The Stability of an Isotropic Cosmological Singularity in Higher-Order Gravity

We study the stability of the isotropic vacuum Friedmann universe in gravity theories with higher-order curvature terms of the form $(R_{ab}R^{ab})^{n}$ added to the Einstein-Hilbert Lagrangian of general relativity on approach to an initial cosmological singularity. Earlier, we had shown that, when $$, a special isotropic vacuum solution exists which behaves like the radiation-dominated Friedmann universe and is stable to anisotropic and small inhomogeneous perturbations of scalar, vector and tensor type. This is completely different to the situation that holds in general relativity, where an isotropic initial cosmological singularity is unstable in vacuum and under a wide range of non-vacuum conditions. We show that when $n\neq 1$, although a special isotropic vacuum solution found by Clifton and Barrow always exists, it is no longer stable when the initial singularity is approached. We find the particular stability conditions under the influence of tensor, vector, and scalar perturbations for general $n$ for both solution branches. On approach to the initial singularity, the isotropic vacuum solution with scale factor $a(t)=t^{P_{-}/3}$ is found to be stable to tensor perturbations for $0.5<n< 1.1309$ and stable to vector perturbations for $0.861425 < n \leq 1$, but is unstable as $t \to 0$ otherwise. The solution with scale factor $a(t)=t^{P_{+}/3}$ is not relevant to the case of an initial singularity for $n>1$ and is unstable as $t \to 0$ for all $n$ for each type of perturbation.Comment: 25 page

Symmetric hyperbolic systems for Bianchi equations

We obtain a family of first-order symmetric hyperbolic systems for the Bianchi equations. They have only physical characteristics: the light cone and timelike hypersurfaces. In the proof of the hyperbolicity, new positivity properties of the Bel tensor are used.Comment: latex, 7 pages, accepted for publication in Class. Quantum Gra

Human bronchial fibroblasts express the 5-lipoxygenase pathway

BACKGROUND: Fibroblasts are implicated in sub-epithelial fibrosis in remodeled asthmatic airways and contribute to airway inflammation by releasing cytokines and other mediators. Fibroblast activity is influenced by members of the leukotriene family of bronchoconstrictor and inflammatory mediators, but it is not known whether human bronchial fibroblasts can synthesize leukotrienes. METHODS: The expression of leukotriene biosynthetic enzymes and receptors was investigated in primary fibroblasts from the bronchi of normal and asthmatic adult subjects using RT-PCR, Western blotting, immunocytochemistry and flow cytometry. RESULTS: These techniques revealed that human bronchial fibroblasts from both subject groups constitutively express 5-lipoxygenase, its activating protein FLAP, the terminal enzymes leukotriene A(4 )hydrolase and leukotriene C(4 )synthase, and receptors for leukotriene B(4 )(BLT1) and cysteinyl-leukotrienes (CysLT(1)). Human bronchial fibroblasts generated immunoreactive leukotriene B(4 )and cysteinyl-leukotrienes spontaneously and in increased amounts after calcium-dependent activation. Flow cytometry showed that human bronchial fibroblasts transformed to a myofibroblast-like phenotype by culture with transforming growth factor-β(1 )expressed 320–400% more immunofluorescence for leukotriene C(4 )synthase and CysLT(1 )receptors, with 60–80% reductions in leukotriene A(4 )hydrolase and BLT1 receptors. CONCLUSION: These results indicate that human bronchial fibroblasts may not only respond to exogenous leukotrienes but also generate leukotrienes implicated in narrowing, inflammation and remodeling of the asthmatic airway

The Journal of the Friends' Historical Society vol. 2 No. 3

1. Notices. 2. Notes and Queries. 3. The First Publishers of Truth III. 4. Edmund Peckover, ex-soldier and Quaker. 5. County Tipperary Friends' Records II. 6. Bevan and Naish Library, Birmingham. 7. Decline Literature II. 8. The Price of Candles. 9. Friends on the Atlantic I. 10. Extracts from the Bishop of Chester's Visitation, 1665 I. 11. Meetings in Yorkshire, 1668 III. 12. The Will of Margaret Fox. 13. William Keynell, of Dorsetshire. 14. William Miller at the King's Gardens I. 15. Springett Penn to James Logan. 16. Occurrences for the Progress of Truth I. 17. Friends' in Current Literature. 18. Friends' Reference Library, Devonshire House. 19. Sixth List of Members. 20. Editors' Notes

Twistor geometry of a pair of second order ODEs

We discuss the twistor correspondence between path geometries in three dimensions with vanishing Wilczynski invariants and anti-self-dual conformal structures of signature $(2, 2)$. We show how to reconstruct a system of ODEs with vanishing invariants for a given conformal structure, highlighting the Ricci-flat case in particular. Using this framework, we give a new derivation of the Wilczynski invariants for a system of ODEs whose solution space is endowed with a conformal structure. We explain how to reconstruct the conformal structure directly from the integral curves, and present new examples of systems of ODEs with point symmetry algebra of dimension four and greater which give rise to anti--self--dual structures with conformal symmetry algebra of the same dimension. Some of these examples are $(2, 2)$ analogues of plane wave space--times in General Relativity. Finally we discuss a variational principle for twistor curves arising from the Finsler structures with scalar flag curvature.Comment: Final version to appear in the Communications in Mathematical Physics. The procedure of recovering a system of torsion-fee ODEs from the heavenly equation has been clarified. The proof of Prop 7.1 has been expanded. Dedicated to Mike Eastwood on the occasion of his 60th birthda

Complex-Distance Potential Theory and Hyperbolic Equations

An extension of potential theory in R^n is obtained by continuing the Euclidean distance function holomorphically to C^n. The resulting Newtonian potential is generated by an extended source distribution D(z) in C^n whose restriction to R^n is the delta function. This provides a natural model for extended particles in physics. In C^n, interpreted as complex spacetime, D(z) acts as a propagator generating solutions of the wave equation from their initial values. This gives a new connection between elliptic and hyperbolic equations that does not assume analyticity of the Cauchy data. Generalized to Clifford analysis, it induces a similar connection between solutions of elliptic and hyperbolic Dirac equations. There is a natural application to the time-dependent, inhomogeneous Dirac and Maxwell equations, and the `electromagnetic wavelets' introduced previously are an example.Comment: 25 pages, submited to Proceedings of 5th Intern. Conf. on Clifford Algebras, Ixtapa, June 24 - July 4, 199

Lorentzian spin foam amplitudes: graphical calculus and asymptotics

The amplitude for the 4-simplex in a spin foam model for quantum gravity is defined using a graphical calculus for the unitary representations of the Lorentz group. The asymptotics of this amplitude are studied in the limit when the representation parameters are large, for various cases of boundary data. It is shown that for boundary data corresponding to a Lorentzian simplex, the asymptotic formula has two terms, with phase plus or minus the Lorentzian signature Regge action for the 4-simplex geometry, multiplied by an Immirzi parameter. Other cases of boundary data are also considered, including a surprising contribution from Euclidean signature metrics.Comment: 30 pages. v2: references now appear. v3: presentation greatly improved (particularly diagrammatic calculus). Definition of "Regge state" now the same as in previous work; signs change in final formula as a result. v4: two references adde

Scattering Amplitudes and BCFW Recursion in Twistor Space

Twistor ideas have led to a number of recent advances in our understanding of scattering amplitudes. Much of this work has been indirect, determining the twistor space support of scattering amplitudes by examining the amplitudes in momentum space. In this paper, we construct the actual twistor scattering amplitudes themselves. We show that the recursion relations of Britto, Cachazo, Feng and Witten have a natural twistor formulation that, together with the three-point seed amplitudes, allows us to recursively construct general tree amplitudes in twistor space. We obtain explicit formulae for $n$-particle MHV and NMHV super-amplitudes, their CPT conjugates (whose representations are distinct in our chiral framework), and the eight particle N^2MHV super-amplitude. We also give simple closed form formulae for the N=8 supergravity recursion and the MHV and conjugate MHV amplitudes. This gives a formulation of scattering amplitudes in maximally supersymmetric theories in which superconformal symmetry and its breaking is manifest. For N^kMHV, the amplitudes are given by 2n-4 integrals in the form of Hilbert transforms of a product of $n-k-2$ purely geometric, superconformally invariant twistor delta functions, dressed by certain sign operators. These sign operators subtly violate conformal invariance, even for tree-level amplitudes in N=4 super Yang-Mills, and we trace their origin to a topological property of split signature space-time. We develop the twistor transform to relate our work to the ambidextrous twistor diagram approach of Hodges and of Arkani-Hamed, Cachazo, Cheung and Kaplan.Comment: v2: minor corrections + extra refs. v3: further minor corrections, extra discussion of signature issues + more ref

Structure and stability of the Lukash plane-wave spacetime

We study the vacuum, plane-wave Bianchi $VII{}_{h}$ spacetimes described by the Lukash metric. Combining covariant with orthonormal frame techniques, we describe these models in terms of their irreducible kinematical and geometrical quantities. This covariant description is used to study analytically the response of the Lukash spacetime to linear perturbations. We find that the stability of the vacuum solution depends crucially on the background shear anisotropy. The stronger the deviation from the Hubble expansion, the more likely the overall linear instability of the model. Our analysis addresses rotational, shear and Weyl curvature perturbations and identifies conditions sufficient for the linear growth of these distortions.Comment: Revised version, references added. To appear in Class. Quantum Gra