Expectations for the Difference Between Local and Global Measurements of the Hubble Constant

There are irreducible differences between the Hubble constant measured locally and the global value. They are due to density perturbations and finite sample volume (cosmic variance) and finite number of objects in the sample (sampling variance). We quantify these differences for a suite of COBE-normalized CDM models that are consistent with the observed large-scale structure. For small samples of objects that only extend out to 10,000 km/sec, the variance can approach 4%. For the largest samples of Type Ia supernovae (SNeIa), which include about 40 objects and extend out to almost 40,000 km/sec, the variance is 1-2% and is dominated by sampling variance. Sampling and cosmic variance may be an important consideration in comparing local determinations of the Hubble constant with precision determinations of the global value that will be made from high-resolution maps of CBR anisotropy.Comment: 10 pages, Latex, 2 figures, version accepted for Ap.

Gravitational Collapse in One Dimension

We simulate the evolution of one-dimensional gravitating collisionless systems from non- equilibrium initial conditions, similar to the conditions that lead to the formation of dark- matter halos in three dimensions. As in the case of 3D halo formation we find that initially cold, nearly homogeneous particle distributions collapse to approach a final equilibrium state with a universal density profile. At small radii, this attractor exhibits a power-law behavior in density, {\rho}(x) \propto |x|^(-{\gamma}_crit), {\gamma}_crit \simeq 0.47, slightly but significantly shallower than the value {\gamma} = 1/2 suggested previously. This state develops from the initial conditions through a process of phase mixing and violent relaxation. This process preserves the energy ranks of particles. By warming the initial conditions, we illustrate a cross-over from this power-law final state to a final state containing a homogeneous core. We further show that inhomogeneous but cold power-law initial conditions, with initial exponent {\gamma}_i > {\gamma}_crit, do not evolve toward the attractor but reach a final state that retains their original power-law behavior in the interior of the profile, indicating a bifurcation in the final state as a function of the initial exponent. Our results rely on a high-fidelity event-driven simulation technique.Comment: 14 Pages, 13 Figures. Submitted to MNRA

Nonexistence theorems for traversable wormholes

Gauss-Bonnet formula is used to derive a new and simple theorem of nonexistence of vacuum static nonsingular lorentzian wormholes. We also derive simple proofs for the nonexistence of lorentzian wormhole solutions for some classes of static matter such as, for instance, real scalar fields with a generic potential obeying $\phi V'(\phi) \ge 0$ and massless fermions fields

Lensing of the CMB: Non Gaussian aspects

We study the generation of CMB anisotropies by gravitational lensing on small angular scales. We show these fluctuations are not Gaussian. We prove that the power spectrum of the tail of the CMB anisotropies on small angular scales directly gives the power spectrum of the deflection angle. We show that the generated power on small scales is correlated with the large scale gradient. The cross correlation between large scale gradient and small scale power can be used to test the hypothesis that the extra power is indeed generated by lensing. We compute the three and four point function of the temperature in the small angle limit. We relate the non-Gaussian aspects presented in this paper as well as those in our previous studies of the lensing effects on large scales to the three and four point functions. We interpret the statistics proposed in terms of different configurations of the four point function and show how they relate to the statistic that maximizes the S/N.Comment: Changes to match accepted version in PRD, 20 pages 10 figures. Better resolution images of the figures can be found at http://www.sns.ias.edu/~matiasz/RESEARCH/cmblensing.htm

Kinetic decoupling of neutralino dark matter

After neutralinos cease annihilating in the early Universe, they may still scatter elastically from other particles in the primordial plasma. At some point in time, however, they will eventually stop scattering. We calculate the cross sections for neutralino elastic scattering from standard-model particles to determine the time at which this kinetic decoupling occurs. We show that kinetic decoupling occurs above a temperature $T\sim$ MeV. Thereafter, neutralinos act as collisionless cold dark matter.Comment: Replaced with revised version, new references adde

Using the acoustic peak to measure cosmological parameters

Recent measurements of the cosmic microwave background radiation by the Boomerang experiment indicate that the universe is spatially flat. Here some simple back-of-the-envelope calculations are used to explain their result. The main result is a simple formula for the angular scale of the acoustic peak in terms of the standard cosmological parameters: l=193*[1+3(1-Omega_0)/5+(1-h)/5+Omega_Lambda/35].Comment: 4 pages, 1 figure, Explanations have been clarifie

Direct Signature of Evolving Gravitational Potential from Cosmic Microwave Background

We show that time dependent gravitational potential can be directly detected from the cosmic microwave background (CMB) anisotropies. The signature can be measured by cross-correlating the CMB with the projected density field reconstructed from the weak lensing distortions of the CMB itself. The cross-correlation gives a signal whenever there is a time dependent gravitational potential. This method traces dark matter directly and has a well defined redshift distribution of the window projecting over the density perturbations, thereby avoiding the problems plaguing other proposed cross-correlations. We show that both MAP and Planck will be able to probe this effect for observationally relevant curvature and cosmological constant models, which will provide additional constraints on the cosmological parameters.Comment: 4 pages, 2 figures. Submitted to PR