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We discuss in the framework of the excursion set formalism a recent discovery from N-body simulations that the clustering of haloes of given mass depends on their formation history. We review why the standard implementation of this formalism is unable to explain such dependencies, and we show that this can, in principle, be rectified by implementing in full an ellipsoidal collapse model where collapse depends not only on the overdensity but also on the shape of the initial density field. We also present an alternative remedy for this deficiency, namely the inclusion of collapse barriers for pancakes and filaments, together with the assumption that formation history depends on when these barriers are crossed. We implement both these extensions in a generalised excursion set method, and run large Monte Carlo realisations to quantify the effects. Our results suggest that effects as large as those found in simulations can only arise in the excursion set formalism if the formation history of a halo does indeed depend on the size of its progenitor filaments and pancakes. We also present conditional distributions of progenitor pancakes and filaments for low-mass haloes identified at present epoch, and discuss a recent claim by Mo et.al. that most low-mass haloes were embedded in massive pancakes at $z\sim 2$., Comment: 11 pages, 8 figures, submitted to MNRAS

We describe a method to estimate the mass distribution of a gravitational lens and the position of the sources from combined strong and weak lensing data. The algorithm combines weak and strong lensing data in a unified way producing a solution which is valid in both the weak and strong lensing regimes. We study how the result depends on the relative weighting of the weak and strong lensing data and on choice of basis to represent the mass distribution. We find that combining weak and strong lensing information has two major advantages: it eliminates the need for priors and/or regularization schemes for the intrinsic size of the background galaxies (this assumption was needed in previous strong lensing algorithms) and it corrects for biases in the recovered mass in the outer regions where the strong lensing data is less sensitive. The code is implemented into a software package called WSLAP (Weak & Strong Lensing Analysis Package) which is publicly available at http://darwin.cfa.harvard.edu/SLAP/, Comment: 10 pages. 9 figures. MNRAS submitted

We present the mass distribution in the central area of the cluster A1689 by fitting over 100 multiply lensed images with the non-parametric Strong Lensing Analysis Package (SLAP, Diego et al. 2004). The surface mass distribution is obtained in a robust way finding a total mass of 0.25E15 M_sun/h within a 70'' circle radius from the central peak. Our reconstructed density profile fits well an NFW profile with small perturbations due to substructure and is compatible with the more model dependent analysis of Broadhurst et al. (2004a) based on the same data. Our estimated mass does not rely on any prior information about the distribution of dark matter in the cluster. The peak of the mass distribution falls very close to the central cD and there is substructure near the center suggesting that the cluster is not fully relaxed. We also examine the effect on the recovered mass when we include the uncertainties in the redshift of the sources and in the original shape of the sources. Using simulations designed to mimic the data, we identify some biases in our reconstructed mass distribution. We find that the recovered mass is biased toward lower masses beyond 1 arcmin (150 kpc) from the central cD and that in the very center we may be affected by degeneracy problems. On the other hand, we confirm that the reconstructed mass between 25'' and 70'' is a robust, unbiased estimate of the true mass distribution and is compatible with an NFW profile., Comment: 11 pages, 12 figures. MNRAS submitted. A full resolution of the paper can be found in http://darwin.physics.upenn.edu/SLAP/

We revisit the issue of non-parametric gravitational lens reconstruction and present a new method to obtain the cluster mass distribution using strong lensing data without using any prior information on the underlying mass. The method relies on the decomposition of the lens plane into individual cells. We show how the problem in this approximation can be expressed as a system of linear equations for which a solution can be found. Moreover, we propose to include information about the null space. That is, make use of the pixels where we know there are no arcs above the sky noise. The only prior information is an estimation of the physical size of the sources. No priors on the luminosity of the cluster or shape of the halos are needed thus making the results very robust. In order to test the accuracy and bias of the method we make use of simulated strong lensing data. We find that the method reproduces accurately both the lens mass and source positions and provide error estimates., Comment: This is the accepted version in MNRAS. Thsi includes improvements suggested by the referee and one new plot. Additional material can be found in http://darwin.cfa.harvard.edu/SLAP/index.aspx

We measure cosmological parameters using the three-dimensional power spectrum P(k) from over 200,000 galaxies in the Sloan Digital Sky Survey (SDSS) in combination with WMAP and other data. Our results are consistent with a ``vanilla'' flat adiabatic Lambda-CDM model without tilt (n=1), running tilt, tensor modes or massive neutrinos. Adding SDSS information more than halves the WMAP-only error bars on some parameters, tightening 1 sigma constraints on the Hubble parameter from h~0.74+0.18-0.07 to h~0.70+0.04-0.03, on the matter density from Omega_m~0.25+/-0.10 to Omega_m~0.30+/-0.04 (1 sigma) and on neutrino masses from <11 eV to <0.6 eV (95%). SDSS helps even more when dropping prior assumptions about curvature, neutrinos, tensor modes and the equation of state. Our results are in substantial agreement with the joint analysis of WMAP and the 2dF Galaxy Redshift Survey, which is an impressive consistency check with independent redshift survey data and analysis techniques. In this paper, we place particular emphasis on clarifying the physical origin of the constraints, i.e., what we do and do not know when using different data sets and prior assumptions. For instance, dropping the assumption that space is perfectly flat, the WMAP-only constraint on the measured age of the Universe tightens from t0~16.3+2.3-1.8 Gyr to t0~14.1+1.0-0.9 Gyr by adding SDSS and SN Ia data. Including tensors, running tilt, neutrino mass and equation of state in the list of free parameters, many constraints are still quite weak, but future cosmological measurements from SDSS and other sources should allow these to be substantially tightened., Comment: Minor revisions to match accepted PRD version. SDSS data and ppt figures available at http://www.hep.upenn.edu/~max/sdsspars.html

We formulate a simple extension of general relativity which incorporates space-time variations in the Newtonian gravitation 'constant', $G$, and the fine structure 'constant', $\alpha $, which generalises Brans-Dicke theory and our theory of varying $\alpha .$ We determine the behaviour of Friedmann universes in this theory. In the radiation and dust-dominated eras $\alpha G$ approaches a constant value and the rate of variation of $\alpha $ is equal to the magnitude of the rate of variation in $G$. The expansion dynamics of the universe are dominated by the variation of $G$ but the variation of $G$ has significant effects upon the time variation of $\alpha .$ Time variations in $\alpha $ are extinguished by the domination of the expansion by spatial curvature or quintessence fields, as in the case with no $G$ variation., Comment: 8 pages, 2 figures. Submitted to Phys. Lett. B

We study inhomogeneous cosmological variations in the fine structure 'constant', $\alpha ,$ in Friedmann universes. Inhomogeneous motions of the scalar field driving changes in $\alpha $ display spatial oscillations that decrease in amplitude with increasing time. The inhomogeneous evolution quickly approaches that found for exact Friedmann universes. We prove a theorem to show that oscillations of $\alpha $ in time (or redshift) cannot occur in Friedmann universes in the BSBM theories considered here., Comment: 7 pages, no figures. Final version: improved discussion and addition of new theorem excluding time oscillations

In some cosmological theories with varying constants there are anthropic reasons why the expansion of the universe must not be too {\it close} to flatness or the cosmological constant too close to zero. Using exact theories which incorporate time-variations in $\alpha $ and in $G$ we show how the presence of negative spatial curvature and a positive cosmological constant play an essential role in bringing to an end variations in the scalar fields driving time change in these 'constants' during any dust-dominated era of a universe's expansion. In spatially flat universes with $\Lambda =0$ the fine structure constant grows to a value which makes the existence of atoms impossible., Comment: 7 pages, 5 figures, Corrected sign error and made necessary modifications. This version is accepted for publication in Phys.Rev.D

We determine the behaviour of a time-varying fine structure 'constant' $\alpha (t)$ during the early and late phases of universes dominated by the kinetic energy of changing $\alpha (t)$, radiation, dust, curvature, and lambda, respectively. We show that after leaving an initial vacuum-dominated phase during which $\alpha$ increases, $\alpha$ remains constant in universes like our own during the radiation era, and then increases slowly, proportional to a logarithm of cosmic time, during the dust era. If the universe becomes dominated by negative curvature or a positive cosmological constant then $\alpha$ tends rapidly to a constant value. The effect of an early period of de Sitter or power-law inflation is to drive $\alpha$ to a constant value. Various cosmological consequences of these results are discussed with reference to recent observational studies of the value of $\alpha$ from quasar absorption spectra and to the existence of life in expanding universes., Comment: 9 pages, 4 figures, Submitted to PRD

We investigate the cosmological consequences of a simple theory in which the electric charge $e$ is allowed to vary. The theory is locally gauge and Lorentz invariant, and satisfies general covariance. We find that in this theory the fine structure 'constant', $\alpha $, remains almost constant in the radiation era, undergoes small increase in the matter era, but approaches a constant value when the universe starts accelerating because of the presence of a positive cosmological constant. This model satisfies geonuclear, nucleosynthesis, and CMB constraints on time-variation in $\alpha $, while fitting simultaneously the observed accelerating universe and the recent high-redshift evidence for small $\alpha $ variations in quasar spectra. The model also places specific restrictions on the nature of the dark matter. Further tests, involving stellar spectra and the E\"otv\"os experiment, are proposed., Comment: 4 pages, 2 figures, Accepted for publication in Phys.Rev.Lett. Minor sign error corrected. Added references

We consider soliton solutions to Bekenstein's theory, for which the fine structure constant $\alpha=e^2/(4\pi\hbar c)$ is allowed to vary due to the presence of a dielectric field pervading the vacuum. More specifically we investigate the effects of a varying $\alpha$ upon a complex scalar field with a U(1) electromagnetic gauge symmetry subject to spontaneous symmetry breaking. We find vortex solutions to this theory, similar to the Nielsen-Olesen vortex. Near the vortex core the electric charge is typically much larger than far away from the string, lending these strings a superconducting flavour. In general the dielectric field coats the usual local string with a global string envelope. We discuss the cosmological implications of networks of such strings, with particular emphasis on their ability to generate inhomogeneous recombination scenarios. We also consider the possibility of the dielectric being a charged free field. Even though the vacuum of such a field is trivial, we find that the dielectric arranges itself in the shape of a local string, with a quantized magnetic flux at the core -- presumably borrowing these topological features from the underlying Nielsen-Olesen vortex., Comment: 7 pages, 1 figure

We extend a previous bispectrum analysis of the COBE-DMR 4 year maps, allowing for the presence of correlations between all possible angular scales. We find that the non-Gaussian signal found earlier for bispectrum components including adjacent modes does not extend to triplets of modes with larger separations. Indeed for all separations $\Delta\ell >1$ we find that the COBE-DMR data is very Gaussian. The implication seems to be that the previously detected non-Gaussian scale-scale correlation falls off very quickly with mode separation., Comment: 10 pages, 5 figures

Magnetohydrodynamic (MHD) waves are analysed in the early Universe, in the inflationary era, assuming the Universe to be filled with a nonviscous fluid of the Zel'dovich type ($p=\rho$) in a metric of the de Sitter form. A spatially uniform, time dependent, magnetic field ${\bf B_0}$ is assumed to be present. The Einstein equations are first solved to give the time dependence of the scale factor, assuming that the matter density, but not the magnetic field, contribute as source terms. The various modes are thereafter analysed; they turn out to be essentially of the same kind as those encountered in conventional nongravitational MHD, although the longitudinal magnetosonic wave is not interpretable as a physical energy-transporting wave as the group velocity becomes superluminal. We determine the phase speed of the various modes; they turn out to be scale factor independent. The Alfv\'{e}n velocity of the transverse magnetohydrodynamic wave becomes extremely small in the inflationary era, showing that the wave is in practice 'frozen in'., Comment: 19 pages, LaTeX, no figures. Minor additions to the Summary section and Acknowledgments section. Two new references. Version to appear in Phys. Rev. D