Atiyah-Hitchin M-Branes

We present new M2 and M5 brane solutions in M-theory based on transverse Atiyah-Hitchin space and other self-dual geometries. One novel feature of these solutions is that they have bolt-like fixed points yet still preserve 1/4 of the supersymmetry. All the solutions can be reduced down to ten dimensional intersecting brane configurations.Comment: 18 pages, 5 figures, one paragraph added in the conclusions, typos correcte

New Reducible Five-brane Solutions in M-theory

We construct new M-theory solutions of M5 branes that are a realization of the fully localized ten dimensional NS5/D6 and NS5/D5 brane intersections. These solutions are obtained by embedding self-dual geometries lifted to M-theory. We reduce these solutions down to ten dimensions, obtaining new D-brane systems in type IIA/IIB supergravity. The worldvolume theories of the NS5-branes are new non-local, non-gravitational, six dimensional, T-dual little string theories with eight supersymmetries.Comment: 19 pages, 4 figures, two paragraphs added in conclusions, typos correcte

Gibbons-Hawking M-branes

We present new M2 and M5-brane solutions in M-theory based on transverse Gibbons-Hawking spaces. These solutions provide realizations of fully localized type IIA D2/D6 and NS5/D6 brane intersections. One novel feature of these solutions is that the metric functions depend on more than two transverse coordinates (unlike all the other previous known solutions). All the solutions have eight preserved supersymmetries and the world-volume theories of the NS5-branes are new non-local, non-gravitational, six dimensional, T-dual little string theories with eight supersymmetries. We discuss the limits in which the dynamics of the D2 and NS5-branes decouple from the bulk for these solutions.Comment: 32 pages, 7 figures, few sentences added, a couple of typos corrected, to appear in JHE

Symmetries of a class of nonlinear fourth order partial differential equations

In this paper we study symmetry reductions of a class of nonlinear fourth order partial differential equations \be u_{tt} = \left(\kappa u + \gamma u^2\right)_{xx} + u u_{xxxx} +\mu u_{xxtt}+\alpha u_x u_{xxx} + \beta u_{xx}^2, \ee where $\alpha$, $\beta$, $\gamma$, $\kappa$ and $\mu$ are constants. This equation may be thought of as a fourth order analogue of a generalization of the Camassa-Holm equation, about which there has been considerable recent interest. Further equation (1) is a ``Boussinesq-type'' equation which arises as a model of vibrations of an anharmonic mass-spring chain and admits both ``compacton'' and conventional solitons. A catalogue of symmetry reductions for equation (1) is obtained using the classical Lie method and the nonclassical method due to Bluman and Cole. In particular we obtain several reductions using the nonclassical method which are no} obtainable through the classical method

Qualitative Properties of Magnetic Fields in Scalar Field Cosmology

We study the qualitative properties of the class of spatially homogeneous Bianchi VI_o cosmological models containing a perfect fluid with a linear equation of state, a scalar field with an exponential potential and a uniform cosmic magnetic field, using dynamical systems techniques. We find that all models evolve away from an expanding massless scalar field model in which the matter and the magnetic field are negligible dynamically. We also find that for a particular range of parameter values the models evolve towards the usual power-law inflationary model (with no magnetic field) and, furthermore, we conclude that inflation is not fundamentally affected by the presence of a uniform primordial magnetic field. We investigate the physical properties of the Bianchi I magnetic field models in some detail.Comment: 12 pages, 2 figures in REVTeX format. to appear in Phys. Rev.

Testing homogeneity with the fossil record of galaxies

The standard Friedmann model of cosmology is based on the Copernican Principle, i.e. the assumption of a homogeneous background on which structure forms via perturbations. Homogeneity underpins both general relativistic and modified gravity models and is central to the way in which we interpret observations of the CMB and the galaxy distribution. It is therefore important to probe homogeneity via observations. We describe a test based on the fossil record of distant galaxies: if we can reconstruct key intrinsic properties of galaxies as functions of proper time along their worldlines, we can compare such properties at the same proper time for our galaxy and others. We achieve this by computing the lookback time using radial Baryon Acoustic Oscillations, and the time along galaxy world line using stellar physics, allowing us to probe homogeneity, in principle anywhere inside the past light cone. Agreement in the results would be an important consistency test -- although it would not in itself prove homogeneity. Any significant deviation in the results however would signal a breakdown of homogeneity.Comment: Accepted for publication in JCAP. Matches published version. Minor changes: ref. added and longer discussion on performing the test observationally. Results unchange

A note on the minimum effort control problem

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/33486/1/0000891.pd

Do primordial Lithium abundances imply there's no Dark Energy?

Explaining the well established observation that the expansion rate of the universe is apparently accelerating is one of the defining scientific problems of our age. Within the standard model of cosmology, the repulsive 'dark energy' supposedly responsible has no explanation at a fundamental level, despite many varied attempts. A further important dilemma in the standard model is the Lithium problem, which is the substantial mismatch between the theoretical prediction for 7-Li from Big Bang Nucleosynthesis and the value that we observe today. This observation is one of the very few we have from along our past worldline as opposed to our past lightcone. By releasing the untested assumption that the universe is homogeneous on very large scales, both apparent acceleration and the Lithium problem can be easily accounted for as different aspects of cosmic inhomogeneity, without causing problems for other cosmological phenomena such as the cosmic microwave background. We illustrate this in the context of a void model.Comment: 14 pages, 4 figures. v2: minor rearrangements in the text, comments and references expanded, results unchange

The Planetary Nebula Luminosity Function at the Dawn of Gaia

The [O III] 5007 Planetary Nebula Luminosity Function (PNLF) is an excellent extragalactic standard candle. In theory, the PNLF method should not work at all, since the luminosities of the brightest planetary nebulae (PNe) should be highly sensitive to the age of their host stellar population. Yet the method appears robust, as it consistently produces < 10% distances to galaxies of all Hubble types, from the earliest ellipticals to the latest-type spirals and irregulars. It is therefore uniquely suited for cross-checking the results of other techniques and finding small offsets between the Population I and Population II distance ladders. We review the calibration of the method and show that the zero points provided by Cepheids and the Tip of the Red Giant Branch are in excellent agreement. We then compare the results of the PNLF with those from Surface Brightness Fluctuation measurements, and show that, although both techniques agree in a relative sense, the latter method yields distances that are ~15% larger than those from the PNLF. We trace this discrepancy back to the calibration galaxies and argue that, due to a small systematic error associated with internal reddening, the true distance scale likely falls between the extremes of the two methods. We also demonstrate how PNLF measurements in the early-type galaxies that have hosted Type Ia supernovae can help calibrate the SN Ia maximum magnitude-rate of decline relation. Finally, we discuss how the results from space missions such as Kepler and Gaia can help our understanding of the PNLF phenomenon and improve our knowledge of the physics of local planetary nebulae.Comment: 12 pages, invited review at the conference "The Fundamental Cosmic Distance Scale: State of the Art and Gaia Perspective", to appear in Astrophysics and Space Scienc