Survival of a diffusing particle in an expanding cage

We consider a Brownian particle, with diffusion constant D, moving inside an expanding d-dimensional sphere whose surface is an absorbing boundary for the particle. The sphere has initial radius L_0 and expands at a constant rate c. We calculate the joint probability density, p(r,t|r_0), that the particle survives until time t, and is at a distance r from the centre of the sphere, given that it started at a distance r_0 from the centre.Comment: 5 page

Time-Dependent Vacuum Energy Induced by D-Particle Recoil

We consider cosmology in the framework of a `material reference system' of D particles, including the effects of quantum recoil induced by closed-string probe particles. We find a time-dependent contribution to the cosmological vacuum energy, which relaxes to zero as $\sim 1/ t^2$ for large times $t$. If this energy density is dominant, the Universe expands with a scale factor $R(t) \sim t^2$. We show that this possibility is compatible with recent observational constraints from high-redshift supernovae, and may also respect other phenomenological bounds on time variation in the vacuum energy imposed by early cosmology.Comment: 14 pages LATEX, no figure

Two-fluid evolving Lorentzian wormholes

We investigate the evolution of a family of wormholes sustained by two matter components: one with homogeneous and isotropic properties $\rho(t)$ and another inhomogeneous and anisotropic $\rho_{in}(t,r)$. The rate of expansion of these evolving wormholes is only determined by the isotropic and homogeneous matter component $\rho(t)$. Particularly, we consider a family of exact two-fluid evolving wormholes expanding with constant velocity and satisfying the dominant and the strong energy conditions in the whole spacetime. In general, for the case of vanishing isotropic fluid $\rho(t)$ and cosmological constant $\Lambda$ the space expands with constant velocity, and for $\rho(t)=0$ and $\Lambda \neq 0$ the rate of expansion is determined by the cosmological constant. The considered here two-fluid evolving wormholes are a generalization of single fluid models discussed in previous works of the present authors [Phys.\ Rev.\ D {\bf 78}, 104006 (2008); Phys.\ Rev.\ D {\bf 79}, 024005 (2009)].Comment: 8 pages, to be published in Phys. Rev

One more fitting (D=5) of Supernovae red shifts

Supernovae red shifts are fitted in a simple 5D model: the galaxies are assumed to be enclosed in a giant S^3-spherical shell which expands (ultra) relativistically in a (1+4)D Minkowski space. This model, as compared with the kinematical (1+3)D model of Prof Farley, goes in line with the Copernican principle: any galaxy observes the same isotropic distribution of distant supernovae, as well as the same Hubble plot of distance modulus \mu vs red shift z. A good fit is obtained (no free parameters); it coincides with Farley's fit at low z, while shows some more luminosity at high z, leading to 1% decrease in the true distance modulus (and 50% increase in luminosity) at z\sim 2. The model proposed can be also interpreted as a FLRW-like model with the scale factor a(t)=t/t_0; this could not be a solution of general relativity (5D GR is also unsuitable--it has no longitudinal polarization). However, there still exists the other theory (with D=5 and no singularities in solutions), the other game in the town, which seems to be able to do the job.Comment: 5 pages, 3 figure

Expansion Aspect of Color Transparency on the Lattice

The opportunity to observe color transparency (CT) is determined by how rapidly a small-sized hadronic wave packet expands. Here we use SU(2) lattice gauge theory with Wilson fermions in the quenched approximation to investigate the expansion. The wave packet is modeled by a point hadronic source, often used as an interpolating field in lattice calculations. The procedure is to determine the Euclidean time (t), pion channel, Bethe-Salpeter amplitude $\Psi(r,t)$, and then evaluate $b^2(t)=\int d^3 r \Psi(r,t) r^2 sin^2 \theta \Psi_{\pi}(r)$. This quantity represents the soft interaction of a small-sized wave packet with a pion. The time dependence of $b^2(t)$ is fit as a superposition of three states, which is found sufficient to reproduce a reduced size wave packet. Using this superposition allows us to make the analytic continuation required to study the wave packet expansion in real time. We find that the matrix elements of the soft interaction $\hat b^2$ between the excited and ground state decrease rapidly with the energy of the excited state.Comment: 19 pages, latex, 4 figure

Charm-Meson tt-channel Singularities in an Expanding Hadron Gas

We study the time evolution of the numbers of charm mesons after the kinetic freezeout of the expanding hadron gas produced by the hadronization of the quark-gluon plasma from a central heavy-ion collision. The $\pi D$ reaction rates have contributions from a $D^\ast$ resonance in the $s$ channel. The $\pi D^\ast$ reaction rates are enhanced by $t$-channel singularities from an intermediate $D$. The contributions to reaction rates from $D^\ast$ resonances and $D$-meson $t$-channel singularities are sensitive to thermal mass shifts and thermal widths. In the expanding hadron gas, the $t$-channel singularities are regularized by the thermal $D$ widths. After kinetic freezeout, the thermal $D$ widths are dominated by coherent pion forward scattering. The contributions to $\pi D^\ast$ reaction rates from $t$-channel singularities are inversely proportional to the pion number density, which decreases to 0 as the hadron gas expands. The $t$-channel singularities produce small but significant changes in charm-meson ratios from those predicted using the known $D^\ast$-decay branching fractions.Comment: 41 pages, 12 figure