arXiv subjects

David Sloan

Publications and source records attributed to David Sloan.

At least 19 recordsLinked to original sources

arXiv2026

Towards a Connection Formulation of Action-Dependent Palatini Gravity

Previous work has shown that first-order Palatini gravity may be cast as a non-conservative Herglotz Lagrangian field theory, which excludes the conformal mode from its space of dynamical variables. In the present work, we analyse the role of the $SO(1,3)$ gauge connection in the construction of this action-dependent theory. The connection may be algebraically decomposed into complementary sectors which we interpret as `shape' and `scale' components. Only the former is retained within the Herglotz theory, while the latter is incorporated into the action-dependent sector. It is shown that the choice of connection decomposition is a space that can be smoothly parameterised. Such an observation leads to the finding that there exists a `moduli space of frictional field theories', in which each point corresponds to a distinct algebraic splitting of the connection into shape and scale pieces. Movement within the moduli space transitions between Herglotz Lagrangians whose on-shell dynamics all reproduce first-order Palatini gravity. The distinction lies in how the reproduction of the scale dynamics of the original theory is partitioned between action dependence and dynamical torsion.

gr-qc↗

arXiv2026

Classical General Relativity as a Non-Conservative Action-Dependent Field Theory

Previous work has provided the mathematical framework within which to analyse dynamical similarities for classical theories of fields. This formalism has been extended to those theories which, in addition to scaling symmetries, also possess gauge degrees of freedom. In this article, we apply these ideas to the analysis of the first-order Palatini formulation of General Relativity. It is shown that the conformal mode of the spacetime metric may be identified as the generator of a dynamical similarity. Further, we demonstrate that the dynamical content of the Hilbert-Palatini action may be reformulated in terms of an action-dependent field theory, which makes no reference to the conformal mode. Finally, we consider the linearised limit of the equations of motion derived from the scale-reduced action. We find that, in the harmonic gauge, the first-order metric perturbations satisfy a free wave equation, as expected. However, the elimination of the conformal factor requires a qualitative reinterpretation of the physics at second order. Conventionally, one considers the second-order perturbations to be sourced by quadratic combinations of first-order terms. These are packaged into an object identified as an `effective stress-energy tensor'. This interpretation must be amended for the action-dependent theory, where the presence of terms that couple the action sector with the geometrical degrees of freedom shows that our construction is inherently non-conservative.

gr-qc↗

arXiv2026

Constrained Symplectic and Contact Hamiltonian Systems: A Review

Singular theories, characterised by the presence of degeneracies in their Lagrangian or Hamiltonian descriptions, require the systematic implementation of constraints in order to obtain well-defined dynamics. While the symplectic framework provides the standard geometrical setting for conservative mechanical systems, those theories which exhibit dissipative effects are most appropriately discussed within the context of contact geometry. In this review, we present the geometrical structure underlying pre-symplectic and pre-contact manifolds, and develop the corresponding constraint algorithms that determine the admissible subset of phase space upon which consistent Hamiltonian evolution exists. We then close the discussion of each of the constraint algorithms with an example.

math-ph↗

arXiv2025

Systematically Evaluating Equivalent Purpose for Digital Maps

Digital geographic maps remain largely inaccessible to blind and low-vision individuals (BLVIs), despite global legislation adopting the Web Content Accessibility Guidelines (WCAG). A critical gap exists in defining "equivalent purpose" for maps under WCAG Success Criterion 1.1.1, which requires that non-text content provide a text alternative that serves the "equivalent purpose". This paper proposes a systematic framework for evaluating map accessibility, called the Map Equivalent-Purpose Framework (MEP Framework), defining purpose through three items (Generalized, Spatial Information, and Spatial Relationships), and establishing 15 measurable criteria for equivalent information communication. Eight text map representations were evaluated against visual map baselines using the proposed MEP Framework. Results show that legacy methods such as tables and turn-by-turn directions fail to meet the MEP Framework criteria, while Audiom Maps, Multi User Domain (MUD) Maps, and Audio Descriptions meet the criteria. The evaluation highlights the necessity of holistic, systematic approaches to ensure non-visual maps convey all generalized spatial information and relationships present in visual maps. The MEP Framework provides a replicable methodology for comprehensively assessing digital map accessibility, clarifying WCAG's "equivalent purpose", and guiding compliant and usable map creation. Compliant maps will support BLVIs' participation in map-dependent professions and civic engagement.

cs.HC↗

arXiv2025

Gauge Symmetries, Contact Reduction, and Singular Field Theories

The symmetry reduction of dynamical systems that are invariant under changes of global scale is well-understood for classical theories of particles, and fields. The excision of the superfluous degree of freedom generating such rescalings leads to a dynamically-equivalent theory, which is frictional in nature. In this article, we extend the formalism to physical models, of both particles and fields, described by singular Lagrangians. In order to work with a finite-dimensional (velocity) phase space, our construction requires that we treat classical field theories within the De Donder-Weyl formalism, in which a multisymplectic structure is introduced on the first jets of the bundle of fields. The results obtained are subsequently applied to a number of physically-motivated examples, as well as a discussion presented on the implications of our work for classical General Relativity.

gr-qc↗

arXiv2025

Dynamical Similarity in Multisymplectic Field Theory

Symmetry under a particular class of non-strictly canonical transformation may be used to identify, and subsequently excise degrees of freedom which do not contribute to the closure of the algebra of dynamical observables. Such redundant degrees of freedom may physically be identified with empirically-inaccessible measures of global scale. In this article, we present a mathematical framework which extends the symmetry reduction procedure to theories of classical fields, in both the Lagrangian and Hamiltonian settings. In order to maintain Lorentz covariance, while simultaneously working with a finite-dimensional phase space, we employ the De Donder-Weyl formalism, for which the natural description is formulated in terms of the fibered manifolds of multisymplectic geometry. We subsequently analyse a number of simple examples, and provide a discussion of the broader implications of our construction.

hep-th↗

arXiv2025

Dynamical Similarity in Higher-Order Classical Symplectic Systems

Many theories of physical interest, which admit a Hamiltonian description, exhibit symmetries under a particular class of non - strictly canonical transformation, known as dynamical similarities. The presence of such symmetries allows a reduction process to be carried out, eliminating a single degree of freedom from the system, which we associate with an overall scale. This process of `contact reduction' leads to theories of a frictional nature, in which the physically-observable quantities form an autonomous subsystem, that evolves in a predictable manner. We demonstrate that this procedure has a natural generalisation to theories of higher order; detailed examples are provided, and physical implications discussed.

math-ph↗

arXiv2024

Dynamical Similarity in Field Theories

In previous work I have shown that Herglotz actions reproduce the dynamics of classical mechanical theories which exhibit dynamical similarities. Recent work has shown how to extend field theories in both the Lagrangian and de Donder-Weyl formalism to contact geometry. In this article I show how dynamical similarity applies in field theory. This is applied in both the Lagrangian and Hamiltonian frameworks, producing the contact equivalents. The result can be applied to general relativity where I demonstrate how to construct a complete description of the dynamics, equivalent to those derived from the Einstein-Hilbert action, without reference to the conformal factor.

physics.class-ph↗

arXiv2024

Continuation of Bianchi Spacetimes Through The Big Bang

In this paper we present a framework in which the relational description of General Relativity can be used to smoothly continue cosmological dynamical systems through the Big Bang without invoking quantum gravity effects. Cosmological spacetimes contain as a key dynamical variable a notion of scale through the volume factor $\nu$. However no cosmological observer is ever able to separate their measuring apparatus from the system they are measuring, in that sense every measurement is a relative one and measurable dynamical variables are in fact dimensionless ratios. This is manifest in the identification of a scaling symmetry or ``Dynamical Similarity" in the Einstein-Hilbert action associated with the volume factor. By quotienting out this scaling symmetry, we form a relational system defined on a contact manifold whose dynamical variables are decoupled from scale. When the phase space is reduced to shape space, we show that there exist unique solutions to the equations of motion that pass smoothly through the initial cosmological singularity in flat FLRW, Bianchi I and Quiescent Bianchi IX cosmologies.

gr-qc↗

arXiv2024

How closed is cosmology?

Classical cosmology exhibits a particular kind of scaling symmetry. The dynamics of the invariants of this symmetry forms a system that exhibits many of the features of open systems such as the non-conservation of mechanical energy and the focusing of measures along the dynamical flow. From these properties, we show that important dynamical features emerge that are not present in closed systems. In particular, a large and physically plausible class of cosmological models give rise to a natural arrow of time. We then argue that the appropriate notion of closure in cosmology is dynamical closure - that a system can be integrated without reference to external factors. This is realised in physical systems in terms of the algebraic closure of the equations of motion such that the system is autonomous. Remarkably, in a growing class of models it can be shown that the autonomous system obtained remains regular and can be integrated through the big bang.

gr-qc↗

arXiv2022

Regularization of Single Field Inflation Models

There are many single field inflationary models that are consistent with the recent Planck 2018 measurements of the spectral index $n_s$ and tensor-to-scalar ratio $r$. Despite good agreement with observational data some of these models suffer from having unregularized potentials which would produce a collapsing universe shortly after the end of inflation. In this paper we show that how one chooses to correct the behaviour potential towards the end of inflation can have a significant effect on the inflationary predictions of the model, specifically in the case of quartic hilltop and radiatively corrected Higgs inflation.

astro-ph.CO↗

arXiv2022

Herglotz Action for Homogeneous Cosmology

We present an action from which the dynamics of homogeneous cosmologies can be derived. The action has no dependence on scale within the system and hence is more parsimonious in its description than the Einstein-Hilbert action. The form of the action follows that pioneered by Herglotz and hence allows for a direct interpretation of the system as being both autonomous and frictional.

gr-qc↗

arXiv2022

Scaling Symmetries, Contact Reduction and Poincaré's dream

A symplectic Hamiltonian system admitting a scaling symmetry can be reduced to an equivalent contact Hamiltonian system in which some physically-irrelevant degree of freedom has been removed. As a consequence, one obtains an equivalent description for the same physical phenomenon, but with fewer inputs needed, thus realizing "Poincaré's dream" of a scale-invariant description of the universe. This work is devoted to a thorough analysis of the mathematical framework behind such reductions. We show that generically such reduction is possible and the reduced (fundamental) system is a contact Hamiltonian system. The price to pay for this level of generality is that one is compelled to consider the coupling constants appearing in the original Hamiltonian as part of the dynamical variables of a lifted system. This however has the added advantage of removing the hypothesis of the existence of a scaling symmetry for the original system at all, without breaking the sought-for reduction in the number of inputs needed. Therefore a large class of Hamiltonian (resp. Lagrangian) theories can be reduced to scale-invariant contact Hamiltonian (resp. Herglotz variational) theories.

math-ph↗

arXiv2021

Squared Quartic Hilltop Inflation

A correction to the Quartic Hilltop inflationary model is proposed to account for stabilising terms in the potential. We derive analytical predictions for the spectral index $n_s$ and tensor-scalar ratio $r$ which lie within the Planck 2018 survey bounds. The reheating predictions of the corrected model are investigated and by considering the reheating temperature we further constrain the $(n_s,r)$ parameter space. It is shown that the correction terms are physically important during inflation and generally need to be accounted for when considering Hilltop models as a candidate for inflation.

gr-qc↗

arXiv2021

When scale is surplus

We study a long-recognised but under-appreciated symmetry called "dynamical similarity" and illustrate its relevance to many important conceptual problems in fundamental physics. Dynamical similarities are general transformations of a system where the unit of Hamilton's principal function is rescaled, and therefore represent a kind of dynamical scaling symmetry with formal properties that differ from many standard symmetries. To study this symmetry, we develop a general framework for symmetries that distinguishes the observable and surplus structures of a theory by using the minimal freely specifiable initial data for the theory that is necessary to achieve empirical adequacy. This framework is then applied to well-studied examples including Galilean invariance and the symmetries of the Kepler problem. We find that our framework gives a precise dynamical criterion for identifying the observables of those systems, and that those observables agree with epistemic expectations. We then apply our framework to dynamical similarity. First we give a general definition of dynamical similarity. Then we show, with the help of some previous results, how the dynamics of our observables leads to singularity resolution and the emergence of an arrow of time in cosmology.

physics.hist-ph↗

arXiv2021

Through a Black Hole Singularity

We show that the Kantowski--Sachs model of a Schwarzschild black hole interior can be slightly generalized in order to accommodate spatial metrics of different orientations, and in this formulation the equations of motion admit a variable redefinition that makes the system regular at the singularity. This system will then traverse the singularity in a deterministic way (information will be conserved through it), and evolve into a time-reversed and orientation-flipped Schwarzschild white hole interior.

gr-qc↗

arXiv2021

Scale Symmetry and Friction

Dynamical similarities are non-standard symmetries found in a wide range of physical systems that identify solutions related by a change of scale. In this paper we will show through a series of examples how this symmetry extends to the space of couplings, as measured through observations of a system. This can be exploited to focus on observations that can be used distinguish between different theories, and identify those which give rise to identical physical evolutions. These can be reduced into a description which makes no reference to scale. The resultant systems can be derived from Herglotz's principle and generally exhibit friction. Here we will demonstrate this through three example systems: The Kepler problem, the N-body system and Friedmann-Lemaître-Robertson-Walker cosmology.

gr-qc↗

arXiv2020

A New Action for Cosmology

We present a new action which reproduces the cosmological sector of general relativity in both the Friedmann-Lemaitre-Robertson-Walker (FLRW) and Bianchi models. This action makes no reference to the scale factor, and is of a frictional type first examined by Herglotz. We demonstrate that the extremization of this action reproduces the usual dynamics of physical observables, and the symplectification of this action is the Einstein-Hilbert action for cosmological models. We end by discussing some of the increased explanatory power produced by considering the reduced physical ontology resulting from eliminating scale.

gr-qc↗