String dynamics in cosmological and black hole backgrounds: The null string expansion

We study the classical dynamics of a bosonic string in the $D$--dimensional flat Friedmann--Robertson--Walker and Schwarzschild backgrounds. We make a perturbative development in the string coordinates around a {\it null} string configuration; the background geometry is taken into account exactly. In the cosmological case we uncouple and solve the first order fluctuations; the string time evolution with the conformal gauge world-sheet $\tau$--coordinate is given by $X^0(\sigma, \tau)=q(\sigma)\tau^{1\over1+2\beta}+c^2B^0(\sigma, \tau)+\cdots$, $B^0(\sigma,\tau)=\sum_k b_k(\sigma)\tau^k$ where $b_k(\sigma)$ are given by Eqs.\ (3.15), and $\beta$ is the exponent of the conformal factor in the Friedmann--Robertson--Walker metric, i.e. $R\sim\eta^\beta$. The string proper size, at first order in the fluctuations, grows like the conformal factor $R(\eta)$ and the string energy--momentum tensor corresponds to that of a null fluid. For a string in the black hole background, we study the planar case, but keep the dimensionality of the spacetime $D$ generic. In the null string expansion, the radial, azimuthal, and time coordinates $(r,\phi,t)$ are $r=\sum_n A^1_{n}(\sigma)(-\tau)^{2n/(D+1)}~,$ $\phi=\sum_n A^3_{n}(\sigma)(-\tau)^{(D-5+2n)/(D+1)}~,$ and $t=\sum_n A^0_{n} (\sigma)(-\tau)^{1+2n(D-3)/(D+1)}~.$ The first terms of the series represent a {\it generic} approach to the Schwarzschild singularity at $r=0$. First and higher order string perturbations contribute with higher powers of $\tau$. The integrated string energy-momentum tensor corresponds to that of a null fluid in $D-1$ dimensions. As the string approaches the $r=0$ singularity its proper size grows indefinitely like $\sim(-\tau)^{-(D-3)/(D+1)}$. We end the paper giving three particular exact string solutions inside the black hole.Comment: 17 pages, REVTEX, no figure

Mass Spectrum of Strings in Anti de Sitter Spacetime

We perform string quantization in anti de Sitter (AdS) spacetime. The string motion is stable, oscillatory in time with real frequencies $\omega_n= \sqrt{n^2+m^2\alpha'^2H^2}$ and the string size and energy are bounded. The string fluctuations around the center of mass are well behaved. We find the mass formula which is also well behaved in all regimes. There is an {\it infinite} number of states with arbitrarily high mass in AdS (in de Sitter (dS) there is a {\it finite} number of states only). The critical dimension at which the graviton appears is $D=25,$ as in de Sitter space. A cosmological constant $\Lambda\neq 0$ (whatever its sign) introduces a {\it fine structure} effect (splitting of levels) in the mass spectrum at all states beyond the graviton. The high mass spectrum changes drastically with respect to flat Minkowski spacetime. For $\Lambda\sim \mid\Lambda\mid N^2,$ {\it independent} of $\alpha',$ and the level spacing {\it grows} with the eigenvalue of the number operator, $N.$ The density of states $\rho(m)$ grows like \mbox{Exp}[(m/\sqrt{\mid\Lambda\mid}\;)^{1/2}] (instead of \rho(m)\sim\mbox{Exp}[m\sqrt{\alpha'}] as in Minkowski space), thus {\it discarding} the existence of a critical string temperature. For the sake of completeness, we also study the quantum strings in the black string background, where strings behave, in many respects, as in the ordinary black hole backgrounds. The mass spectrum is equal to the mass spectrum in flat Minkowski space.Comment: 31 pages, Latex, DEMIRM-Paris-9404

Highlights and Conclusions of the Chalonge 14th Paris Cosmology Colloquium 2010: `The Standard Model of the Universe: Theory and Observations'

The Chalonge 14th Paris Cosmology Colloquium was held on 22-24 July 2010 in Paris Observatory on the Standard Model of the Universe: News from WMAP7, BICEP, QUAD, SPT, AMI, ACT, Planck, QUIJOTE and Herschel; dark matter (DM) searches and galactic observations; related theory and simulations. %aiming synthesis, progress and clarification. P Biermann, D Boyanovsky, A Cooray, C Destri, H de Vega, G Gilmore, S Gottlober, E Komatsu, S McGaugh, A Lasenby, R Rebolo, P Salucci, N Sanchez and A Tikhonov present here their highlights of the Colloquium. Inflection points emerged: LambdaWDM (Warm DM) emerges impressively over LambdaCDM whose galactic scale problems are ever-increasing. Summary and conclusions by H. J. de Vega, M. C. Falvella and N. G. Sanchez stress among other points: (i) Primordial CMB gaussianity is confirmed. Inflation effective theory predicts a tensor to scalar ratio 0.05-0.04 at reach/border line of next CMB observations, early fast-roll inflation provides lowest multipoles depression. SZ amplitudes are smaller than expected: CMB and X-ray data agree but intracluster models need revision and relaxed/non-relaxed clusters distinction. (ii) cosmic ray positron excess is explained naturally by astrophysical processes, annihilating/decaying dark matter needs growing tailoring. (iii) Cored (non cusped) DM halos and warm (keV scale mass) DM are increasingly favored from theory and observations, naturally producing observed small scale structures, wimps turn strongly disfavoured. LambdaWDM 1 keV simulations well reproduce observations. Evidence that LambdaCDM does not work at small scales is staggering. P Biermann presents his live minutes of the Colloquium and concludes that a keV sterile neutrino is the most interesting DM candidate. Photos of the Colloquium are included.Comment: 58 pages, 20 figures. Three contributions added: G. Gilmore, S. Gottlober and E. Komats

String Instabilities in Black Hole Spacetimes

We study the emergence of string instabilities in $D$ - dimensional black hole spacetimes (Schwarzschild and Reissner - Nordstr\o m), and De Sitter space (in static coordinates to allow a better comparison with the black hole case). We solve the first order string fluctuations around the center of mass motion at spatial infinity, near the horizon and at the spacetime singularity. We find that the time components are always well behaved in the three regions and in the three backgrounds. The radial components are {\it unstable}: imaginary frequencies develop in the oscillatory modes near the horizon, and the evolution is like $(\tau-\tau_0)^{-P}$, $(P>0)$, near the spacetime singularity, $r\to0$, where the world - sheet time $(\tau-\tau_0)\to0$, and the proper string length grows infinitely. In the Schwarzschild black hole, the angular components are always well - behaved, while in the Reissner - Nordstr\o m case they develop instabilities inside the horizon, near $r\to0$ where the repulsive effects of the charge dominate over those of the mass. In general, whenever large enough repulsive effects in the gravitational background are present, string instabilities develop. In De Sitter space, all the spatial components exhibit instability. The infalling of the string to the black hole singularity is like the motion of a particle in a potential $\gamma(\tau-\tau_0)^{-2}$ where $\gamma$ depends on the $D$ spacetime dimensions and string angular momentum, with $\gamma>0$ for Schwarzschild and $\gamma<0$ for Reissner - Nordstr\o m black holes. For $(\tau-\tau_0)\to0$ the string ends trapped by the black hole singularity.Comment: 26pages, Plain Te

Multi-String Solutions by Soliton Methods in De Sitter Spacetime

{\bf Exact} solutions of the string equations of motion and constraints are {\bf systematically} constructed in de Sitter spacetime using the dressing method of soliton theory. The string dynamics in de Sitter spacetime is integrable due to the associated linear system. We start from an exact string solution $q_{(0)}$ and the associated solution of the linear system $\Psi^{(0)} (\lambda)$, and we construct a new solution $\Psi(\lambda)$ differing from $\Psi^{(0)}(\lambda)$ by a rational matrix in $\lambda$ with at least four poles $\lambda_{0},1/\lambda_{0},\lambda_{0}^*,1/\lambda_{0}^*$. The periodi- city condition for closed strings restrict $\lambda _{0}$ to discrete values expressed in terms of Pythagorean numbers. Here we explicitly construct solu- tions depending on $(2+1)$-spacetime coordinates, two arbitrary complex numbers (the 'polarization vector') and two integers $(n,m)$ which determine the string windings in the space. The solutions are depicted in the hyperboloid coor- dinates $q$ and in comoving coordinates with the cosmic time $T$. Despite of the fact that we have a single world sheet, our solutions describe {\bf multi- ple}(here five) different and independent strings; the world sheet time $\tau$ turns to be a multivalued function of $T$.(This has no analogue in flat space- time).One string is stable (its proper size tends to a constant for $T\to\infty$, and its comoving size contracts); the other strings are unstable (their proper sizes blow up for $T\to\infty$, while their comoving sizes tend to cons- tants). These solutions (even the stable strings) do not oscillate in time. The interpretation of these solutions and their dynamics in terms of the sinh- Gordon model is particularly enlighting.Comment: 25 pages, latex. LPTHE 93-44. Figures available from the auhors under reques

Towards the Chalonge 17th Paris Cosmology Colloquium 2013: highlights and conclusions of the Chalonge 16th Paris Cosmology Colloquium 2012

LWDM (Warm Dark Matter) is progressing impressively.The galactic scale crisis and decline of LCDM+baryons are staggering. The 16th Paris Chalonge Colloquium 2012 combined real cosmological/astrophysical data and hard theory predictive approach in the LWDM Standard Model. News and reviews from ACT,WMAP,SPT,QUIET,Planck,Herschel,JWST,UFFO,KATRIN and MARE experiments; astrophysics, particle and nuclear physics WDM searches, galactic observations, related theory and simulations, with the aim of synthesis and clarification. Here highlights by P Biermann, C Burigana, C Conselice, A Cooray, H de Vega, C Giunti & M Laveder, J Kormendi & K Freeman, E Ma, J Mather, L Page, G Smoot, N Sanchez. Summary and conclusions by de Vega, Falvella and Sanchez. Data confirm primordial CMB gaussianity. Effective (Ginsburg-Landau) Inflation theory predicts r about 0.04-0.05, negligeable running of ns, the inflation energy scale (GUT scale) and the set of CMB observables in agreement with the data. WMAP9 and Planck measurements are compatible with one or two Majorana sterile neutrinos in the eV mass scale. Cored (non cusped) DM halos and keV WDM are strongly favored by theory and observations, Wimps are strongly disfavoured. LambdaCDM with baryons do not work at small scales. Inside galaxy cores, quantum WDM effects are important. Quantum WDM calculations (Thomas-Fermi) provide galaxy masses, velocity dispersions and cored profiles and their sizes in agreement with observations. A WDM fermion of about 2 keV naturally reproduces galaxy, large scale and cosmological observations. WDM keV particles deserve dedicated astronomical and laboratory searches, theoretical work and numerical simulations. KATRIN can be adapted to look to keV scale sterile neutrinos. It will be a fantastic discovery to detect dark matter in beta decay. Photos of the Colloquium are includedComment: 58 pages, 15 figures. arXiv admin note: substantial text overlap with arXiv:1203.3562, arXiv:1305.7452, arXiv:1009.3494, arXiv:1304.075

Towards the Chalonge 16th Paris Cosmology Colloquium 2012: Highlights and Conclusions of the Chalonge 15th Paris Cosmology Colloquium 2011

The Chalonge 15th Paris Cosmology Colloquium 2011 was held on 20-22 July in the historic Paris Observatory's Perrault building, in the Chalonge School spirit combining real cosmological/astrophysical data and hard theory predictive approach connected to them in the Warm Dark Matter Standard Model of the Universe: News and reviews from Herschel, QUIET, Atacama Cosmology Telescope (ACT), South Pole Telescole (SPT), Planck, PIXIE, the JWST, UFFO, KATRIN and MARE experiments; astrophysics, particle and nuclear physics warm dark matter (DM) searches and galactic observations, related theory and simulations, with the aim of synthesis, progress and clarification. Philippe Andre, Peter Biermann, Pasquale Blasi, Daniel Boyanovsky, Carlo Burigana, Hector de Vega, Joanna Dunkley, Gerry Gilmore, Alexander Kashlinsky, Alan Kogut, Anthony Lasenby, John Mather, Norma Sanchez, Alexei Smirnov, Sylvaine Turck-Chieze present here their highlights of the Colloquium. Ayuki Kamada and Sinziana Paduroiu present here their poster highlights. LambdaWDM (Warm Dark Matter) is progressing impressively over LambdaCDM whose galactic scale crisis and decline are staggering. The International School Daniel Chalonge issued an statement of strong support to the James Webb Space Telescope (JSWT). The Daniel Chalonge Medal 2011 was awarded to John C. Mather, Science PI of the JWST. Summary and conclusions are presented by H. J. de Vega, M. C. Falvella and N. G. Sanchez. Overall, LambdaWDM and keV scale DM particles deserve dedicated astronomical and laboratory experimental searches, theoretical work and simulations. KATRIN experiment in the future could perhaps adapt its set-up to look to keV scale sterile neutrinos. It will be a a fantastic discovery to detect dark matter in a beta decay. Photos of the Colloquium are included. (Abridged)Comment: 65 pages, 21 figure

On the rise and fall of networked societies

We review recent results on the dynamics of social networks which suggest that the interplay between the network formation process and volatility may lead to the occurrence of discontinuous phase transitions and phase coexistence in a large class of models. We then investigate the effects of negative links -- links inhibiting local growth of the network -- and of a geographical distribution of the agents in such models. We show, by extensive numerical simulations, that both effects enhance this phenomenology, i.e. it increases the size of the coexistence region.Comment: 6 pages, 4 figures, Proceedings of Granada Workshop 200

Planetoid strings : solutions and perturbations

A novel ansatz for solving the string equations of motion and constraints in generic curved backgrounds, namely the planetoid ansatz, was proposed recently by some authors. We construct several specific examples of planetoid strings in curved backgrounds which include Lorentzian wormholes, spherical Rindler spacetime and the 2+1 dimensional black hole. A semiclassical quantisation is performed and the Regge relations for the planetoids are obtained. The general equations for the study of small perturbations about these solutions are written down using the standard, manifestly covariant formalism. Applications to special cases such as those of planetoid strings in Minkowski and spherical Rindler spacetimes are also presented.Comment: 24 pages (including two figures), RevTex, expanded and figures adde

Strings in Cosmological and Black Hole Backgrounds: Ring Solutions

The string equations of motion and constraints are solved for a ring shaped Ansatz in cosmological and black hole spacetimes. In FRW universes with arbitrary power behavior [R(X^0) = a\;|X^0|^{\a}\, ], the asymptotic form of the solution is found for both $X^0 \to 0$ and $X^0 \to \infty$ and we plot the numerical solution for all times. Right after the big bang ($X^0 = 0$), the string energy decreasess as $R(X^0)^{-1}$ and the string size grows as $R(X^0)$ for $0 1$. Very soon [ $X^0 \sim 1$] , the ring reaches its oscillatory regime with frequency equal to the winding and constant size and energy. This picture holds for all values of \a including string vacua (for which, asymptotically, \a = 1). In addition, an exact non-oscillatory ring solution is found. For black hole spacetimes (Schwarzschild, Reissner-Nordstr\oo m and stringy), we solve for ring strings moving towards the center. Depending on their initial conditions (essentially the oscillation phase), they are are absorbed or not by Schwarzschild black holes. The phenomenon of particle transmutation is explicitly observed (for rings not swallowed by the hole). An effective horizon is noticed for the rings. Exact and explicit ring solutions inside the horizon(s) are found. They may be interpreted as strings propagating between the different universes described by the full black hole manifold.Comment: Paris preprint PAR-LPTHE-93/43. Uses phyzzx. Includes figures. Text and figures compressed using uufile