the free theory around flat space is already non-trivial and in a sense already displays some spontaneous symmetry breaking. We show that the fluctuating fields form multiplets whose mass matrices imply that the fields propagate into each other not only with the expected 1/ p ² but also through propagators with improved ultraviolet properties, namely 1/ p ⁴ and 1/ p ⁶, despite the fact that the action contains a maximum of two space-time derivatives.

The geometrical formulation of gravity is not unique and can be set up in a variety of spacetimes. Even though the gravitational sector enjoys this freedom of different geometrical interpretations, consistent matter couplings have to be assured for a steady foundation of gravity. In generalised geometries, further ambiguities arise in the matter couplings unless the minimal coupling principle (MCP) is adopted that is compatible with the principles of relativity, universality and inertia. In this work, MCP is applied to all standard model gauge fields and matter fields in a completely general (linear) affine geometry. This is also discussed from an effective field theory perspective. It is found that the presence of torsion generically leads to theoretical problems. However, symmetric teleparallelism, wherein the affine geometry is integrable and torsion-free, is consistent with MCP. The generalised Bianchi identity is derived and shown to determine the dynamics of the connection in a unified fashion. Also, the parallel transport with respect to a teleparallel connection is shown to be free of second clock effects.

Given spherically symmetric characteristic initial data for the Einstein-scalar field system with a positive cosmological constant, we provide a criterion, in terms of the dimensionless size and dimensionless renormalized mass content of an annular region of the data, for the formation of a future trapped surface. This corresponds to an extension of Christodoulou’s classical criterion by the inclusion of the cosmological term.

In this introductory review, we argue that a quantum structure of space-time naturally entails a higher-spin theory, to avoid significant Lorentz violation. A suitable framework is provided by Yang–Mills matrix models, which allow to consider space-time as a physical system, which is treated on the same footing as the fields that live on it. We discuss a specific quantum space-time solution, whose internal structure leads to a consistent and ghost-free higher-spin gauge theory. The spin 2 modes give rise to metric perturbations, which include the standard gravitons as well as the linearized Schwarzschild solution.

With the arrival of the era of gravitational wave astronomy, the strong gravitational field regime will be explored soon in various aspects. In this article, we provide a general review over cylindrical systems in Einstein’s theory of general relativity. In particular, we first review the general properties, both local and global, of several important solutions of Einstein’s field equations, including the Levi-Civita and Lewis solutions and their extensions to include the cosmological constant and matter fields, and pay particular attention to properties that represent the generic features of the theory, such as the formation of the observed extragalactic jets and gravitational Faraday rotation. We also review studies of cylindrical wormholes, gravitational collapse and hoop conjecture, and polarizations of gravitational waves. In addition, by rigorously defining cylindrically symmetric spacetimes, we clarify various (incorrect) claims existing in the literature, regarding to the generality of such spacetimes.

We review current theoretical cosmology, including fundamental and mathematical cosmology and physical cosmology (as well as cosmology in the quantum realm), with an emphasis on open questions.

This topical review gives a comprehensive overview and assessment of recent results in causal dynamical triangulations, a modern formulation of lattice gravity, whose aim is to obtain a theory of quantum gravity nonperturbatively from a scaling limit of the lattice-regularized theory. In this manifestly diffeomorphism-invariant approach one has direct, computational access to a Planckian spacetime regime, which is explored with the help of invariant quantum observables. During the last few years, there have been numerous new and important developments and insights concerning the theory’s phase structure, the roles of time, causality, diffeomorphisms and global topology, the application of renormalization group methods and new observables. We will focus on these new results, primarily in four spacetime dimensions, and discuss some of their geometric and physical implications.

Teleparallel gravity and its popular generalization gravity can be formulated as fully invariant (under both coordinate transformations and local Lorentz transformations) theories of gravity. Several misconceptions about teleparallel gravity and its generalizations can be found in the literature, especially regarding their local Lorentz invariance. We describe how these misunderstandings may have arisen and attempt to clarify the situation. In particular, the central point of confusion in the literature appears to be related to the inertial spin connection in teleparallel gravity models. While inertial spin connections are commonplace in special relativity, and not something inherent to teleparallel gravity, the role of the inertial spin connection in removing the spurious inertial effects within a given frame of reference is emphasized here. The careful consideration of the inertial spin connection leads to the construction of a fully invariant theory of teleparallel gravity and its generalizations. Indeed, it is the nature of the spin connection that differentiates the relationship between what have been called good tetrads and bad tetrads and clearly shows that, in principle, any tetrad can be utilized. The field equations for the fully invariant formulation of teleparallel gravity and its generalizations are presented and a number of examples using different assumptions on the frame and spin connection are displayed to illustrate the covariant procedure. Various modified teleparallel gravity models are also briefly reviewed.

In the existing implementations of the Cartan–Karlhede procedure for characterization and classification of spacetimes, a prominent rôle is played by multi-index two-component spinors symmetrized over both types of index. This paper considers the conditions for, and detection of, null rotational invariance of such spinors, and corrects a previous discussion.

High purity fused silica has become the cornerstone choice for use in the final monolithic stage of the mirror suspensions in the gravitational wave observatories Advanced LIGO (aLIGO) and Advanced Virgo (AdV). The ultra-low thermal noise contributed by these suspensions is one of the key improvements that permitted the Nobel prize winning first direct measurement of gravitational waves in 2015. This paper outlines the first in situ study undertaken to analyse the thermal noise of the final monolithic stage of the aLIGO Hanford detector mirror suspensions. We analysed short operational periods of this detector, when high excitation of the transverse ‘violin’ modes of the silica suspension fibres occurred. This allowed detailed measurements of the Q-factor of violin modes up to order 8 of individual fibres on separate masses. We demonstrate the highest silica fibre violin mode Q-factors yet measured of up to 2 × 10 ⁹. From finite element modelling, the dominant surface and weld losses have been calculated to be a factor of 3 to 4 better than previously accepted, and as a result, we demonstrate that the level of noise in the aLIGO final stage silica suspensions is around 30%–40% better than previously estimated between frequencies of 10–500 Hz. This leads to an increase in the estimated event rate by a factor of 2 for aLIGO, if suspension thermal noise became the main limitation to the sensitivity of the detector.

The regular black hole solution arising as a spherically symmetric vacuum solution of Born–Infeld gravity possesses an asymptotic interior structure which is very well described by a four-dimensional generalization of the non-rotating BTZ metric. According to this picture no singularity exists, and instead, infalling observers experience a constant curvature manifold as they travel towards future null infinity. This is characterized by the BTZ event horizon. The exterior structure of the black hole is also studied, and it is shown that it corresponds to the Schwarzschild solution provided the black hole mass is not too small. In this way, the regular black hole state can be seen as a spacetime which connects two constant curvature asymptotic spaces, namely, the flat Minkowski spacetime in the outside region, and the locally AdS constant negative curvature one characterizing the BTZ-like asymptotic interior.

We present an analytic computation of an explicit renormalisation group flow for cosmological states in loop quantum gravity. A key ingredient in our analysis are Perelomov coherent states for the Lie group SU(1, 1) whose representation spaces are embedded into the standard loop quantum cosmology (LQC) Hilbert space. The SU(1, 1) group structure enters our analysis by considering a classical set of phase space functions that generates the Lie algebra . We implement this Poisson algebra as operators on the LQC Hilbert space in a non-anomalous way. This task requires a rather involved ordering choice, whose existence is one of the main results of the paper. As a consequence, we can transfer recently established results on coarse graining cosmological states from direct quantisations of the above Poisson algebra to the standard LQC Hilbert space and full theory embeddings thereof. We explicitly discuss how the representation spaces used in this latter approach are embedded into the LQC Hilbert space and how the representation label sets a lower cut-off for the loop quantum gravity spins (=U(1) representation labels in LQC). Our results provide an explicit example of a non-trivial renormalisation group flow with a scale set by the representation label and interpreted as the minimally resolved geometric scale.

We describe a spacetime endowed with a non-metricity tensor which effectively serves as a model of a spacetime foam. We explore the consequences of the non-metricity in several f( R) theories.

In this paper we develop the mathematics required in order to provide a description of the observables for quantum fields on low-regularity spacetimes. In particular we consider the case of a massless scalar field ϕ on a globally hyperbolic spacetime M with C ^1,1 metric g. This first entails showing that the (classical) Cauchy problem for the wave equation is well-posed for initial data and sources in Sobolev spaces and then constructing low-regularity advanced and retarded Green operators as maps between suitable function spaces. In specifying the relevant function spaces we need to control the norms of both ϕ and □ _g ϕ in order to ensure that □ _g ◦ G ^± and G ^±◦□ _g are the identity maps on those spaces. The causal propagator G = G ⁺ − G ⁻ is then used to define a symplectic form ω on a normed space V( M) which is shown to be isomorphic to ker(□ _g ). This enables one to provide a locally covariant description of the quantum fields in terms of the elements of quasi-local C*-algebras.

We extend various recent results regarding the derivation of effective cosmological Friedmann equations from the dynamics of group field theory (GFT). Restricting ourselves to a single GFT field mode (or fixed values of Peter–Weyl representation labels), we first consider dynamics given by a quadratic Hamiltonian, which takes the form of a squeezing operator, and then add a quartic interaction that can be seen as a toy model for interactions in full GFT. Our derivation of effective Friedmann equations does not require a mean-field approximation; we mostly follow a general approach in which these equations in fact hold for any state. The resulting cosmological equations exhibit corrections to classical Friedmann dynamics similar to those of loop quantum cosmology, leading to generic singularity resolution, but also involve further state-dependent terms. We then specify these equations to various types of coherent states, such as Fock coherent states or Perelomov–Gilmore states based on the su(1, 1) structure of harmonic quantum cosmology. We compute relative uncertainties of volume and energy in these states, clarifying whether they can be interpreted as semiclassical. In the interacting case, both analytical and numerical approximations are used to obtain modified cosmological dynamics. Our results clarify how effective cosmological equations derived from GFT can provide reliable approximations to the full dynamics.

It is well known that linearized gravity in spacetimes with compact Cauchy surfaces and continuous symmetries suffers from linearization instabilities: solutions to classical linearized gravity in such a spacetime must satisfy so-called linearization stability conditions (or constraints) for them to extend to solutions in the full non-linear theory. Moncrief investigated implications of these conditions in linearized quantum gravity in such background spacetimes and found that the quantum linearization stability constraints lead to the requirement that all physical states must be invariant under the symmetries generated by these constraints. He studied these constraints for linearized quantum gravity in flat spacetime with the spatial sections of toroidal topology in detail. Subsequently, his result was reproduced by the method of group-averaging. In this paper the quantum linearization stability conditions are studied for simple supergravity in this spacetime. In addition to the linearization stability conditions corresponding to the spacetime symmetries, i.e. spacetime translations, there are also fermionic linearization stability conditions corresponding to the background supersymmetry. We construct all states satisfying these quantum linearization stability conditions, including the fermionic ones, and show that they are obtained by group-averaging over the supergroup of the global supersymmetry of this theory.

We present a method for solving the constraint equations in the Hassan–Rosen bimetric theory to determine the initial data for the gravitational collapse of spherically symmetric dust. The setup leads to equations similar to those for a polytropic fluid in general relativity, here called Lane–Emden-like equations. Using a numerical code which solves the evolution equations in the standard 3 + 1 form, we also obtain a short-term development of the initial data for these bimetric spherical clouds. The evolution highlights some important features of the bimetric theory such as the interwoven and oscillating null cones representing the essential nonbidiagonality in the dynamics of the two metrics. The simulations are in the strong-field regime and show that, at least at an early stage, if the bimetric initial data are close to those for general relativity, the bimetric evolution stays close to the evolution in general relativity as well, and with no instabilities, albeit with small oscillations in the metric fields. In addition, we determine initial data and first evolution for vacuum bimetric spherically symmetric nonstationary solutions, providing generic counterexamples to a statement analog to Jebsen–Birkhoff theorem in bimetric relativity.

We offer further evidence that discreteness of the sort inherent in a causal set cannot, in and of itself, serve to break Poincaré invariance. In particular we prove that a Poisson sprinkling of Minkowski spacetime cannot endow spacetime with a distinguished spatial or temporal orientation, or with a distinguished lattice of spacetime points, or with a distinguished lattice of timelike directions (corresponding respectively to breakings of reflection-invariance, translation-invariance, and Lorentz invariance). Along the way we provide a proof from first principles of the zero-one law on which our new arguments are based.