Sanjeev S. Seahra

University of New Brunswick · Department of Mathematics and Statistics

The dynamics of the vacuum Kantowski-Sachs space-time are studied in the so-called limiting curvature mimetic gravity theory. It is shown that in this theory the vacuum Kantowski-Sachs space-time is always singular. While the departures from general relativity due to the limiting curvature mimetic theory do provide an upper bound on the magnitude o...

In certain models of conformal gravity, the propagation of gravitational waves is governed by a fourth order scalar partial differential equation. We study the initial value problem for a generalization of this equation, and derive a Kirchhoff-like explicit solution in terms of the field and its first three time derivatives evaluated on an initial...

Several approaches to quantum gravity suggest that Lorentz invariance will be broken at high energy. This can lead to modified dispersion relations for wave propagation, which can be concretely realized in effective field theories where the equation of motion involves higher order spatial derivatives in a preferred frame. We consider such a model i...

In certain models of conformal gravity, the propagation of gravitational waves is governed by a fourth order scalar partial differential equation. We study the initial value problem for a generalization of this equation, and derive a Kirchhoff-like explicit solution in terms of the field and its first three time derivatives evaluated on an initial...

Several approaches to quantum gravity suggest that Lorentz invariance will be broken at high energy. This can lead to modified dispersion relations for wave propagation, which can be concretely realized in effective field theories where the equation of motion involves higher order spatial derivatives in a preferred frame. We consider such a model i...

We study the polymer quantization of a homogeneous massive scalar field in the early universe using a prescription inequivalent to those previously appearing in the literature. Specifically, we assume a Hilbert space for which the scalar field momentum is well defined but its amplitude is not. We show that in the semi-classical approximation, the m...

We demonstrate that Huygens’ principle for gravitational waves fails in quadratic gravity models that exhibit conformal symmetry at high energies. This results in the blurring of gravitational wave signals over finite timescales related to the energy scale of new physics $M_{\star}$ . Furthermore, on very small scales the gravitational wave Green’s...

We examine the cosmological sector of a gauge theory of gravity based on the SO(4,2) conformal group of Minkowski space. We allow for conventional matter coupled to the spacetime metric as well as matter coupled to the field that gauges special conformal transformations. An effective cosmological constant is generated dynamically via solution of th...

We reconsider a gauge theory of gravity in which the gauge group is the conformal group SO(4,2) and the action is of the Yang-Mills form, quadratic in the curvature. The resulting gravitational theory exhibits local conformal symmetry and reduces to Weyl-squared gravity under certain conditions. When the theory is linearized about flat spacetime, w...

We consider the semi-classical dynamics of a free massive scalar field in a homogeneous and isotropic cosmological spacetime. The scalar field is quantized using the polymer quantization method assuming that it is described by a gaussian coherent state. For quadratic potentials, the semi-classical equations of motion yield a universe that has an ea...

We study the effects of exotic kinetic terms on parametric resonance during the preheating epoch of the early universe. Specifically, we consider modifications to the action of ordinary matter fields motivated by generalized uncertainty principles, polymer quantization, as well as Dirac-Born-Infeld and k-essence models. To leading order in an "exot...

We study the implications of deformed quantum algebras for the generation of primordial perturbations from slow-roll inflation. Specifically, we assume that the quantum commutator of the inflaton's amplitude and momentum in Fourier space gets modified at energies above some threshold $M_{\star}$. We show that when the commutator is modified to be a...

Quantization prescriptions that realize generalized uncertainty relations (GUP) are motivated by quantum gravity arguments that incorporate a fundamental length scale. We apply two such methods, polymer and deformed Heisenberg quantization, to scalar field theory in Fourier space. These alternative quantizations modify the oscillator spectrum for e...

We consider the Yang-Mills flow on hyperbolic 3-space. The gauge connection is constructed from the frame-field and (not necessarily compatible) spin connection components. The fixed points of this flow include zero Yang-Mills curvature configurations, for which the spin connection has zero torsion and the associated Riemannian geometry is one of c...

Quantum mechanics with a generalized uncertainty principle arises through a representation of the commutator $[\hat{x}, \hat{p}] = i f(\hat{p})$. We apply this deformed quantization to free scalar field theory for $f_\pm =1\pm \beta p^2$. The resulting quantum field theories have a rich fine scale structure. For small wavelength modes, the Green's...

We study the generation of primordial fluctuations in pure de Sitter inflation where the quantum scalar field dynamics are governed by polymer (not Schrodinger) quantization. This quantization scheme is related to, but distinct from, the structures employed in Loop Quantum Gravity; and it modifies standard results above a polymer energy scale $M_{\...

We describe a non-perturbative approach to studying the gravitational collapse of a scalar field in spherical symmetry with quantum gravity corrections. Quantum effects are described by a phase space function that modifies the constraints of general relativity but does not affect the closure of their algebra. The model may be viewed as one that inc...

We develop analytic solutions for the linear evolution of metric perturbations in the Dvali-Gabadadze-Porrati braneworld modified gravity scenario including near-horizon and superhorizon modes where solutions in the bulk are required. These solutions apply to both the self-accelerating and normal branch and elucidate the nature of coordinate singul...

We study a class of Hamiltonian deformations of the massless Einstein-Klein-Gordon system in spherical symmetry for which the Dirac constraint algebra closes. The system may be regarded as providing effective equations for quantum gravitational collapse. Guided by the observation that scalar field fluxes do not follow metric null directions due to...

We analyze the $\delta=2$ Tomimatsu-Sato spacetime in the context of the proposed Kerr/CFT correspondence. This 4-dimensional vacuum spacetime is asymptotically flat and has a well-defined ADM mass and angular momentum, but also involves several exotic features including a naked ring singularity, and two disjoint Killing horizons separated by a reg...

We study free scalar field theory on flat spacetime using a background independent (polymer) quantization procedure. Specifically we compute the propagator using a method that takes the energy spectrum and position matrix elements of the harmonic oscillator as inputs. We obtain closed form results in the infrared and ultraviolet regimes that give L...

It is shown that polymer quantization leads to a modified uncertainty principle similar to that obtained from string theory and non-commutative geometry. When applied to quantum field theory on general background spacetimes, corrections to the uncertainty principle acquire a metric dependence. For Friedmann-Robertson-Walker cosmology this translate...

We present a brief overview of the stability analysis of the Einstein static universe in various modified theories of gravity, like f(R) gravity, Gauss-Bonnet or f(G) gravity, and Horava-Lifshitz gravity.

We consider a polymer quantization of a free massless scalar field in a homogenous and isotropic classical cosmological spacetime. This quantization method assumes that field translations are fundamentally discrete, and is related to but distinct from that used in loop quantum gravity. The semiclassical Friedmann equation yields a universe that is...

We study gravitational waves in the black string Randall-Sundrum braneworld. We present a reasonably self-contained and complete derivation of the equations governing the evolution of gravitational perturbations in the presence of a brane localized source, and then specialize to the case of spherical radiation from a pointlike body in orbit around...

We apply a type of background independent "polymer" quantization to a free scalar field in a flat spacetime. Using semi-classical states, we find an effective wave equation that is both nonlinear and Lorentz invariance violating. We solve this equation perturbatively for several cases of physical interest, and show that polymer corrections to solut...

We study Einstein static universes in the context of generic f(R) models. It is shown that Einstein static solutions exist for a wide variety of modified gravity models sourced by a barotropic perfect fluid with equation of state w=p/rho, but these solutions are always unstable to either homogeneous or inhomogeneous perturbations. Our general resul...

The observation of filamentary extended red emission (ERE) structures in reflection nebulae is found to be consistent with the establishment of an equilibrium between the deactivation of small grains of hydrogenated amorphous carbon (HAC) by UV radiation and rehydrogenation by H atoms created by photodissociation of H2 by the same UV field. Laborat...

We investigate the extinction produced by small carbon particles consisting of aromatic rings in configurations similar to those of polycyclic aromatic hydrocarbon (PAH) molecules, but with varying degrees of hydrogenation, ionization, and defects. Extinction produced by candidate particles is calculated using the discrete dipole array (DDA) formal...

We have simulated extended red emission (ERE) spectra using a model in which this emission arises as photoluminescence from small carbon particles of mixed sp2/sp3 hybridized bonding characteristics. The emission efficiency from such particles can be highly efficient when their size is such that geminate recombination of photoexcited electron hole...

Theoretical infrared absorption spectra of aromatic ring molecules having up to 102 carbon atoms and with various edge hydrogenations have been obtained using a classic mechanical model and a simplified valence force field. Force constants have been adapted from those available for smaller molecules. Spectral line intensities are calculated in a do...

Using a combination of algebraic and computer work, we embed the standard spatially flat four-dimensional cosmological models and inflationary models in a flat five-dimensional space and thereby obtain pictures of the big bang. Such embeddings have important implications for astrophysics, notably in regard to particle masses and background radiatio...

Using a theoretical model previously developed to study the UV extinction produced by small carbon particles, we present results that show that the observed strength, profile and central wavelength of the interstellar 2175 Å absorption band can be reproduced with a two-component mixture of these particles. These consist of small dehydrogenated coro...

We study the evolution of wormhole geometries under the Ricci flow using numerical methods. Depending on values of initial data parameters, wormhole throats either pinch off or evolve to a monotonically growing state. The transition between these two behaviors exhibits a form of critical phenomena reminiscent of that observed in gravitational colla...

A longstanding problem in braneworld cosmology is quantifying the dynamics of cosmological perturbations. This is because, unlike the 4-dimensional case, fluctuations are governed by non-separable partial differential equations (PDEs). We have developed a fast and accurate code to solve the relevant equations of motion, and hence extract observatio...

We solve for the behaviour of cosmological perturbations in the Dvali-Gabadadze-Porrati (DGP) braneworld model using a new numerical method. Unlike some other approaches in the literature, our method uses no approximations other than linear theory and is valid on large scales. We examine the behaviour of late-universe density perturbations for both...

We study the behaviour of scalar perturbations in the radiation-dominated era of Randall-Sundrum braneworld cosmology by numerically solving the coupled bulk and brane master wave equations. We find that density perturbations with wavelengths less than a critical value (set by the bulk curvature length) are amplified during horizon re-entry. This m...

We report on the possibility of detecting a submillimetre-sized extra dimension by observing gravitational waves (GWs) emitted by point-like objects orbiting a braneworld black hole. Matter in the 'visible' universe can generate a discrete spectrum of high frequency GWs with amplitudes moderately weaker than the predictions of general relativity, w...

We consider the evolution of a bulk scalar field in anti-de Sitter (AdS) spacetime linearly coupled to a scalar field on a de Sitter boundary brane. We present results of a spectral analysis of the system, and find that the model can exhibit both bound and continuum resonant modes. We find that zero, one, or two bound states may exist, depending up...

Motivated by the problem of the evolution of bulk gravitational waves in Randall-Sundrum cosmology, we develop a characteristic numerical scheme to solve 1+1 dimensional wave equations in the presence of a moving timelike boundary. The scheme exhibits quadratic convergence, is capable of handling arbitrary brane trajectories, and is easily extendib...

We show the geometrical equivalence of two five-dimensional metrics, one describing a cosmology which smoothly embeds the standard Friedmann-Robertson-Walker-Lematre models, and another describing an object which topologically is a black hole. The solutions can be interpreted using either membrane or induced-matter theory. We outline the main physi...

We investigate the analogue of the Randall Sundrum braneworld in the case when the bulk contains a black hole. Instead of the static vacuum Minkowski brane of the RS model, we have an Einstein static vacuum brane. We find that the presence of the bulk black hole has a dramatic effect on the gravity that is felt by brane observers. In the RS model,...

We investigate in detail gravitational waves in an Schwarzschild-anti-de Sitter bulk spacetime surrounded by an Einstein static brane with generic matter content. Such a model provides a useful analogy to braneworld cosmology at various stages of its evolution, and generalizes our previous work [gr-qc/0504023] on pure tension Einstein-static branes...

Motivated by stringy considerations, Randall & Sundrum have proposed a model where all the fields and particles of physics, save gravity, are confined on a 4-dimensional brane embedded in 5-dimensional anti-deSitter space. Their scenario features a stable bound state of bulk gravity waves and the brane that reproduces standard general relativity. W...

Using the black string between two branes as a model of a brane-world black hole, we compute the gravity-wave perturbations and identify the features arising from the additional polarizations of the graviton. The standard four-dimensional gravitational wave signal acquires late-time oscillations due to massive modes of the graviton. The Fourier tra...

In the Randall-Sundrum scenario, our universe is a 4-dimensional `brane' living in a 5-dimensional bulk spacetime. By studying the scattering of bulk gravity waves, we show that this brane rings with a characteristic set of complex quasinormal frequencies, much like a black hole. To a bulk observer these modes are interpreted as metastable gravity...

By utilizing non-standard slicings of 5-dimensional Schwarzschild and Schwarzschild-AdS manifolds based on isotropic coordinates, we generate static and spherically symmetric braneworld spacetimes containing shell-like naked null singularities. For planar slicings, we find that the brane-matter sourcing the solution is a perfect fluid with an exoti...

We review the circumstances under which test particles can be localized around a spacetime section \Sigma_0 smoothly contained within a codimension-1 embedding space M. If such a confinement is possible, \Sigma_0 is said to be totally geodesic. Using three different methods, we derive a stability condition for trapped test particles in terms of int...

We clarify the status of two known solutions to the 5-dimensional vacuum Einstein field equations derived by Liu, Mashhoon & Wesson (LMW) and Fukui, Seahra & Wesson (FSW), respectively. Both 5-metrics explicitly embed 4-dimensional Friedman-Lemaitre-Robertson-Walker cosmologies with a wide range of characteristics. We show that both metrics are als...

Motivated by the Randall-Sundrum brane-world scenario, we discuss the classical and quantum dynamics of a (d+1)-dimensional boundary wall between a pair of (d+2)-dimensional topological Schwarzschild-AdS black holes. We assume there are quite general -- but not completely arbitrary -- matter fields living on the boundary ``brane universe'' and its...

Stated succinctly, the original version of the Campbell-Magaard theorem says that it is always possible to locally embed any solution of 4-dimensional general relativity in a 5-dimensional Ricci-flat manifold. We discuss the proof of this theorem (and its variants) in n dimensions, and its application to current theories that postulate that our uni...

In this thesis, we study various aspects of physics in higher-dimensional manifolds involving a single extra dimension. After giving some historical perspective on the motivation for studying higher-dimensional theories of physics, we describe classical tests for a non-compact extra dimension utilizing test particles and pointlike gyroscopes. We th...

We take Mach’s principle to mean that the local properties of a test particle should depend on the global properties of the geometry. Using a complex wave-like metric and an appropriate redefinition of the energy-momentum tensor, we show this to be possible in principle within the context of general relativity. We outline implications for higher-di...

We study the dynamics of test particles and pointlike gyroscopes in 5D manifolds like those used in the Randall-Sundrum brane world and non-compact Kaluza-Klein models. Our analysis is based on a covariant foliation of the manifold using 3+1 dimensional spacetime slices orthogonal to the extra dimension, and is hence similar to the ADM 3+1 split in...

We give relations for the embedding of spatially-flat Friedmann-Robertson-Walker cosmological models of Einstein's theory in flat manifolds of the type used in Kaluza-Klein theory. We present embedding diagrams that depict different 4D universes as hypersurfaces in a higher dimensional flat manifold. The morphology of the hypersurfaces is found to...

We analyze a class of 5D non-compact warped-product spaces characterized by metrics that depend on the extra coordinate via a conformal factor. Our model is closely related to the so-called canonical coordinate gauge of Mashhoon et al. We confirm that if the 5D manifold in our model is Ricci-flat, then there is an induced cosmological constant in t...

An exact class of solutions of the 5D vacuum Einstein field equations (EFEs) is obtained. The metric coefficients are found to be non-separable functions of time and the extra coordinate $l$ and the induced metric on $l$ = constant hypersurfaces has the form of a Friedmann-Robertson-Walker cosmology. The 5D manifold and 3D and 4D submanifolds are i...

We give an exact solution of the five-dimensional field equations which describes a shock wave moving in time and the extra (Kaluza-Klein) coordinate. The matter in four-dimensional spacetime is a cosmology with good physical properties. The solution suggests to us that the 4D big bang was a 5D shock wave.

Following recent results from the Super-Kamiokande experiment which indicate that neutrinos may have finite masses and provide at least part of the dark matter in the Universe, we re-examine the decaying neutrino hypothesis of Sciama, including for the first time the effects of absorption by intergalactic dust. We consider several dust models, incl...

Following recent results from the Super-Kamiokande experiment, we reexamine the decaying neutrino hypothesis of Sciama, including for the first time the effects of absorption by intergalactic dust. We find that the theory can (likely) be ruled out on observational grounds.

We have measured the integrated absorbance, A (in units of cm molecule−1), for the spectral components of the 3.4 μm CHn absorption band in hydrogenated amorphous carbon (HAC) for samples deposited at 300 and 77 K. For the asymmetric CH3 stretching band in HAC, A is found to be significantly weaker than that occurring in pure saturated aliphatic hy...

In this article, we present the black string model of a braneworld black hole and analyze its perturbations. We develop the perturbation formalism for Randall–Sundrum model from first principles and discuss the weak-field limit of the model in the solar system. We derive explicit equations of motion for the axial and spherical gravitational waves i...

Abstract We review the “standard candles” method for determining cosmological parameters. We discuss recent observations of Type Ia Supernovae that suggest that the cosmo- logical constant is nonzero and we live in an accelerating universe. We explore the possibility that such conclusions are compromised by the presence of intergalactic dust. In or...

We examine the quantum field theory of scalar field in non-Minkowski space-times. We first develop a model of a uniformly accelerating particle detector and demonstrate that it will detect a thermal spectrum of particles when the field is in an "empty" state (according to inertial observers). We then develop a formalism for relating field theories...

Thesis (Ph. D.)--University of Waterloo, 2003. Includes bibliographical references.