On formation of domain wall lattices

We study the formation of domain walls in a phase transition in which an S_5\times Z_2 symmetry is spontaneously broken to S_3\times S_2. In one compact spatial dimension we observe the formation of a stable domain wall lattice. In two spatial dimensions we find that the walls form a network with junctions, there being six walls to every junction. The network of domain walls evolves so that junctions annihilate anti-junctions. The final state of the evolution depends on the relative dimensions of the simulation domain. In particular we never observe the formation of a stable lattice of domain walls for the case of a square domain but we do observe a lattice if one dimension is somewhat smaller than the other. During the evolution, the total wall length in the network decays with time as t^{-0.71}, as opposed to the usual t^{-1} scaling typical of regular Z_2 networks.Comment: 7 pages, 4 figures. Minor changes, final version accepted for publication in Phys. Rev.

Symmetries within domain walls

The comparison of symmetries in the interior and the exterior of a domain wall is relevant when discussing the correspondence between domain walls and branes, and also when studying the interaction of walls and magnetic monopoles. I discuss the symmetries in the context of an SU(N) times Z_2 model (for odd N) with a single adjoint scalar field. Situations in which the wall interior has less symmetry than the vacuum are easy to construct while the reverse situation requires significant engineering of the scalar potential.Comment: 5 pages. Added reference

Domain Walls in SU(5)

We consider the Grand Unified SU(5) model with a small or vanishing cubic term in the adjoint scalar field in the potential. This gives the model an approximate or exact Z$_2$ symmetry whose breaking leads to domain walls. The simplest domain wall has the structure of a kink across which the Higgs field changes sign ($\Phi \to -\Phi$) and inside which the full SU(5) is restored. The kink is shown to be perturbatively unstable for all parameters. We then construct a domain wall solution that is lighter than the kink and show it to be perturbatively stable for a range of parameters. The symmetry in the core of this domain wall is smaller than that outside. The interactions of the domain wall with magnetic monopole is discussed and it is shown that magnetic monopoles with certain internal space orientations relative to the wall pass through the domain wall. Magnetic monopoles in other relative internal space orientations are likely to be swept away on collision with the domain walls, suggesting a scenario where the domain walls might act like optical polarization filters, allowing certain monopole ``polarizations'' to pass through but not others. As SU(5) domain walls will also be formed at small values of the cubic coupling, this leads to a very complicated picture of the evolution of defects after the Grand Unified phase transition.Comment: 6 pages, 1 figure. Animations can be viewed at http://theory4.phys.cwru.edu/~levon/figures.htm

Kink interactions in SU(N)×Z2SU(N)\times Z_2

There are $N-1$ classes of kink solutions in $SU(N)\times Z_2$. We show how interactions between various kinks depend on the classes of individual kinks as well as on their orientations with respect to each other in the internal space. In particular, we find that the attractive or repulsive nature of the interaction depends on the trace of the product of charges of the two kinks. We calculate the interaction potential for all combinations of kinks and antikinks in $SU(5)\times Z_2$ and study their collisions. The outcome of kink-antikink collisions, as expected from previous studies, is sensitive to their initial relative velocity. We find that heavier kinks tend to break up into lighter ones, while interactions between the lightest kinks and antikinks in this model can be repulsive as well as attractive.Comment: 11 pages, 9 figures. Two insignificant sign errors corrected in the revised versio

Still flat after all these years

The Universe could be spatially flat, positively curved or negatively curved. Each option has been popular at various times, partly affected by an understanding that models tend to evolve away from flatness. The curvature of the Universe is amenable to measurement, through tests such as the determination of the angles of sufficiently large triangles. The angle subtended by the characteristic scale on the Cosmic Microwave sky provides a direct test, which has now been realised through a combination of exquisite results from a number of CMB experiments. After a long and detailed investigation, with many false clues, it seems that the mystery of the curvature of the Universe is now solved. It's an open and shut case: the Universe is flat.Comment: 7 pages, 2 figures, submitted to the Gravity Research Foundation Essay Competition for 200

Observational signatures of f(R) dark energy models that satisfy cosmological and local gravity constraints

We discuss observational consequences of f(R) dark energy scenarios that satisfy local gravity constraints (LGC) as well as conditions of the cosmological viability. The model we study is given by m(r)=C(-r-1)^p (C>0, p>1) with m=Rf_{,RR}/f_{,R} and r=-Rf_{,R}/f, which cover viable f(R) models proposed so far in a high-curvature region designed to be compatible with LGC. The equation of state of dark energy exhibits a divergence at a redshift z_c that can be as close as a few while satisfying sound horizon constraints of Cosmic Microwave Background (CMB). We study the evolution of matter density perturbations in details and place constraints on model parameters from the difference of spectral indices of power spectra between CMB and galaxy clustering. The models with p>5 can be consistent with those observational constraints as well as LGC. We also discuss the evolution of perturbations in the Ricci scalar R and show that an oscillating mode (scalaron) can easily dominate over a matter-induced mode as we go back to the past. This violates the stability of cosmological solutions, thus posing a problem about how the over-production of scalarons should be avoided in the early universe.Comment: 13 pages, 7 figures, version to appear in Physical Review

Space of kink solutions in SU(N)\times Z_2

We find $(N+1)/2$ distinct classes (``generations'') of kink solutions in an $SU(N)\times Z_2$ field theory. The classes are labeled by an integer $q$. The members of one class of kinks will be globally stable while those of the other classes may be locally stable or unstable. The kink solutions in the $q^{th}$ class have a continuous degeneracy given by the manifold $\Sigma_q=H/K_q$, where $H$ is the unbroken symmetry group and $K_q$ is the group under which the kink solution remains invariant. The space $\Sigma_q$ is found to contain incontractable two spheres for some values of $q$, indicating the possible existence of certain incontractable spherical structures in three dimensions. We explicitly construct the three classes of kinks in an SU(5) model with quartic potential and discuss the extension of these ideas to magnetic monopole solutions in the model.Comment: 11 pages, 3 figures. Several minor changes made. Matches the version accepted to PR

A Rotating Charged Black Hole Solution in f(R) Gravity

In the context of f(R) theories of gravity, we address the problem of finding a rotating charged black hole solution in the case of constant curvature. The new metric is obtained by solving the field equations and we show that the behavior of it is typical of a rotating charged source. In addition, we analyze the thermodynamics of the new black hole. The results ensures that the thermodynamical properties in f(R) gravities are qualitatively similar to those of standard General Relativity.Comment: 9 pages, no figure

Scaling configurations of cosmic superstring networks and their cosmological implications

We study the cosmic microwave background temperature and polarisation spectra sourced by multi-tension cosmic superstring networks. First we obtain solutions for the characteristic length scales and velocities associated with the evolution of a network of F-D strings, allowing for the formation of junctions between strings of different tensions. We find two distinct regimes describing the resulting scaling distributions for the relative densities of the different types of strings, depending on the magnitude of the fundamental string coupling g_s. In one of them, corresponding to the value of the coupling being of order unity, the network's stress-energy power spectrum is dominated by populous light F and D strings, while the other regime, at smaller values of g_s, has the spectrum dominated by rare heavy D strings. These regimes are seen in the CMB anisotropies associated with the network. We focus on the dependence of the shape of the B-mode polarisation spectrum on g_s and show that measuring the peak position of the B-mode spectrum can point to a particular value of the string coupling. Finally, we assess how this result, along with pulsar bounds on the production of gravitational waves from strings, can be used to constrain a combination of g_s and the fundamental string tension mu_F. Since CMB and pulsar bounds constrain different combinations of the string tensions and densities, they result in distinct shapes of bounding contours in the (mu_F, g_s) parameter plane, thus providing complementary constraints on the properties of cosmic superstrings.Comment: 23 pages, 8 figures, 3 tables; V2: matches published version (PRD

The circular loop equation of a cosmic string with time-varying tension

The equation of circular loops of cosmic string with time-dependent tension is studied in the Minkowski spacetime and Robertson-Walker universe. We find that, in the case where the tension depends on some power of the cosmic time, cosmic string loops with time-varying tension should not collapse to form a black hole if the power is lower than a critical value.Comment: 8 pages, 3 figures. accepted by Modern Physics Letters