Automorphism Inducing Diffeomorphisms, Invariant Characterization of Homogeneous 3-Spaces and Hamiltonian Dynamics of Bianchi Cosmologies

An invariant description of Bianchi Homogeneous (B.H.) 3-spaces is presented, by considering the action of the Automorphism Group on the configuration space of the real, symmetric, positive definite, $3\times 3$ matrices. Thus, the gauge degrees of freedom are removed and the remaining (gauge invariant) degrees, are the --up to 3-- curvature invariants. An apparent discrepancy between this Kinematics and the Quantum Hamiltonian Dynamics of the lower Class A Bianchi Types, occurs due to the existence of the Outer Automorphism Subgroup. This discrepancy is satisfactorily removed by exploiting the quantum version of some classical integrals of motion (conditional symmetries) which are recognized as corresponding to the Outer Automorphisms.Comment: 18 pages, LaTeX2e, no figures, one table, to appear in Communications in Mathematical Physic

String Thermalization in Static Spacetimes

We study the evolution, the transverse spreading and the subsequent thermalization of string states in the Weyl static axisymmetric spacetime. This possesses a singular event horizon on the symmetry axis and a naked singularity along the other directions. The branching diffusion process of string bits approaching the singular event horizon provides the notion of temperature that is calculated for this process. We find that the solution of the Fokker-Planck equation in the phase space of the transverse variables of the string, can be factored as a product of two thermal distributions, provided that the classical conjugate variables satisfy the uncertainty principle. We comment on the possible physical significance of this result.Comment: 16 pages, no figures, Late

Pre-Inflation in the Presence of Conformal Coupling

We consider a massless scalar field, conformally coupled to the Ricci scalar curvature, in the pre-inflation era of a closed FLRW Universe. The scalar field potential can be of the form of the Coleman-Weinberg one-loop potential, which is flat at the origin and drives the inflationary evolution. For positive values of the conformal parameter \xi, less than the critical value xi_c=(1/6), the model admits exact solutions with non-zero scale factor and zero initial Hubble parameter. Thus these solutions can be matched smoothly to the so called Pre-Big-Bang models. At the end of this pre-inflation era one can match inflationary solutions by specifying the form of the potential and the whole solution is of the class C^(1).Comment: 11 pages, 5 figures, LaTeX, Accepted for publication in MPL

Domain Walls on the Brane

We show that all branes admit worldvolume domain wall solutions. We find one class of solutions for which the tension of the brane changes discontinuously along the domain wall. These solutions are not supersymmetric. We argue that there is another class of domain wall solutions which is supersymmetric. A particular case concerns supersymmetric domain wall solutions on IIB D-5- and NS-5-branes.Comment: 18 pages, Tex, uses phyzz

On amplitude zeros at threshold

The occurrence of zeros of 2 to n amplitudes at threshold in scalar theories is studied. We find a differential equation for the scalar potential, which incorporates all known cases where the 2 to n amplitudes at threshold vanish for all sufficiently large $n$, in all space-time dimensions, $d\ge 1$. This equation is related to the reflectionless potentials of Quantum Mechanics and to integrable theories in 1+1 dimensions. As an application, we find that the sine-Gordon potential and its hyperbolic version, the sinh-Gordon potential, also have amplitude zeros at threshold, ${\cal A}(2\to n)=0$, for $n\ge 4$ and $d\ge 2$, independently of the mass and the coupling constant.Comment: 6 pages, Latex, CERN-TH.6762/9

Multiscalar production amplitudes beyond threshold

We present exact tree-order amplitudes for $H^* \to n~H$, for final states containing one or two particles with non-zero three-momentum, for various interaction potentials. We show that there are potentials leading to tree amplitudes that satisfy unitarity, not only at threshold but also in the above kinematical configurations and probably beyond. As a by-product, we also calculate $2\to n$ tree amplitudes at threshold and show that for the unbroken $\phi^4$ theory they vanish for $n>4~$, for the Standard Model Higgs they vanish for $n\ge 3~$ and for a model potential, respecting tree-order unitarity, for $n$ even and $n>4~$. Finally, we calculate the imaginary part of the one-loop $1\to n$ amplitude in both symmetric and spontaneously broken $\phi^4$ theory.Comment: 11 pages, Latex, 3 figures (available on request

Molecular and atomic line surveys of galaxies I: the dense, star-forming phase as a beacon

We predict the space density of molecular gas reservoirs in the Universe, and place a lower limit on the number counts of carbon monoxide (CO), hydrogen cyanide (HCN) molecular and [CII] atomic emission lines in blind redshift surveys in the submillimeter-centimeter spectral regime. Our model uses: (a) recently available HCN Spectral Line Energy Distributions (SLEDs) of local Luminous Infrared Galaxies (LIRGs, L_IR>10^11 L_sun), (b) a value for epsilon=SFR/M_dense(H_2) provided by new developments in the study of star formation feedback on the interstellar medium and (c) a model for the evolution of the infrared luminosity density. Minimal 'emergent' CO SLEDs from the dense gas reservoirs expected in all star-forming systems in the Universe are then computed from the HCN SLEDs since warm, HCN-bright gas will necessarily be CO-bright, with the dense star-forming gas phase setting an obvious minimum to the total molecular gas mass of any star-forming galaxy. We include [CII] as the most important of the far-infrared cooling lines. Optimal blind surveys with the Atacama Large Millimeter Array (ALMA) could potentially detect very distant (z~10-12) [CII] emitters in the >ULIRG galaxy class at a rate of ~0.1-1 per hour (although this prediction is strongly dependent on the star formation and enrichment history at this early epoch), whereas the (high-frequency) Square Kilometer Array (SKA) will be capable of blindly detecting z>3 low-J CO emitters at a rate of ~40-70 per hour. The [CII] line holds special promise for the detection of metal-poor systems with extensive reservoirs of CO-dark molecular gas where detection rates with ALMA can reach up to 2-7 per hour in Bands 4-6.Comment: 16 pages, 9 figures, accepted for publication in Ap

Recursive actions for scalar theories

We introduce a class of self-interacting scalar theories in which the various coupling contants obey a recursive relation. These imply a particularly simple form for the generating function of the Feynman amplitudes with vanishing external momenta, as well as for the effective potential. In addition we discuss an interesting duality inherent in these models. Specializing to the case of zero spacetime dimensions we find intriguing nullification properties for the amplitudes.Comment: 28 pages, 2 figures Replaced contract numbe