Representations of SU(1,1) in Non-commutative Space Generated by the Heisenberg Algebra

SU(1,1) is considered as the automorphism group of the Heisenberg algebra H. The basis in the Hilbert space K of functions on H on which the irreducible representations of the group are realized is explicitly constructed. The addition theorems are derived.Comment: Latex, 8 page

Binary Cosmic Strings

The properties of cosmic strings have been investigated in detail for their implications in early-universe cosmology. Although many variations of the basic structure have been discovered, with implications for both the microscopic and macroscopic properties of cosmic strings, the cylindrical symmetry of the short-distance structure of the string is generally unaffected. In this paper we describe some mechanisms leading to an asymmetric structure of the string core, giving the defects a quasi-two-dimensional character. We also begin to investigate the consequences of this internal structure for the microscopic and macroscopic physics.Comment: 19 pages; uses harvmac (not included

Weak-Field Gravity of Revolving Circular Cosmic Strings

A weak-field solution of Einstein's equations is constructed. It is generated by a circular cosmic string revolving in its plane about the centre of the circle. (The revolution is introduced to prevent the string from collapsing.) This solution exhibits a conical singularity, and the corresponding deficit angle is the same as for a straight string of the same linear energy density, irrespective of the angular velocity of the string.Comment: 13 pages, LaTe

Fractional Super Lie Algebras and Groups

n^{th} root of a Lie algebra and its dual (that is fractional supergroup) based on the permutation group $S_n$ invariant forms are formulated in the Hopf algebra formalism. Detailed discussion of $S_3$-graided $sl(2)$ algebras is done.Comment: 13 pages, detailed discussion of $S_3$-graided $sl(2)$ is adde

Relic gravitational waves: latest revisions and preparations for new data

The forthcoming release of data from the Planck mission, and possibly from the next round of Wilkinson Microwave Anisotropy Probe (WMAP) observations, make it necessary to revise the evaluations of relic gravitational waves in the existing data and, at the same time, to refine the assumptions and data analysis techniques in preparation for the arrival of new data. We reconsider with the help of the commonly used CosmoMC numerical package the previously found indications of relic gravitational waves in the 7-year (WMAP7) data. The CosmoMC approach reduces the confidence of these indications from approximately 2$\sigma$ level to approximately 1$\sigma$ level, but the indications do not disappear altogether. We critically analyze the assumptions that are currently used in the Cosmic Microwave Background (CMB) data analyzes and outline the strategy that should help avoid the oversight of relic gravitational waves in the future CMB data. In particular, it is important to keep away from the unwarranted assumptions about density perturbations. The prospects of confident detection of relic gravitational waves by the Planck satellite have worsened, but they are still good. It appears that more effort will be required in order to mitigate the foreground contamination.Comment: 11 pages, 4 figures, 3 tables; v.3: improvements, published versio

Dynamics of domain walls intersecting black holes

Previous studies concerning the interaction of branes and black holes suggested that a small black hole intersecting a brane may escape via a mechanism of reconnection. Here we consider this problem by studying the interaction of a small black hole and a domain wall composed of a scalar field and simulate the evolution of this system when the black hole acquires an initial recoil velocity. We test and confirm previous results, however, unlike the cases previously studied, in the more general set-up considered here, we are able to follow the evolution of the system also during the separation, and completely illustrate how the escape of the black hole takes place.Comment: 4 pages, 6 figure

Spherical functions on the de Sitter group

Matrix elements and spherical functions of irreducible representations of the de Sitter group are studied on the various homogeneous spaces of this group. It is shown that a universal covering of the de Sitter group gives rise to quaternion Euler angles. An explicit form of Casimir and Laplace-Beltrami operators on the homogeneous spaces is given. Different expressions of the matrix elements and spherical functions are given in terms of multiple hypergeometric functions both for finite-dimensional and unitary representations of the principal series of the de Sitter group.Comment: 40 page

Why is Spacetime Lorentzian?

We expand on the idea that spacetime signature should be treated as a dynamical degree of freedom in quantum field theory. It has been argued that the probability distribution for signature, induced by massless free fields, is peaked at the Lorentzian value uniquely in D=4 dimensions. This argument is reviewed, and certain consistency constraints on the generalized signature (i.e. the tangent space metric \eta_{ab}(x)=\mbox{diag}[e^{i\theta(x)},1,1,1]) are derived. It is shown that only one dynamical "Wick angle" $\theta(x)$ can be introduced in the generalized signature, and the magnitude of fluctuations away from Lorentzian signature $\delta \theta = \pi - \theta$ is estimated to be of order $(l_P/R)^3$, where $l_P$ is the Planck length, and $R$ is the length scale of the Universe. For massless fields, the case of D=2 dimensions and the case of supersymmetry are degenerate, in the sense that no signature is preferred. Mass effects lift this degeneracy, and we show that a dynamical origin of Lorentzian signature is also possible for (broken) supersymmetry theories in D=6 dimensions, in addition to the more general non-supersymmetric case in D=4 dimensions.Comment: 26 pages, plain LaTeX, NBI-HE-93-3

Imprints of cosmic strings on the cosmological gravitational wave background

The equation which governs the temporal evolution of a gravitational wave (GW) in curved space-time can be treated as the Schrodinger equation for a particle moving in the presence of an effective potential. When GWs propagate in an expanding Universe with constant effective potential, there is a critical value (k_c) of the comoving wave-number which discriminates the metric perturbations into oscillating (k > k_c) and non-oscillating (k < k_c) modes. As a consequence, if the non-oscillatory modes are outside the horizon they do not freeze out. The effective potential is reduced to a non-vanishing constant in a cosmological model which is driven by a two-component fluid, consisting of radiation (dominant) and cosmic strings (sub-dominant). It is known that the cosmological evolution gradually results in the scaling of a cosmic-string network and, therefore, after some time (\Dl \ta) the Universe becomes radiation-dominated. The evolution of the non-oscillatory GW modes during \Dl \ta (while they were outside the horizon), results in the distortion of the GW power spectrum from what it is anticipated in a pure radiation-model, at present-time frequencies in the range 10^{-16} Hz < f < 10^5 Hz.Comment: 8 pages, 1 figure, accepted for publication to Physical Review

Evading the cosmological domain wall problem

Discrete symmetries are commonplace in field theoretical models but pose a severe problem for cosmology since they lead to the formation of domain walls during spontaneous symmetry breaking in the early universe. However if one of the vacuua is favoured over the others, either energetically, or because of initial conditions, it will eventually come to dominate the universe. Using numerical methods, we study the evolution of the domain wall network for a variety of field configurations in two and three dimensions and quantify the rate at which the walls disappear. Good agreement is found with a recent analytic estimate of the termination of the scaling regime of the wall network.Comment: 17 pages (revtex), including 9 figures (epsf); Revised to include test of numerical approximation used; No change in results or conclusions; accepted for publication in Phys Rev D. PostScript available at ftp://ftp.physics.ox.ac.uk/pub/local/users/sarkar/Domainwalls.ps.g