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

Dynamics of the infinitely-thin kink

We consider the dynamics of the domain-wall kink soliton, in particular we study the zero mode of translation. In the infinitely-thin kink limit, we show that the zero mode is almost completely frozen out, the only remnant being a dynamically constrained four-dimensional mode of a single but arbitrary frequency. In relation to this result, we show that the usual mode expansion for dealing with zero modes -- implicit collective coordinates -- is not in fact a completely general expansion, and that one must use instead a traditional generalised Fourier analysis.Comment: 13 pages; v2: added references, to appear in Phys Lett

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

A Note on the evolution of cosmic string/superstring networks

In the context of brane world scenario, cosmic superstrings can be formed in D-brane annihilation at the end of the brane inflationary era. The cosmic superstring network has a scaling solution and the characteristic scale of the network is proportional to the square root of the reconnection probability.Comment: 13 pages, 12 figures (revised version

A class of kinks in SU(N)\times Z_2

In a classical, quartic field theory with $SU(N) \times Z_2$ symmetry, a class of kink solutions can be found analytically for one special choice of parameters. We construct these solutions and determine their energies. In the limit $N\to \infty$, the energy of the kink is equal to that of a kink in a $Z_2$ model with the same mass parameter and quartic coupling (coefficient of ${\rm Tr}(\Phi^4)$). We prove the stability of the solutions to small perturbations but global stability remains unproven. We then argue that the continuum of choices for the boundary conditions leads to a whole space of kink solutions. The kinks in this space occur in classes that are determined by the chosen boundary conditions. Each class is described by the coset space $H/I$ where $H$ is the unbroken symmetry group and $I$ is the symmetry group that leaves the kink solution invariant.Comment: 7 pages; included discussion of gauge fields and other improvement

Anthropic predictions for vacuum energy and neutrino masses

It is argued that the observed vacuum energy density and the small values of the neutrino masses could be due to anthropic selection effects. Until now, these two quantities have been treated separately from each other and, in particular, anthropic predictions for the vacuum energy were made under the assumption of zero neutrino masses. Here we consider two cases. In the first, we calculate predictions for the vacuum energy for a fixed (generally non-zero) value of the neutrino mass. In the second we allow both quantities to vary from one part of the universe to another. We find that the anthropic predictions for the vacuum energy density are in a better agreement with observations when one allows for non-zero neutrino masses. We also find that the individual distributions for the vacuum energy and the neutrino masses are reasonably robust and do not change drastically when one adds the other variable.Comment: 9 pages, 4 figure

Cosmic strings and Natural Inflation

In the present work we discuss cosmic strings in natural inflation. Our analysis is based entirely on the CMB quadrupole temperature anisotropy and on the existing upper bound on the cosmic string tension. Our results show that the allowed range for both parameters of the inflationary model is very different from the range obtained recently if cosmic strings are formed at the same time with inflation, while if strings are formed after inflation we find that the parameters of the inflationary model are similar to the ones obtained recently.Comment: 12 pages, 0 tables, 4 figures, accepted for publication in JHE

An Index Theorem for Domain Walls in Supersymmetric Gauge Theories

The supersymmetric abelian Higgs model with N scalar fields admits multiple domain wall solutions. We perform a Callias-type index calculation to determine the number of zero modes of this soliton. We confirm that the most general domain wall has 2(N-1) zero modes, which can be interpreted as the positions and phases of (N-1) constituent domain walls. This implies the existence of moduli for a D-string interpolating between N D5-branes in IIB string theory.Comment: 9 pages, REVTeX4; v2: reference adde

Observational constraints on cosmic strings: Bayesian analysis in a three dimensional parameter space

Current data exclude cosmic strings as the primary source of primordial density fluctuations. However, in a wide class of inflationary models, strings can form at later stages of inflation and have potentially detectable observational signatures. We study the constraints from WMAP and SDSS data on the fraction of primordial fluctuations sourced by local cosmic strings. The Bayesian analysis presented in this brief report is restricted to the minimal number of parameters. Yet it is useful for two reasons. It confirms the results of Pogosian et al (2003) using an alternative statistical method. Secondly, it justifies the more costly multi-parameter analysis. Already, varying only three parameters -- the spectral index and the amplitudes of the adiabatic and string contributions -- we find that the upper bound on the cosmic string contribution is of order 10%. We expect that the full multi-parameter study, currently underway, will likely loosen this bound.Comment: v3: 4 pages, 5 figures, slight modifications to match published versio

Multiple universes, cosmic coincidences, and other dark matters

Even when completely and consistently formulated, a fundamental theory of physics and cosmological boundary conditions may not give unambiguous and unique predictions for the universe we observe; indeed inflation, string/M theory, and quantum cosmology all arguably suggest that we can observe only one member of an ensemble with diverse properties. How, then, can such theories be tested? It has been variously asserted that in a future measurement we should observe the a priori most probable set of predicted properties (the ``bottom-up'' approach), or the most probable set compatible with all current observations (the ``top-down'' approach), or the most probable set consistent with the existence of observers (the ``anthropic'' approach). These inhabit a spectrum of levels of conditionalization and can lead to qualitatively different predictions. For example, in a context in which the densities of various species of dark matter vary among members of an ensemble of otherwise similar regions, from the top-down or anthropic viewpoints -- but not the bottom-up -- it would be natural for us to observe multiple types of dark matter with similar contributions to the observed dark matter density. In the anthropic approach it is also possible in principle to strengthen this argument and the limit the number of likely dark matter sub-components. In both cases the argument may be extendible to dark energy or primordial density perturbations. This implies that the anthropic approach to cosmology, introduced in part to explain "coincidences" between unrelated constituents of our universe, predicts that more, as-yet-unobserved coincidences should come to light.Comment: 18 JCAP-style pages, accepted by JCAP. Revised version adds references and some clarification