Papers

We numerically find the solutions for slowly moving Schwarzschild black holes in Einstein–aether theory. We use these solutions to compute the sensitivity parameter which describes the coupling of the black hole to the aether field within point-particle effective theory. A simple analytic approximation for the dependence of the sensitivity on the Einstein–aether parameters is derived.

Extensions of relativity that include superluminal reference frames have recently been proposed by Dragan and Ekert as a way to reconcile relativistic symmetry with quantum uncertainty. In this work, we develop a causal modelling framework to formally study this proposal and prove a no-go theorem demonstrating that a theory permitting superluminal reference frames can avoid superluminal signalling only if it severely constrains which spacetime regions are accessible to operational protocols, if the choice of reference frame has observable consequences or if free variables do not exist or their existence depends on the reference frame. Crucially, our result goes beyond the familiar intuition that superluminal transformations may lead to superluminal signalling; our no-go result shows that Dragan and Ekert's proposal of introducing objective uncertainty does not, by itself, eliminate this conflict. In fact, because superluminal signalling might instead be avoided by relaxing other fundamental assumptions in the presence of superluminal reference frames, the proposed objective uncertainty may not be necessary at all. Our results clarify the limitations of uncertainty-based resolutions and the causal trade-offs faced by superluminal extensions of relativity.

In a previous work 2511.21852, we explored the hypothesis that in general theories of quantum gravity, spacetime regions known as generalized entanglement wedges (introduced by Bousso and Penington) have an associated subalgebra of observables in a semiclassical limit. We defined an entropy associated with these subalgebras that obeys the same monotonicity and strong subadditivity properties as the generalized gravitational entropy of generalized entanglement wedges. Here, we test aspects of these ideas making use of tensor network toy models for holography. In this context, the analog of a generalized entanglement wedge is a region for which no region containing it has a smaller number of boundary legs. In the limit of large bond dimension (analogous to the semiclassical limit), we argue that each such region has a canonically associated subalgebra of the full algebra of observables on the boundary Hilbert space, as well as a family of unitarily related von Neumann factor subalgebras. We investigate in detail how various algebraic operations on these subalgebras (e.g. their intersections, joins, and commutants) are related to corresponding geometrical operations on the tensor network regions. We study to what extent the monotonicity and strong subadditivity properties of generalized entropy for generalized entanglement wedges follow from properties of our algebraic entropy. We also introduce an alternative entropic quantity $S(\omega || \omega \circ E_{\mathcal{A}'})$ associated with a subalgebra $\mathcal{A}$ that also obeys monotonicity and strong subadditivity properties with suitable conditions. Finally, we explain how to define a type $II_1$ von Neumann algebra based on an infinite family of random tensor networks with increasing bond dimension such that the regions corresponding to generalized entanglement wedges can be associated with exact subalgebras of this full algebra.

We formulate fermionic particle creation in a time-dependent curved spacetime as the exact evolution of a physical Bloch vector. Each Dirac momentum mode reduces to a two-level system, and its instantaneous occupation is obtained by projecting the physical state onto the instantaneous energy basis. This construction is equivalent to the standard Bogoliubov description while retaining the complete finite-time state trajectory in a compact real geometry. It also makes the fermionic occupation bound manifest without attributing its microscopic origin to geometry alone. For a massive Dirac field in de Sitter spacetime, the dynamics reduces to a universal function of the physical momentum in Hubble units and the mass-to-Hubble ratio. We identify a mass-controlled nonadiabatic scale and a singular small-mass boundary layer that resolves the noncommuting massless and late-time limits. Independent Cartesian Bloch, angular Bloch, and Bogoliubov integrations verify the analytical results and recover the standard Gibbons–Hawking Fermi–Dirac plateau.

Starobinsky's original model of inflation, driven by the trace anomaly of conformal fields, and its $R+R^2$ (scalaron) formulation are often treated separately. The original anomaly-driven evolution connects an early de Sitter phase supported by the Euler anomaly to a scalaron regime, where the observable modes leave the horizon. Building on this known background connection, we compute the scalar and tensor spectra on the exact background and find that the anomaly corrections are controlled by $aN_*/(18b)$, where $a$ and $b$ are the Euler-anomaly and $R^2$ coefficients and $N_*$ the number of e-folds after the pivot exits the horizon; scalaron inflation is recovered as this parameter vanishes. The observed tilt at $N_*=60$ then requires only $b/a\simeq35$, rather than the $b/a\gtrsim10^9$ of early realizations. At this benchmark the scalar spectrum is redder than in scalaron inflation at fixed $N_*$, and the tensor-to-scalar ratio is about 17% lower at fixed tilt, a quantitative signature of the anomaly. For minimal gravitational reheating, $N_*\simeq53$, the tilt remains within $1\sigma$ of the Planck value for $b/a\gtrsim35$. In the de Sitter analysis, a finite range of the Weyl coupling excludes an extra real spin-two pole and keeps the causal response decaying. A companion paper gives the full analysis.

In the framework of Scalar-Tensor-Vector Gravity (STVG), this paper investigates the quasinormal modes and time-domain evolution of Reissner-Nordström Modified Gravity (MOG) black holes under massless scalar, electromagnetic, and gravitational perturbations. Quasinormal frequencies are calculated by extending the 3rd- to 6th-order WKB method and combining it with Padé approximation to the 13th order, while complete time-domain waveforms are obtained using a finite-difference method based on light-cone coordinates. The results indicate that increasing the MOG parameter $\alpha$ raises the effective mass of the black holes, leading to a decrease in the damping rate $|\omega_I|$ and a slower ringdown decay. An increase in charge $Q$ produces a similar effect, with the damping approaching zero in the near-extremal limit. Regarding the ringdown decay times for the three types of perturbations, the gravitational field has the longest duration, the electromagnetic field is intermediate, and the scalar field is the shortest. The oscillations and decay observed in the time-domain waveforms are qualitatively consistent with the frequency-domain results, and the power-law exponent governing the late-time tail aligns with that of asymptotically flat spacetimes. This study provides a systematic theoretical reference for testing modified gravity theories using black hole spectroscopy.

The Kerr stability conjecture has been proved in the slowly rotating case, i.e., $|a|\ll m$, in the sequence of works \cite{KS-GCM1} \cite{KS-GCM2} \cite{KS:Kerr} by Sergiu Klainerman and the author, \cite{GKS22} by Elena Giorgi, Sergiu Klainerman and the author, and \cite{Shen} by Dawei Shen, and extended in \cite{Sze}, by the author, to the full subextremal range $|a|<m$, thereby completing the proof of the Kerr stability conjecture. The proof in \cite{Sze} crucially relies on the two companion papers \cite{MaSz24} \cite{MaSz26} by Siyuan Ma and the author, in which we prove energy-Morawetz estimates respectively for the scalar wave equation and for Teukolsky equations on perturbations of Kerr with $|a|<m$. In addition, two results in \cite{Sze}, concerning the derivation of the Teukolsky wave-transport system in perturbations of Kerr and energy-Morawetz estimates for Teukolsky in the setting of \cite{Sze}, are stated without proofs. The goal of the present paper companion paper to \cite{Sze} is to provide the proof of these two results.

We uncover a connection between the classical limit of the Magnus expansion in quantum field theory and the Malvenuto-Reutenauer Hopf algebra of permutations. We study a cubic scalar theory describing a massive particle coupled to massless scalar quanta, which captures the propagator structure relevant to classical scattering in gravity and scalar QED. Using a Schwinger parametrisation of the massive propagators, we compute the classical limit of Magnus amplitudes at tree level in this theory. First, we prove that all hyperclassical contributions cancel at the level of the Schwinger proper-time integrand, before integration. Then, we show that the classical Magnus amplitude precisely matches expectations from worldline quantum field theory. Both results rely on cancellations of disconnected diagrams which we relate to the Hopf algebra, specifically to the action of the adjoint first Eulerian projector, which annihilates the shuffle products associated with disconnected contributions. Moreover, the worldline diagrams include generic directed-tree topologies, whereas the field-theory diagrams only include directed chains. The correspondence we establish between the two therefore leads to a new formula for generic Murua coefficients in terms of simpler directed chain coefficients. Finally, we observe a suggestive connection between Magnus amplitudes and the web-mixing matrices governing the exponentiation of multiple Wilson lines.

How do cosmological waveforms approximate waveforms from isolated systems for a small cosmological constant? This question is motivated by the observed small value of the cosmological constant, and also by Misner's idea to regulate the formally singular terms introduced into the Einstein equations by conformal compactification. We investigate this question quantitatively using scalar waves on Schwarzschild–de Sitter backgrounds. A suitable flat limit requires the foliation to remain regular at the future conformal boundary. We compare bridge foliations extending from the black hole horizon to the cosmological horizon with a regular asymptotically flat limit. Comparisons of cosmological and asymptotically flat waveforms on geometrically matched data show that the flat limit is numerically well behaved and recovers the essential features of the asymptotically flat waveform. We extend Misner's artificial cosmology by introducing a cosmological source that leaves the near-zone geometry unchanged and show that it improves agreement of the ringdown waveform but fails to capture the intermediate polynomial tail behavior accurately.

Combined baryon acoustic oscillation and cosmic microwave background data have begun to mildly favor departures from $\Lambda\mathrm{CDM}$. This is usually framed as 2-parameter dynamical dark energy. However, a 1-parameter "cosmic glitch in gravity" model, whose cosmological gravitational coupling differs from Newton's constant as in Hořava gravity, fits at least as well. $\textit{Planck}$+ACT+SPT and DESI~DR2 give $G_\mathrm{cosmo}/G_\mathrm{N}=0.9920\pm0.0025$, a $3.3\,\sigma$ preference for weaker cosmological gravity, robust to adding CMB lensing and supernovae. Fitted to the CMB alone, the glitch predicts DESI distances; $w_0w_a$CDM does not.

We study photon superradiant scattering by a Kerr black hole in the presence of an axion-photon coupling and investigate how this coupling modifies the electromagnetic amplification factor. We solve the coupled axion and electromagnetic equations in a fully relativistic framework. We distinguish two regimes according to the relation between the sourced axion frequency and the axion mass. In the radiative regime, the axion can propagate to spatial infinity and carry away energy, thereby suppressing photon amplification. In the subthreshold regime, the axion is confined by the mass barrier and exchanges energy with the black-hole horizon through quasibound-state excitations. In this regime, photon amplification can be either enhanced or suppressed, depending on whether the relevant axion modes satisfy the superradiance condition.

In the present paper, we extend the results in the sequence of works \cite{KS-GCM1} \cite{KS-GCM2} \cite{KS:Kerr} by Sergiu Klainerman and the author, \cite{GKS22} by Elena Giorgi, Sergiu Klainerman and the author, and \cite{Shen} by Dawei Shen from the slowly rotating regime $|a|\ll m$ to the full subextremal range $|a|<m$, thereby completing the proof of the Kerr stability conjecture. The restriction $|a|\ll m$ enters in fact only through the estimates for wave equations and for the Bianchi system established in \cite{GKS22}. To remove this restriction, we crucially rely on the two companion papers \cite{MaSz24} \cite{MaSz26} by Siyuan Ma and the author, in which we prove energy-Morawetz estimates respectively for the inhomogeneous scalar wave equation and for inhomogeneous Teukolsky equations on perturbations of Kerr with $|a|<m$. Additionally, some of the results of the present paper are proved in our companion paper \cite{Sze}.

We investigate generalized projective symmetry and its breaking in four-dimensional parity-even metric-affine gravity, considering an action linear in curvature and at most quadratic in torsion and nonmetricity. We derive the action of the generalized projective transformation on the irreducible components of the affine geometry and determine the coupling relations defining the axial, metric-trace, and fully projectively invariant theories. Complete invariance reduces the $12$ gravitational coefficients to a five-parameter family and generates four vectorial Noether identities for the connection equations. Projective invariance makes the connection operator singular, thus we develop a symmetry-adapted method for solving its vacuum field equations. We then analyze couplings to Dirac, electromagnetic, and complex Klein-Gordon fields. Locally exact axial-projective transformations correspond to chiral rotations for massless fermions at the classical level, while a combination of covectors acts as an Abelian connection linking a locally exact vector-projective representative to scalar $U(1)$ symmetry. Standard Maxwell theory is independent of the affine connection, whereas a torsion-dependent Maxwell-like extension can preserve both electromagnetic and projective invariance through compensating Stückelberg fields. Exact gravitational projective invariance makes the corresponding connection directions nondynamical and forces matter currents sourcing them to vanish. Controlled explicit breaking lifts these zero modes and converts them into auxiliary fields. Thus, projective symmetry provides a unified principle for identifying affine gauge modes, constraining matter couplings, and relating symmetry breaking in the gravitational sector to effective matter interactions.

We show that the space of vacuum initial data sets on a closed manifold often has many non-trivial homotopy groups. The starting point is a result of the second named author, which constructs non-trivial elements in the homotopy groups of the space of initial data sets satisfying the strict dominant energy condition, together with a later result in joint work with Bernd Ammann showing that these elements often persist when the strictness assumption is dropped. In this work, we use a parametrized version of the conformal method to show that these elements may also be represented by maps into the space of vacuum initial data sets. This requires two results that may be of independent interest: metrics admitting conformal Killing vectors can be removed from the space of metrics without changing its weak homotopy type, and over the remaining metrics the York decomposition can be carried out in families, the TT-tensors forming a trivial Hilbert bundle. To our knowledge, this is the first result on the global topology of this space.

We compute analytically greybody factors for d-dimensional large spherically symmetric black holes with Gauss-Bonnet corrections in the high frequency limit. Our calculations include both the eikonal limit, where the real part of the frequency of the scattered wave is much larger than the imaginary part, and the highly damped case,where the imaginary part of the frequency is much larger than the real part, addressing the emission of gravitons and test scalar fields, and yielding full transmission and reflection scattering coefficients. We consider tensorial, vectorial and scalar gravitational perturbations, obtaining the same result for the three cases in the highly damped limit, but not in the eikonal limit.

We study equilibrium configurations and linear perturbations of a Lorentz-violating Kalb–Ramond field with a quartic symmetry-breaking potential and a non-minimal Riemann coupling on a fixed Schwarzschild background. The electric equilibrium is determined algebraically by a characteristic function that can develop a finite-radius double root. Approaching this configuration, the electric monopole response scales as $|\widehat e(\omega,r_c)|\propto(\gamma_c-\gamma)^{-1/2}$, while the propagating monopole remains regular. For higher multipoles we obtain the exact axial zero-mode tower $\xi_{\ell n}=-(\ell+n+1)(\ell+n+2)/3$. At $\ell=1$ a complementary static mode gives a second low-frequency branch. Increasing the positive Riemann coupling causes two purely imaginary growing modes to collide and form an oscillatory unstable pair, with square-root real-part splitting. Independent numerical checks confirm that this behavior persists under changes of the equilibrium parameters. The corrected bare sign removes the monopole ghost, but a constrained high-momentum negative-energy direction remains on the asymptotically electric branch. We therefore distinguish the existence of classical growing modes from the stronger requirement of a positive-energy theory.

We investigate strong-field orbital dynamics for static spherically symmetric charged bumblebee black holes featuring spontaneous Lorentz-violating effects. Analysis of null and timelike circular geodesics yields the photon-sphere radius, the innermost stable circular orbit (ISCO) radius, and characteristic orbital frequencies for test particles. Within the relativistic precession model for high-frequency quasi-periodic oscillations (HFQPOs), observed twin-peak frequencies are governed by the full set of fundamental parameters $M$, $X=r/M$, $l_1$, $l_2$, and $Q_0/M$. Among them, $l_1$, $l_2$, and $Q_0/M$ enter frequency expressions only in combined forms, giving rise to intrinsic parameter degeneracy. An effective-parameter set $\Theta=(M,X,C,\beta)$ is accordingly introduced to characterize these composite contributions. Bayesian MCMC parameter inference is carried out using HFQPO observational data from three black-hole X-ray binaries: GRO J1655–40, XTE J1550–564, and GRS 1915+105. The 68% credible intervals of composite parameter $C$ all contain the Reissner–Nordström limit $C=1$, revealing no statistically significant net Lorentz-violating correction under our model assumptions. Distinct triples $(l_1,l_2,Q_0/M)$ yield identical QPO predictions, so HFQPO observations alone cannot disentangle Lorentz-violating and charge-related effects; precise constraints on these fundamental quantities require additional, more precise observational data.

In the context of a spatially flat FLRW background, we perform a symmetry classification of $k$-essence models with Lagrangian densities of the form $f_1(\phi)R+f_2(\phi,X)$. The kinetic term $X$ is introduced as an independent degree of freedom via a Lagrange multiplier, and the lapse function is treated as a dynamical variable. The symmetry analysis is applied to the constrained system prior to any gauge fixing. This approach reveals symmetries which otherwise are lost when the lapse is fixed at the level of the action. The derived families of $k$-essence models admitting nontrivial symmetries fall to two general classes: minimally coupled and nonminimally coupled theories to gravity. We use the corresponding Noetherian conservation laws to derive exact cosmological solutions. We find that, when the numerical value of the conserved charges is zero, the field equations reduce to an algebraic relation. We subsequently derive power-law expressions for the scale factor with exponents determined by the particular $k$-essence function.

The large-distance behaviour of a sandwich gravitational wave can be approximated by a continuous but not necessarily smooth profile, providing us with a simplified description of particle motion. Our approximate model is consistent with the Carroll symmetry. Our strategy is illustrated by the Poschl-Teller profile. The limits of the sandwich approximation are discussed.

We investigate the scattering and diffraction of scalar plane waves by static conformal anomaly black holes. We determine the truncation requirements for the partial-wave series (PWS) method at finite distances and compute the full waveforms, which display a clear diffraction pattern: on the negative $z$-axis the field reduces to the incident plane wave, while on the positive $z$-axis a distorted plane wave coexists with a scattered spherical wave, and a bright Poisson spot appears at $\theta=0$ surrounded by concentric diffraction rings. We obtain the on-axis intensity of the Poisson spot as a function of the radial coordinate. The intensity is most sensitive to the near-horizon geometry: close to the horizon it differs markedly from that of the RN black hole, whereas in the far field the two curves converge. We trace this to the metric functions, where different values of $f'(r_+)$ produce different phase increments that compress and shift the interference fringes, while the conformal anomaly correction falls off as $O(\tilde{\alpha}M^2/r^4)$. By analyzing the potential barrier we study the absorption cross section, and use the series reduction method to accelerate the PWS convergence for the differential scattering cross section. The low- and high-frequency absorption cross sections are strongly correlated with the $\ell=0$ and $\ell$-dependent parts of the potential barrier, respectively. The differential cross section and glory scattering arise mainly from scattering in a finite region excluding a small neighborhood of the outer horizon. Charge and $\tilde{\alpha}$ have opposite effects on the width of the glory peak but the same effect on its height.

We construct spherically symmetric thin shells in unimodular gravity (UG) and analyze their dynamical stability under radial, symmetry-preserving perturbations. We use the UG junction conditions and adopt non-conservative charged exterior solutions sourced by a radial electric field. As an application, we build charged vacuum bubbles: a Minkowski interior surrounded by a charged thin shell and matched to an exterior UG geometry. The resulting spacetimes are free of event horizons and central singularities, while in de Sitter-like cases a cosmological horizon may exist outside the shell. We compare the stability regions and the matter content with their counterparts in general relativity, finding some differences controlled by the UG non-conservation parameter. This work extends previously published results.

The Dirac equation in stationary curved spacetime implies that describing two-flavor neutrino oscillations requires treating the invariant mass and conserved energy of each propagating state distinctly, as gravity affects energy differently than mass. By re-analysing the publicly released KamLAND dataset, we show that modeling flavor states of massless neutrinos as two-level quantum states with energy-dependent level splitting, analogous to modified Jaynes-Cummings models, results in a higher-likelihood fit to the observed data than the standard massive-neutrino paradigm.

We construct the complete spectrum of gravitational total-transmission modes (TTMs) of Kerr black holes and find four globally continuous families, $n_\infty=1,2,3,4$, each with two complex-conjugate frequency branches. Compared with the three-family classification of Cook and Lu, our global continuation resolves the mirror-related sectors of their $n=2$ family into separate families without introducing additional symmetry-unrelated roots. This organization distinguishes complex conjugation at fixed $m$ from the mirror symmetry connecting the $m$ and $-m$ spectra. The $n_\infty=3$ family approaches the Schwarzschild algebraically special frequency, whereas the $n_\infty=1,2,$ and $4$ families diverge as $\omega\propto a^{-4/3}$ along lower-half-plane directions $-150^\circ$, $-90^\circ$, and $-30^\circ$, respectively. High-precision data up to $\ell=32$ confirm the Cook–Lu small-spin asymptotics and reveal how the divergent branches are embedded in the global four-family spectrum, with a family-dependent relation between the spherical-limit angular labels and the large-$|a\omega|$ ordering. For axisymmetric perturbations, the $n_\infty=2$ and $n_\infty=3$ branches coalesce at genuine exceptional points, where the scattering spectral function develops a second-order zero and the TTM excitation factors are strongly enhanced, offering a different interpretation of the structure previously described by Cook and Lu as an overtone-multiplet splitting. Finally, we identify a previously unreported anomalous proximity between the $n_\infty=3$ TTM family and an unconventional Kerr quasinormal-mode sequence, with frequency separations reaching order $10^{-8}$ in the representative case studied.

We present the results of MADGRAV, a deep-learning-based search for high-mass compact binary coalescences, applied to the data collected by the LIGO interferometers during the third observing run and during the first and second part of the fourth observing run. The MADGRAV pipeline consists of a series of sequential convolutional neural networks that perform anomaly detection, glitch classification, coherence testing, and signal ranking. Data from the Hanford and Livingston LIGO detectors are studied (both individually and in coherence) by way of 1 second Q-transform windows. Of the candidates that survive every stage of the pipeline, 48 reach the significance threshold, and we report 47 gravitational wave detections characterised by a false alarm rate below $1\,{\rm yr}^{-1}$ with a probability of astrophysical origin $p_{\rm astro}>0.9$. Of the 47 detections, 44 are shared with the minimally modelled coherent WaveBurst search. The observed total source-frame masses, extracted from official gravitational wave transient catalogues, are in the $14-236 M_{\odot}$ range with a median of $69 M_{\odot}$, and a median SNR of 16. We note that the recovered fraction of confident detections rises with mass: for LIGO detectors network SNR $>10$ the pipeline recovers $8.1\%$ of confident catalog events below $30 M_{\odot}$, $39.8\%$ between $30$ and $100 M_{\odot}$, and $53.3\%$ above $100 M_{\odot}$, corresponding to $33.3\%$, $45.5\%$ and $53.3\%$ of the events detected by coherent WaveBurst in the same bins. These results suggest that anomaly detection pipelines can serve as an independent detection channel complementary to matched filtering in the high-mass high-SNR regime.

Regular black holes (RBHs) and horizonless black hole mimickers (BHMs) are often studied as stationary alternatives to classical black holes, although their interiors may be unstable or undergoing relaxation. We investigate the phenomenological consequences of this evolution by numerically evolving linear scalar perturbations on prescribed, time-dependent Hayward-like geometries. We consider BHM–RBH–BHM histories in which an initially horizonless object temporarily develops a trapped region before returning to a horizonless configuration, through either a single bounce or a sequence of repeated bounces. Using horizon-penetrating Painlevé–Gullstrand coordinates, we follow the perturbations through the formation and disappearance of trapping horizons and compute the resulting waveforms and scalar-field energy. For histories with identical initial and final geometries, we find that changing the duration of the intermediate regular black hole phase produces differences in the amplitude and phase of the late-time signal, including its echoes. Longer trapped phases also yield greater energy amplification, consistent with the blueshift of outgoing modes near the inner trapping horizon. These results show that the late-time response of a dynamically relaxing BHM need not be determined by its final configuration alone: it can retain a memory of the dynamical history of its interior.

Extending a previous work on the energy-momentum tensor of the linearized gravitational field in Minkowski background, conserved currents in linearized gravity associated with Lorentz transformations, dilatations and special conformal transformations are explored in the framework of Lagrangian field theory. Both outstanding special cases and general parametric families of currents are considered. Regarding the former, the distinguished energy-momentum tensor $T_{\mathrm{lg}}^{ab}$ we found earlier, guided by similarities between linearized gravity and electrodynamics, is supplemented with an angular momentum tensor $M_{\mathrm{lg}}^{abc}$ and a dilatation current $D_{\mathrm{lg}}^a$, associated with Lorentz and dilatation symmetries. Concerning special conformal transformations, a generalization of Noether's theorem that is useful if additional conditions (such as gauge fixing conditions) are imposed is formulated, it is shown that special conformal transformations are Noether symmetries of linearized gravity in the generalized harmonic gauges, and a special conformal tensor $C_{\mathrm{lg}}^{ab}$, accompanying $T_{\mathrm{lg}}^{ab}$, is obtained using the generalized Noether's theorem. The angular momentum tensor, dilatation current and special conformal tensor accompanying two other notable energy-momentum tensors are discussed as well. General multi-parameter families of $M^{abc}$, $D^a$ and $C^{ab}$ tensors accompanying a general family of energy-momentum tensors, which was found earlier and includes canonical energy-momentum tensors, are also determined, and local balance equations that are relevant if matter is present are derived for them. Their members do not depend on higher than first derivatives of the linearized metric.

We investigate the propagation properties and canonical gauge structure of Generalised Non-Linear Electrodynamics (GNLED) in the presence of a non-dynamical background field. Starting from the quadratic photon sector of the theory, we perform a field redefinition that converts the background-induced derivative coupling into a mass-like contribution characterized by the vector \(V_\mu=\partial_\mu\alpha/\alpha\) where $\alpha= \sqrt{\left.\frac{\partial\mathcal{L}}{\partial \mathcal{F}}\right|_B}$. For a constant background, we derive the corresponding dispersion relation and show that, for a purely space-like \(V_\mu\), the propagating mode obeys \(\omega^2=\|\vec k\|^2+\|\vec V\|^2\), defining an effective mass scale \(m_{\rm eff}=|\vec{V}|\) and a finite rest frequency. The resulting phase and group velocities exhibit the characteristic dispersive behaviour of a gapped mode, with subluminal group velocity and superluminal phase velocity. We then construct the propagator and show that the massive pole resides in the transverse sector, while the longitudinal singularity is associated with gauge fixing. A complete Hamiltonian analysis yields two first-class constraints and only two physical degrees of freedom, demonstrating that the effective mass does not introduce an additional polarisation. The associated gauge transformation is a deformed Abelian \(U(1)\) symmetry. Finally, we show that the Hamiltonian is positive definite for purely space-like backgrounds.

We argue that the local violation of null energy condition at the throat of a traversable wormhole does not necessarily indicate that the total volume integrated null energy contribution is negative. It is already known that it can be arbitrarily close to zero. We show that it can even be positive and use this argument to reconstruct a family of wormhole geometries. We also propose a novel classification of traversable wormholes based on the global volume integrated measure of null energy condition.

We study classical solutions of a scalar field with quartic potential in de Sitter space-time. Using the ansatz $\phi=F(X\cdot\xi)$, via embeding coordinate $X_\alpha$ of the ambiend space we find several families of analytic solutions classified by the causal character of the constant vector $\xi$. For time-like $\xi$, the solutions are globally regular and describe either global oscillations around a minimum or global vacuum transition; for space-like $\xi$, they are singular in the global patch but regular in the open slicing. In the Poincaré patch they correspond to contracting bubbles. We compute the classical actions of these solition which are finite only in spacetime dimensions $D \le 5$. We show that the $D=4$ global vacuum transition solution has the radiation equation of state $w=1/3$. In $D=4$ global vacuum transition solution, the retarded Green's function acquires a growing tail as compared to the Green's function on top of vacuum, implying that the transition amplifies the signal at late times.

We investigate the potential of future observations of the Dark Ages 21 cm power spectrum to probe the scale dependence of the primordial power spectrum and distinguish between inflationary models. We find that the Dark Ages 21 cm power spectrum can serve as a powerful probe of inflationary physics on scales beyond the reach of current CMB observations. While models predicting nearly identical running spectral indices may remain difficult to distinguish even with future 21 cm observations, models with unconventional scale dependence can be stringently tested. We further show that combining 21 cm observations with CMB data can significantly improve the constraints, even for a moderate observational configuration. We examine the impact of the choice of pivot scale on the resulting constraints.