Finding a Spherically Symmetric Cosmology from Observations in Observational Coordinates -- Advantages and Challenges

One of the continuing challenges in cosmology has been to determine the large-scale space-time metric from observations with a minimum of assumptions -- without, for instance, assuming that the universe is almost Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW). If we are lucky enough this would be a way of demonstrating that our universe is FLRW, instead of presupposing it or simply showing that the observations are consistent with FLRW. Showing how to do this within the more general spherically symmetric, inhomogeneous space-time framework takes us a long way towards fulfilling this goal. In recent work researchers have shown how this can be done both in the traditional Lema\^{i}tre-Tolman-Bondi (LTB) 3 + 1 coordinate framework, and in the observational coordinate (OC) framework. In this paper we investigate the stability of solutions, and the use of data in the OC field equations including their time evolution and compare both approaches with respect to the singularity problem at the maximum of the angular-diameter distance, the stability of solutions, and the use of data in the field equations. This allows a more detailed account and assessment of the OC integration procedure, and enables a comparison of the relative advantages of the two equivalent solution frameworks. Both formulations and integration procedures should, in principle, lead to the same results. However, as we show in this paper, the OC procedure manifests certain advantages, particularly in the avoidance of coordinate singularities at the maximum of the angular-diameter distance, and in the stability of the solutions obtained. This particular feature is what allows us to do the best fitting of the data to smooth data functions and the possibility of constructing analytic solutions to the field equations.Comment: 31 page

On perfect fluid models in non-comoving observational spherical coordinates

We use null spherical (observational) coordinates to describe a class of inhomogeneous cosmological models. The proposed cosmological construction is based on the observer past null cone. A known difficulty in using inhomogeneous models is that the null geodesic equation is not integrable in general. Our choice of null coordinates solves the radial ingoing null geodesic by construction. Furthermore, we use an approach where the velocity field is uniquely calculated from the metric rather than put in by hand. Conveniently, this allows us to explore models in a non-comoving frame of reference. In this frame, we find that the velocity field has shear, acceleration and expansion rate in general. We show that a comoving frame is not compatible with expanding perfect fluid models in the coordinates proposed and dust models are simply not possible. We describe the models in a non-comoving frame. We use the dust models in a non-comoving frame to outline a fitting procedure.Comment: 8 pages, 1 figure. To appear in Phys.Rev.

An anisotropic cosmological model with isotropic background radiation

We present an exact solution of Einstein equations that describes a Bianchi type III spacetime with conformal expansion. The matter content is given by an anisotropic scalar field and two perfect fluids representing dust and isotropic radiation. Based on this solution, we construct a cosmological model that respects the evolution of the scale factor predicted in standard cosmology.Comment: 4 pages; contribution to the Proceedings of the 24th Spanish Relativity Meeting (ERE2001

The Lemaitre Model and the Generalisation of the Cosmic Mass

We consider the spherically symmetric metric with a comoving perfect fluid and non-zero pressure -- the Lemaitre metric -- and present it in the form of a calculational algorithm. We use it to review the definition of mass, and to look at the apparent horizon relations on the observer's past null cone. We show that the introduction of pressure makes it difficult to separate the mass from other physical parameters in an invariant way. Under the usual mass definition, the apparent horizon relation, that relates the diameter distance to the cosmic mass, remains the same as in the Lemaitre-Tolman case.Comment: latex, 16 pages, Revision has minor changes due to referee's comments

Conditions for spontaneous homogenization of the Universe

The present-day Universe appears to be homogeneous on very large scales. Yet when the casual structure of the early Universe is considered, it becomes apparent that the early Universe must have been highly inhomogeneous. The current paradigm attempts to answer this problem by postulating the inflation mechanism However, inflation in order to start requires a homogeneous patch of at least the horizon size. This paper examines if dynamical processes of the early Universe could lead to homogenization. In the past similar studies seem to imply that the set of initial conditions that leads to homogenization is of measure zero. This essay proves contrary: a set of initial conditions for spontaneous homogenization of cosmological models can form a set of non-zero measure.Comment: 7 pages. Fifth Award in the 2010 Gravity Research Foundation essay competitio

Large Deviations for Random Trees

We consider large random trees under Gibbs distributions and prove a Large Deviation Principle (LDP) for the distribution of degrees of vertices of the tree. The LDP rate function is given explicitly. An immediate consequence is a Law of Large Numbers for the distribution of vertex degrees in a large random tree. Our motivation for this study comes from the analysis of RNA secondary structures.Comment: 10 page

Supersymmetry Without Prejudice

We begin an exploration of the physics associated with the general CP-conserving MSSM with Minimal Flavor Violation, the pMSSM. The 19 soft SUSY breaking parameters in this scenario are chosen so as to satisfy all existing experimental and theoretical constraints assuming that the WIMP is a conventional thermal relic, ie, the lightest neutralino. We scan this parameter space twice using both flat and log priors for the soft SUSY breaking mass parameters and compare the results which yield similar conclusions. Detailed constraints from both LEP and the Tevatron searches play a particularly important role in obtaining our final model samples. We find that the pMSSM leads to a much broader set of predictions for the properties of the SUSY partners as well as for a number of experimental observables than those found in any of the conventional SUSY breaking scenarios such as mSUGRA. This set of models can easily lead to atypical expectations for SUSY signals at the LHC.Comment: 61 pages, 24 figs. Refs., figs, and text added, typos fixed; This version has reduced/bitmapped figs. For a version with better figs please go to http://www.slac.stanford.edu/~rizz

Agnesi Weighting for the Measure Problem of Cosmology

The measure problem of cosmology is how to assign normalized probabilities to observations in a universe so large that it may have many observations occurring at many different spacetime locations. I have previously shown how the Boltzmann brain problem (that observations arising from thermal or quantum fluctuations may dominate over ordinary observations if the universe expands sufficiently and/or lasts long enough) may be ameliorated by volume averaging, but that still leaves problems if the universe lasts too long. Here a solution is proposed for that residual problem by a simple weighting factor 1/(1+t^2) to make the time integral convergent. The resulting Agnesi measure appears to avoid problems other measures may have with vacua of zero or negative cosmological constant.Comment: 26 pages, LaTeX; discussion is added of how Agnesi weighting appears better than other recent measure

Further investigation of a relic neutralino as a possible origin of an annual-modulation effect in WIMP direct search

We analyze the annual-modulation effect, measured by the DAMA Collaboration with the new implementation of a further two-years running, in the context of a possible interpretation in terms of relic neutralinos. We impose over the set of supersymmetric configurations, selected by the annual-modulation data, the constraints derived from WIMP indirect measurements, and discuss the features of the ensuing relic neutralinos. We critically discuss the sources of the main theoretical uncertainties in the analysis of event rates for direct and indirect WIMP searches.Comment: 29 pages, 12 figures, typeset with ReVTeX. In order to reduce size, the version on the archive has low resolution figures. A full version of the paper can be found at http://www.to.infn.it/~fornengo/papers