arXiv subjects

Anthony Lasenby

Publications and source records attributed to Anthony Lasenby.

At least 19 recordsLinked to original sources

arXiv2026

Bessel-Hagen currents for linearised Weyl-squared gravity

We consider the Bessel-Hagen construction for linearised Weyl-squared gravity, whose action depends on the metric perturbation $h_{μν}$ through the linearised Weyl tensor $C^{(1)}_{μνρσ}$. This provides a curvature-based comparison with the Fierz-Pauli theory, in which the action contains first derivatives of $h_{μν}$ whereas the first local gauge-invariant field strength contains two, and the construction determines a gauge-invariant class of Noether currents without selecting a preferred gauge-invariant local energy-momentum tensor. Since the Weyl tensor is the irreducible spin-2 part of the curvature, it is of particular interest to ask whether an action built from it admits a local representative analogous to the Maxwell tensor. We show that the Bessel-Hagen construction extends to the conformal group, acting on the fields on a fixed Minkowski background, and yields a gauge-invariant conserved-current class for each generator. Nonetheless, no nonzero local, polynomial, symmetric rank-two tensor of mass dimension four, quadratic in $h_{μν}$ and with constant dimensionless coefficients and no explicit coordinate dependence, is both strictly invariant under the linearised diffeomorphism and Weyl gauge symmetries and conserved on the Bach shell. The gauge symmetries restrict such a tensor to depend on $C^{(1)}$ and its derivatives, while the dimension and field degree permit only terms quadratic in $C^{(1)}$ without further derivatives. Four-dimensional Weyl identities then reduce all candidates to pure traces, whose conservation requires their coefficients to vanish. Thus, building the action from a gauge-invariant curvature does not recover the electromagnetic result. A first-order gauge-covariant field strength may provide a route to such a representative, although its presence alone is not sufficient.

gr-qc↗

arXiv2026

Bessel-Hagen currents, reducibility charges, and local gravitational energy

We consider whether the translation Noether current of a linearised metric spin-2 theory admits a strictly gauge-invariant local representative. For Fierz-Pauli and dynamically regular pure curvature-squared theories in four dimensions, we show that no such representative exists under the stated locality, polynomiality and covariance assumptions. A direct enumeration first excludes nonzero symmetric rank-two tensors at the dimension and derivative order of the quadratic action: in the curvature-squared case, the parity-even conservation kernel consists of the identically vanishing Lanczos--Lovelock combination, while both parity-odd coefficients vanish. Homogeneity of the actions in total derivative number then allows projection by field degree and derivative number, extending the exclusion to all finite-order local polynomial representatives with constant coefficients and no explicit coordinate dependence. The translation current nevertheless defines a nonzero conserved-current class. Independently, a constant translation is a Killing reducibility parameter of the linearised gauge symmetry and determines a nonzero linear surface-charge class, which is distinct from the quadratic energy current. A separate calculation shows why a direct compensator cancellation available in Maxwell theory fails for the metric spin-2 field, although this calculation is not needed for the current-class result. Maxwell theory, propagating free $p$-forms and Yang--Mills theory linearised about the trivial vacuum provide comparisons in which translations are not reducibility parameters and strictly gauge-invariant stress tensors exist. Gauss--Bonnet and pure flat-space $R^2$ gravity lie outside the regular scope of the result, through variational triviality and dynamical degeneracy, respectively.

gr-qc↗

arXiv2026

Internal translation gauging and local gravitational energy in Weyl gauge theory

We investigate the local gravitational source and charges obtained by introducing translations as an internal Stückelberg redundancy in Weyl gauge theory. The internal-$T(4)$-invariant dressed coframe identifies the source of the translational potential with the existing coframe variational derivative, without introducing new dynamics. We derive an excitation/source equation and balance law whose structure is independent of the constitutive parameters of the parity-even quadratic torsion family. The gravitational self-current, defined relative to a specified gravitational/matter split and boundary representative, gives a density invariant under the internal gauge factors once its frame index is contracted with the coframe; this invariance neither establishes ordinary conservation nor identifies the density with the external translation Noether current. A surface charge follows by contraction with a covariantly constant internal direction, and we separately derive the three-sector Noether superpotential of generalized reducibility, with the asymptotic conditions for conservation of its flux. At the teleparallel equivalent of general relativity (TEGR) the excitation reduces to the teleparallel superpotential and the covariant coframe--connection pair gives the Schwarzschild ADM energy; flat cosmology and transverse-traceless waves give further checks. Away from TEGR, an exact solution of New General Relativity gives a charge whose fractional difference from the Kepler mass is half the deviation of the post-Newtonian spatial-curvature parameter from unity, at the adopted normalisation; independent Hamiltonian charge matching remains open. Finally, the integrable Hamiltonian charge is invariant under covariant Lagrangian boundary terms at fixed reference normalisation and presymplectic representative.

gr-qc↗

arXiv2026

Numerical polology: towards next-generation model-building for cosmology

The dark sector need not be restricted to simple field content. Indeed, simple bosonic configurations, such as scalar-tensor or dark photon models, contrast with the much richer picture painted by many ultraviolet scenarios. Polology is the study of propagator poles, which correspond to particle states in any given theory. We outline a numerical polology framework for discovering perturbative, ghost-free models with consistent interactions, which produces theoretical model priors by sampling the coupling space. The method is tested on tensor field theories of up to rank three. Subsequent observational constraint pipelines are illustrated for black hole superradiance (M33 X-7), dynamical dark energy (DESI DR2, Pantheon and SH0ES) and gravitational waves (GWTC-3).

astro-ph.CO↗

arXiv2026

Bessel-Hagen currents for the Fierz-Pauli action

For electromagnetism in Minkowski spacetime, the Bessel-Hagen method gives a particularly direct Noetherian derivation of the standard gauge-invariant energy-momentum tensor. The key step is to supplement the form variation generated by an infinitesimal coordinate transformation with a compensating electromagnetic gauge transformation. In this paper we ask whether the same idea can be applied to the massless spin-2 field described by the Fierz-Pauli action. We first prove that no nonzero local tensor quadratic in first derivatives of the symmetric field $h_{μν}$ can be strictly invariant under the spin-2 gauge transformation $h_{μν}\mapsto h_{μν}+\partial_μξ_ν+\partial_νξ_μ$; the direct electromagnetic analogue of the Bessel-Hagen construction therefore cannot exist. Once the inexact nature of the Fierz-Pauli gauge symmetry is treated correctly, however, the Bessel-Hagen construction does produce a gauge-invariant equivalence class of Noether currents. Changing the compensating spin-2 gauge parameter changes the current only by terms proportional to the Fierz-Pauli field equations; performing an independent spin-2 gauge transformation on $h_{μν}$ changes the current only by a trivial current given by the divergence of an antisymmetric superpotential plus field-equation terms. This provides the natural spin-2 analogue of Bessel-Hagen's electromagnetic construction, but only in the quotient space of conserved currents, and not as a preferred local gauge-invariant energy-momentum tensor.

gr-qc↗

arXiv2025

The radial metric function does not identify null surfaces

We investigate the conditions under which a hypersurface becomes null through the use of coordinate transformations. We demonstrate that, in static spacetimes, the correct criterion for a surface to be null is $g_{tt} = 0$, rather than $g^{rr} = 0$, in agreement with the results of Vollick. We further show that, if a Kruskal-like coordinate exists, the proxy condition $g^{rr} = 0$ is equivalent to $g_{tt} = 0$ if $\partial_r g_{tt} \neq 0$ and both $g^{rr}$ and $g_{tt}$ vanish at the same rate near the horizon. Our method extends naturally to axisymmetric stationary spacetimes, for which we demonstrate that the condition $\det\big(h_{ab}\big) = 0$ for the induced metric on a null hypersurface is recovered. By contrast with the induced metric approach, our method provides a physical perspective that connects the general null condition with its underlying relationship to photon geodesics.

gr-qc↗

arXiv2025

Every Poincaré gauge theory is conformal: a compelling case for dynamical vector torsion

The Poincaré gauge theory (PGT) of gravity provides a viable formulation of general relativity (Einstein-Cartan theory), and a popular model-building framework for modified gravity with torsion. Notoriously, however, the PGT terms which propagate vector torsion lead to strongly-coupled ghosts: the modern view is that only scalar torsion can propagate. To fix this, we revisit the concept of embedding explicit mass scales in scale-invariant theories, showing how the Klein-Gordon theory naturally leads to a slowly-rolling inflaton. We then show that the unique scale-invariant embedding of PGT leads to two new terms, one of which is the Maxwell term for vector torsion. We provide the full spectrum of quantum particles in the resulting theory. Our result means that every PGT is conformal and - after a two-decade hiatus - vector torsion is back on the menu.

hep-th↗

arXiv2024

Buchdahl bound, photon ring, ISCO and radial acceleration in Einstein-æther theory

Spherically symmetric Einstein-æther (EÆ) theory with a Maxwell-like kinetic term is revisited. We consider a general choice of the metric and the æther field, finding that:~(i) there is a gauge freedom allowing one always to use a diagonal metric; and~(ii) the nature of the Maxwell equation forces the æther field to be time-like in the coordinate basis. We derive the vacuum solution and confirm that the innermost stable circular orbit (ISCO) and photon ring are enlarged relative to general relativity (GR). Buchdahl's theorem in EÆ theory is derived. For a uniform physical density, we find that the upper bound on compactness is always lower than in GR. Additionally, we observe that the Newtonian and EÆ radial acceleration relations run parallel in the low pressure limit. Our analysis of EÆ theory may offer novel insights into its interesting phenomenological generalization: Æther--scalar--tensor theory (ÆST).

gr-qc↗

arXiv2023

Manifestly covariant variational principle for gauge theories of gravity

A variational principle for gauge theories of gravity is presented, which maintains manifest covariance under the symmetries to which the action is invariant, throughout the calculation of the equations of motion and conservation laws. This is performed by deriving explicit manifestly covariant expressions for the Euler--Lagrange variational derivatives and Noether's theorems for a generic action of the form typically assumed in gauge theories of gravity. The approach is illustrated by application to two scale-invariant gravitational gauge theories, namely Weyl gauge theory (WGT) and the recently proposed `extended' Weyl gauge theory (eWGT), where the latter may be considered as a novel gauging of the conformal group, but the method can be straightforwardly applied to other theories with smaller or larger symmetry groups. The approach also enables one easily to establish the relationship between manifestly covariant forms of variational derivatives obtained when one or more of the gauge field strengths is set to zero either before or after the variation is performed. This is illustrated explicitly for both WGT and eWGT in the case where the translational gauge field strength (or torsion) is set to zero before and after performing the variation, respectively.

gr-qc↗

arXiv2022

Conformally-rescaled Schwarzschild metrics do not predict flat galaxy rotation curves

For conformally invariant gravity theories defined on Riemannian spacetime and having the Schwarzschild--de-Sitter (SdS) metric as a solution in the Einstein gauge, we consider whether one may conformally rescale this solution to obtain flat rotation curves, such as those observed in galaxies, without the need for dark matter. Contrary to recent claims in the literature, we show that if one works in terms of quantities that can be physically measured, then in any conformal frame the trajectories followed by `ordinary' matter particles are merely the timelike geodesics of the SdS metric, as one might expect. This resolves the apparent frame dependence of physical predictions and unambiguously yields rotation curves with no flat region. We also show that attempts to model rising rotation curves by fitting the coefficient of the quadratic term in the SdS metric individually for each galaxy are precluded, since this coefficient is most naturally interpreted as proportional to a global cosmological constant. We further extend our analysis beyond static, spherically-symmetric systems to show that the invariance of particle dynamics to the choice of conformal frame holds for arbitrary metrics, again as expected. Moreover, we show that this conclusion remains valid for conformally invariant gravity theories defined on more general Weyl--Cartan spacetimes, which include Weyl, Riemann--Cartan and Riemannian spacetimes as special cases.

gr-qc↗

arXiv2022

Nested sampling for physical scientists

We review Skilling's nested sampling (NS) algorithm for Bayesian inference and more broadly multi-dimensional integration. After recapitulating the principles of NS, we survey developments in implementing efficient NS algorithms in practice in high-dimensions, including methods for sampling from the so-called constrained prior. We outline the ways in which NS may be applied and describe the application of NS in three scientific fields in which the algorithm has proved to be useful: cosmology, gravitational-wave astronomy, and materials science. We close by making recommendations for best practice when using NS and by summarizing potential limitations and optimizations of NS.

stat.CO↗

arXiv2022

Split personalities in Bayesian Neural Networks: the case for full marginalisation

The true posterior distribution of a Bayesian neural network is massively multimodal. Whilst most of these modes are functionally equivalent, we demonstrate that there remains a level of real multimodality that manifests in even the simplest neural network setups. It is only by fully marginalising over all posterior modes, using appropriate Bayesian sampling tools, that we can capture the split personalities of the network. The ability of a network trained in this manner to reason between multiple candidate solutions dramatically improves the generalisability of the model, a feature we contend is not consistently captured by alternative approaches to the training of Bayesian neural networks. We provide a concise minimal example of this, which can provide lessons and a future path forward for correctly utilising the explainability and interpretability of Bayesian neural networks.

stat.ML↗

arXiv2022

Some recent results for $SU(3)$ and Octonions within the Geometric Algebra approach to the fundamental forces of nature

Different ways of representing the group $SU(3)$ within a Geometric Algebra approach are explored. As part of this we consider characteristic multivectors for $SU(3)$, and how these are linked with decomposition of generators into commuting bivectors. The setting for this work is within a 6d Euclidean Clifford Algebra. We then go on to consider whether the fundamental forces of particle physics might arise from symmetry considerations in just the 4d geometric algebra of spacetime -- the STA. As part of this, a representation of $SU(3)$ is found wholly within the STA, involving preservation of a bivector norm. We also show how Octonions can be fully represented within the Spacetime Algebra, which we believe will be useful in making them understandable and accessible to a new community in Physics and Engineering. The two strands of the paper are drawn together in showing how preserving the octonion norm is the same as preserving the timelike part of the Dirac current of a particle. This suggests a new model for the symmetries preserved in particle physics. Following on from work by Günaydin and Gürsey on the link between quarks, and octonions, and by Furey on chains of octonionic multiplications, we show how both of these fit well within our scheme, and give some wholly STA versions of the operations involved, which in the cases considered have easily understandable equivalents in terms of 4d geometry. Links with larger groups containing $SU(3)$, such as $G_2$ and $SU(8)$, are also considered.

physics.gen-ph↗

arXiv2022

Note on the absence of the second clock effect in Weyl gauge theories of gravity

We reconsider the status of the so-called second clock effect in Weyl gauge theories of gravity, which are invariant both under local Poincaré transformations and local changes of scale. In particular, we revisit and extend our previous demonstration that the second clock effect does not occur in such theories, in order both to clarify our argument and confirm our original findings in response to recent counterclaims in the literature.

gr-qc↗

arXiv2022

Fresh perspective on gauging the conformal group

We consider the construction of gauge theories of gravity that are invariant under local conformal transformations. We first clarify the geometric nature of global conformal transformations, in both their infinitesimal and finite forms, and the consequences of global conformal invariance for field theories, before reconsidering existing approaches for gauging the conformal group, namely auxiliary conformal gauge theory and biconformal gauge theory, neither of which is generally accepted as a complete solution. We then demonstrate that, provided any matter fields belong to an irreducible representation of the Lorentz group, the recently proposed extended Weyl gauge theory (eWGT) may be considered as an alternative method for gauging the conformal group, since eWGT is invariant under the full set of local conformal transformations, including inversions, as well as possessing conservation laws that provide a natural local generalisation of those satisfied by field theories with global conformal invariance, and also having an `ungauged' limit that corresponds to global conformal transformations. By contrast, although standard Weyl gauge theory also enjoys the first of these properties, it does not share the other two, and so cannot be considered a valid gauge theory of the conformal group.

gr-qc↗

arXiv2021

Conformal gravity does not predict flat galaxy rotation curves

We reconsider the widely held view that the Mannheim--Kazanas (MK) vacuum solution for a static, spherically-symmetric system in conformal gravity (CG) predicts flat rotation curves, such as those observed in galaxies, without the need for dark matter. This prediction assumes that test particles have fixed rest mass and follow timelike geodesics in the MK metric in the vacuum region exterior to a spherically-symmetric representation of the galactic mass distribution. Such geodesics are not conformally invariant, however, which leads to an apparent discrepancy with the analogous calculation performed in the conformally-equivalent Schwarzschild-de-Sitter (SdS) metric, where the latter does not predict flat rotation curves. This difference arises since the mass of particles in CG must instead be generated dynamically through interaction with a scalar field. The energy-momentum of this required scalar field means that, in a general conformal frame from the equivalence class of CG solutions outside a static, spherically-symmetric matter distribution, the spacetime is not given by the MK vacuum solution. A unique frame does exist, however, for which the metric retains the MK form, since the scalar field energy-momentum vanishes despite the field being non-zero and radially dependent. Nonetheless, we show that in both this MK frame and the Einstein frame, in which the scalar field is constant, massive particles follow timelike geodesics of the SdS metric, thereby resolving the apparent frame dependence of physical predictions and unambiguously yielding rotation curves with no flat region. We also comment on how our analysis resolves the long-standing uncertainty regarding gravitational lensing in the MK metric. (Abridged)

gr-qc↗

arXiv2020

Weyl gauge theories of gravity do not predict a second clock effect

We consider Weyl gauge theories of gravity (WGTs), which are invariant both under local Poincaré transformations and local changes of scale. Such theories may be interpreted as gauge theories in Minkowski spacetime, but their gravitational interactions are most often reinterpreted geometrically in terms of a Weyl--Cartan spacetime, in which any matter fields then reside. Such a spacetime is a straightforward generalisation of Weyl spacetime to include torsion. As first suggested by Einstein, Weyl spacetime is believed to exhibit a so-called second clock effect, which prevents the existence of experimentally observed sharp spectral lines, since the rates of (atomic) clocks depend on their past history. The prevailing view in the literature is that this rules out WGTs as unphysical. Contrary to this viewpoint, we show that if one adopts the natural covariant derivative identified in the geometric interpretation of WGTs, properly takes into account the scaling dimension of physical quantities, and recognises that Einstein's original objection requires the presence of massive matter fields to represent atoms, observers and clocks, then WGTs do not predict a second clock effect.

gr-qc↗

arXiv2020

Compromise-free Bayesian neural networks

We conduct a thorough analysis of the relationship between the out-of-sample performance and the Bayesian evidence (marginal likelihood) of Bayesian neural networks (BNNs), as well as looking at the performance of ensembles of BNNs, both using the Boston housing dataset. Using the state-of-the-art in nested sampling, we numerically sample the full (non-Gaussian and multimodal) network posterior and obtain numerical estimates of the Bayesian evidence, considering network models with up to 156 trainable parameters. The networks have between zero and four hidden layers, either $\tanh$ or $ReLU$ activation functions, and with and without hierarchical priors. The ensembles of BNNs are obtained by determining the posterior distribution over networks, from the posterior samples of individual BNNs re-weighted by the associated Bayesian evidence values. There is good correlation between out-of-sample performance and evidence, as well as a remarkable symmetry between the evidence versus model size and out-of-sample performance versus model size planes. Networks with $ReLU$ activation functions have consistently higher evidences than those with $\tanh$ functions, and this is reflected in their out-of-sample performance. Ensembling over architectures acts to further improve performance relative to the individual BNNs.

stat.ML↗