Topological Defects Formation after Inflation on Lattice Simulation

We consider the formation of topological defects after inflation. In order to take into account the effects of the rescattering of fluctuations, we integrate the classical equation that describes the evolution of a complex scalar field on the two-dimensional lattice with a slab symmetry. The growth of fluctuations during preheating is found not to be enough for defect formation, and rather a long stage of the rescattering of fluctuations after preheating is necessary. We conclude that the topological defects are not formed if the breaking scale \eta is lager than \sim (2 - 3)\times 10^{16} GeV.Comment: 7 pages, RevTex, 10 postscript figures included; version to be published in Phys. Rev.

A concave holomorphic filling of an overtwisted contact 3-sphere

We prove that the closed 4-ball admits non-Kahler complex structures with strongly pseudoconcave boundary. Moreover, the induced contact structure on the boundary 3-sphere is overtwisted

On the Moduli Problem and Baryogenesis in Gauge-mediated SUSY Breaking Models

We investigate whether the Affleck-Dine mechanism can produce sufficient baryon number of the universe in the gauge-mediated SUSY breaking models, while evading the cosmological moduli problem by late-time entropy production. We find that the Q-ball formation renders the scenario very difficult to work, irrespective of the detail mechanism of the entropy production.Comment: 11 pages, RevTeX, 5 postscript figures include

Affleck-Dine mechanism with negative thermal logarithmic potential

We investigate whether the Affleck-Dine (AD) mechanism works when the contribution of the two-loop thermal correction to the potential is negative in the gauge-mediated supersymmetry breaking models. The AD field is trapped far away from the origin by the negative thermal correction for a long time until the temperature of the universe becomes low enough. The most striking feature is that the Hubble parameter becomes much smaller than the mass scale of the radial component of the AD field, during the trap. Then, the amplitude of the AD field decreases so slowly that the baryon number is not fixed even after the onset of radial oscillation. The resultant baryon asymmetry crucially depends on whether the Hubble parameter, $H$, is larger than the mass scale of the phase component of the AD field, $M_\theta$, at the beginning of oscillation. If $H < M_\theta$ holds, the formation of Q balls plays an essential role to determine the baryon number, which is found to be washed out due to the nonlinear dynamics of Q-ball formation. On the other hand, if $H > M_\theta$ holds, it is found that the dynamics of Q-ball formation does not affect the baryon asymmetry, and that it is possible to generate the right amount of the baryon asymmetry.Comment: 18 pages, RevTeX4, 9 postscript figures included, final version to appear in Phys.Rev.

Reheating as a surface effect

We describe a new mechanism for reheating the Universe through evaporation of a surface charge of a fragmented inflaton condensate. We show that for a range of Yukawa coupling of the inflaton to the matter sector evaporation gives rise to a much smaller reheat temperature compared to the standard perturbative decay. As a consequence, reheating through a surface effect could solve the gravitino and moduli over production problem in inflationary models without fine tuning the Yukawa sector.Comment: 4 page

Entropy production by Q-ball decay for diluting long-lived charged particles

The cosmic abundance of a long-lived charged particle such as a stau is tightly constrained by the catalyzed big bang nucleosynthesis. One of the ways to evade the constraints is to dilute those particles by a huge entropy production. We evaluate the dilution factor in a case that non-relativistic matter dominates the energy density of the universe and decays with large entropy production. We find that large Q balls can do the job, which is naturally produced in the gauge-mediated supersymmetry breaking scenario.Comment: 8 pages, 1 figur

Optical RKKY Interaction between Charged Semiconductor Quantum Dots

We show how a spin interaction between electrons localized in neighboring quantum dots can be induced and controlled optically. The coupling is generated via virtual excitation of delocalized excitons and provides an efficient coherent control of the spins. This quantum manipulation can be realized in the adiabatic limit and is robust against decoherence by spontaneous emission. Applications to the realization of quantum gates, scalable quantum computers, and to the control of magnetization in an array of charged dots are proposed.Comment: 4 pages, 2 figure

On embeddings of almost complex manifolds in almost complex Euclidean spaces

We prove that any compact almost complex manifold $(M^{2m}, J)$ of real dimension $2m$ admits a pseudo-holomorphic embedding in $(R^{4m+2}, ilde{J})$ for a suitable positive almost complex structure $ilde J$. Moreover, we give a necessary and sufficient condition, expressed in terms of the Segre class $s_m(M, J)$, for the existence of an embedding or an immersion in $(R^{4m}, ilde{J})$. We also discuss the pseudo-holomorphic embeddings of an almost complex 4-manifold in $(R^6, ilde J)$

The oscillation effects on thermalization of the neutrinos in the universe with low reheating temperature

We study how the oscillations of the neutrinos affect their thermalization process during the reheating period with temperature O(1) MeV in the early universe. We follow the evolution of the neutrino density matrices and investigate how the predictions of big bang nucleosynthesis vary with the reheating temperature. For the reheating temperature of several MeV, we find that including the oscillations makes different predictions, especially for $^4$He abundance. Also, the effects on the lower bound of the reheating temperature from cosmological observations are discussed.Comment: 24 pages, 8 figures; references and explanatory comments added, conclusion unchange

Remarks on Cosmic String Formation during Preheating on Lattice Simulations

We reconsider the formation of (global) cosmic strings during and after preheating by calculating the dynamics of a scalar field on both two- and three- dimensional lattices. We have found that there is little differences between the results in two and three dimensions about the dynamics of fluctuations, at least, during preheating. Practically, it is difficult to determine whether long cosmic strings which may affect the later evolution of the universe could ever be produced from the results of simulations on three-dimensional lattices with smaller box sizes than the horizon. Therefore, using two-dimensional lattices with large box size, we have found that cosmic strings with the breaking scale 0\eta \sim 10^{16} GeV are produced for broad range of parameter space in \eta, while for higher breaking scales (\eta \sim 3\times 10^{16} GeV), their production depends crucially on the value of the breaking scale \eta in our simulations.Comment: 7 pages, RevTex, 14 postscript figures included, to appear in Phys. Rev.