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M. A. Clayton

Publications and source records attributed to M. A. Clayton.

At least 19 recordsLinked to original sources
arXiv2003

Scale Invariant Spectrum from Variable Speed of Light Metric in a Bimetric Gravity Theory

An approximately scale invariant spectrum generating the seeds of structure formation is derived from a bimetric gravity theory. By requiring that the amplitude of the CMB fluctuations from the model matches the observed value, we determine the fundamental length scale in the model to be a factor of 10^5 times larger than the Planck length, which results in a scalar mode spectral index: n_s\approx 0.97, and its running: α_s\approx -5\times 10^{-4}. This is accomplished in the variable speed of light (VSL) metric frame, in which the dynamics of perturbations of the bimetric scalar field are determined by a minimally-coupled Klein-Gordon equation, and it is assumed that modes are born in a ground state at a scale given by the fundamental length scale appearing in the bimetric structure. We show that while this is taking place for scales of interest, the background (primordial) radiation energy density is strongly suppressed as a result of the bimetric structure of the model. Nevertheless, the enlarged lightcone of matter fields ensures that the horizon and flatness problems are solved.

gr-qc↗
arXiv2002

Fluctuation Spectrum from a Scalar-Tensor Bimetric Gravity Theory

Predictions of the CMB spectrum from a bimetric gravity theory (gr-qc/0101126) are presented. The initial inflationary period in BGT is driven by a vanishingly small speed of gravitational waves v_g in the very early universe. This initial inflationary period is insensitive to the choice of scalar field potential and initial values of the scalar field. After this initial period of inflation, v_g will increase rapidly and the effects of a potential will become important. We show that a quadratic potential introduced into BGT yields an approximately flat spectrum with inflation parameters: n_s=0.98, n_t=-0.027, alpha_s=-3.2e-4 and alpha_t=-5.0e-4, with r >= 0.014.

astro-ph↗
arXiv2001

Nonlocal regularization of abelian models with spontaneous symmetry breaking

We demonstrate how nonlocal regularization is applied to gauge invariant models with spontaneous symmetry breaking. Motivated by the ability to find a nonlocal BRST invariance that leads to the decoupling of longitudinal gauge bosons from physical amplitudes, we show that the original formulation of the method leads to a nontrivial relationship between the nonlocal form factors that can appear in the model.

hep-th↗
arXiv2001

Causality, shocks and instabilities in vector field models of Lorentz symmetry breaking

We show that that vector field-based models of the ether generically do not have a Hamiltonian that is bounded from below in a flat spacetime. We also demonstrate that these models possess multiple light cones in flat or curved spacetime, and that the non-lightlike characteristic is associated with an ether degree of freedom that will tend to form shocks. Since the field equations (and propagation speed) of this mode is singular when the timelike component of the ether vector field vanishes, we demonstrate that linearized analyses about such configurations cannot be trusted to produce robust approximations to the theory.

gr-qc↗
arXiv2001

A scalar-tensor cosmological model with dynamical light velocity

The dynamical consequences of a bimetric scalar-tensor theory of gravity with a dynamical light speed are investigated in a cosmological setting. The model consists of a minimally-coupled self-gravitating scalar field coupled to ordinary matter fields in the standard way through the metric: $\metric_{μν}+B\partial_μϕ\partial_νϕ$. We show that in a universe with matter that has a radiation-dominated equation of state, the model allows solutions with a de Sitter phase that provides sufficient inflation to solve the horizon and flatness problems. This behaviour is achieved without the addition of a potential for the scalar field, and is shown to be largely independent of its introduction. We therefore have a model that is fundamentally different than the potential-dominated, slowly-rolling scalar field of the standard models inflationary cosmology. The speed of gravitational wave propagation is predicted to be significantly different from the speed of matter waves and photon propagation in the early universe.

gr-qc↗
arXiv2000

Vector field mediated models of dynamical light velocity

A vector-tensor theory of gravity that was introduced in an earlier publication is analyzed in detail and its consequences for early universe cosmology are examined. The multiple light cone structure of the theory generates different speeds of gravitational and matter wave fronts, and the contraction of these light cones produces acausal, superluminary inflation that can resolve the initial value problems of cosmology.

gr-qc↗
arXiv2000

Scalar-Tensor Gravity Theory For Dynamical Light Velocity

A gravity theory is developed with the metric ${\hat g}_{μν}= {g}_{μν}+B\partial_μϕ\partial_νϕ$. In the present universe the additional contribution from the scalar field in the metric ${\hat g}_{μν}$ can generate an acceleration in the expansion of the universe, without negative pressure and with a zero cosmological constant. In this theory, gravitational waves will propagate at a different speed from non-gravitational waves. It is suggested that gravitational wave experiments could test this observational signature.

gr-qc↗
arXiv1999

Dynamical Mechanism for Varying Light Velocity as a Solution to Cosmological Problems

A dynamical model for varying light velocity in cosmology is developed, based on the idea that there are two metrics in spacetime. One metric $g_{μν}$ describes the standard gravitational vacuum, and the other ${\hat g}_{μν} =g_{μν}+βψ_μψ_ν$ describes the geometry through which matter fields propagate. Matter propagating causally with respect to $\hat{g}_{μν}$ can provide acausal contributions to the matter stress-energy tensor in the field equations for $g_{μν}$, which, as we explicitly demonstrate with perfect fluid and scalar field matter models, provides a mechanism for the solution of the horizon, flatness and magnetic monopole problems in an FRW universe. The field equations also provide a ``graceful exit'' to the inflationary epoch since below an energy scale (related to the mass of $ψ_μ$) we recover exactly the standard FRW field equations.

astro-ph↗
arXiv1998

Canonical general relativity: Matter fields in a general linear frame

Building on the results of previous work, we demonstrate how matter fields are incorporated into the general linear frame approach to general relativity. When considering the Maxwell one-form field, we find that the system that leads naturally to canonical vierbein general relativity has the extrinsic curvature of the Cauchy surface represented by gravitational as well as non-gravitational degrees of freedom. Nevertheless the metric compatibility conditions are undisturbed, and this apparent derivative-coupling is seen to be an effect of working with (possibly orthonormal) linear frames. The formalism is adapted to consider a Dirac Fermion, where we find that a milder form of this apparent derivative-coupling appears.

gr-qc↗
arXiv1998

Canonical General Relativity: the Diffeomorphism constraints and Spatial Frame Transformations

Einstein's general relativity with both metric and vielbein treated as independent fields is considered, demonstrating the existence of a consistent variational principle and deriving a Hamiltonian formalism that treats the spatial metric and spatial vielbein as canonical coordinates. This results in a Hamiltonian in standard form that consists of Hamiltonian and momentum constraints as well as constraints that generate spatial frame transformations---all appearing as primary, first class constraints on phase space. The formalism encompasses the standard coordinate frame and vielbein approaches to general relativity, and the constraint algebra derived herein reproduces known results in either limit.

gr-qc↗
arXiv1998

The Dynamical Instability of Static, Spherically Symmetric Solutions in Nonsymmetric Gravitational Theories

We consider the dynamical stability of a class of static, spherically-symmetric solutions of the nonsymmetric gravitational theory. We numerically reproduce the Wyman solution and generate new solutions for the case where the theory has a nontrivial fundamental length scale μ^{-1}. By considering spherically symmetric perturbations of these solutions we show that the Wyman solutions are generically unstable.

gr-qc↗
arXiv1997

Homothetic Wyman Spacetimes

The time-dependent, spherically symmetric, Wyman sector of the Unified Field Theory is shown to be equivalent to a self-gravitating scalar field with a positive-definite, repulsive self-interaction potential. A homothetic symmetry is imposed on the fundamental tensor, and the resulting autonomous system is numerically integrated. Near the critical point (between the collapsing and non-collapsing spacetimes) the system displays an approximately periodic alternation between collapsing and dispersive epochs.

gr-qc↗
arXiv1997

Issues in Quantum-Geometric Propagation

A discussion of relativistic quantum-geometric mechanics on phase space and its generalisation to the propagation of free, massive, quantum-geometric scalar fields on curved spacetimes is given. It is shown that in an arbitrary coordinate system and frame of reference in a flat spacetime, the resulting propagator is necessarily the same as derived in the standard Minkowski coordinates up to a Lorentz boost acting on the momentum content of the field, which is therefore seen to play the role of Bogolubov transformations in this formalism. These results are explicitly demonstrated in the context of a Milne universe.

gr-qc↗
arXiv1997

The Initial-Value Problem of Spherically Symmetric Wyman Sector Nonsymmetric Gravitational Theory

We cast the four-dimensional field equations of the Nonsymmetric Gravitational Theory (NGT) into a form appropriate for numerical study. In doing so, we have restricted ourselves to spherically symmetric spacetimes, and we have kept only the Wyman sector of the theory. We investigate the well-posedness of the initial-value problem of NGT for a particular data set consisting of a pulse in the antisymmetric field on an asymptotically flat space background. We include some analytic results on the solvability of the initial-value problem which allow us to place limits on the regions of the parameter space where the initial-value problem is solvable. These results are confirmed by numerically solving the constraints.

gr-qc↗
arXiv1997

The Tetrad Frame Constraint Algebra

It is shown via the principle of path independence that the (time gauge) constraint algebra derived in (Class. Quantum Grav. 5 (1988) pg. 1405) for vielbein General Relativity is a generic feature of any covariant theory formulated in a vielbein frame. In the process of doing so, the relationship between the coordinate and orthonormal frame algebera is made explicit.

gr-qc↗
arXiv1996

Linearisation Instabilities of the Massive Nonsymmetric Gravitational Theory

The massive nonsymmetric gravitational theory is shown to posses a linearisation instability at purely GR field configurations, disallowing the use of the linear approximation in these situations. It is also shown that arbitrarily small antisymmetric sector Cauchy data leads to singular evolution unless an ad hoc condition is imposed on the initial data hypersurface.

gr-qc↗
arXiv1996

A Hamiltonian Formulation of Nonsymmetric Gravitational Theories

The dynamics of a class of nonsymmetric gravitational theories is presented in Hamiltonian form. The derivation begins with the first-order action, treating the generalized connection coefficients as the canonical coordinates and the densitised components of the inverse of the fundamental tensor as conjugate momenta. The phase space of the symmetric sector is enlarged compared to the conventional treatments of General Relativity (GR) by a canonical pair that represents the metric density and its conjugate, removable by imposing strongly an associated pair of second class constraints and introducing Dirac brackets. The lapse and shift functions remain undetermined Lagrange multipliers that enforce the diffeomorphism constraints in the standard form of the NGT Hamiltonian. Thus the dimension of the physical constraint surface in the symmetric sector is not enlarged over that of GR. In the antisymmetric sector, all six components of the fundamental tensor contribute conjugate pairs for the massive theory, and the absence of additional constraints gives six configuration space degrees of freedom per spacetime point in the antisymmetric sector. For the original NGT action (or, equivalently, Einstein's Unified Field Theory), the U(1) invariance of the action is shown to remove one of these antisymmetric sector conjugate pairs through an additional first class constraint, leaving five degrees of freedom. The restriction of the dynamics to GR configurations is considered, as well as the form of the surface terms that a rise from the variation of the Hamiltonian. In the resulting Hamiltonian system for the massive theory, singular behavior is found in the relations that determine some of the Lagrange multipliers near GR and certain NGT spacetimes. What this implies about the dynamics of the theory is not clearly understood at

gr-qc↗