N. G. Sanchez

A new approach to string quantization in curved spacetimes

We develop a general scheme for solving the equations of motion and constraints of strings in curved spacetimes, both classically and quantum mechanically. We treat the spacetime geometry exactly and the string excitations small as compared with the energy scales of the metric. [The perturbation (dimensionless) parameter is g=πα′Rc where α′=lPl is the Planck length and Rc the typical curvature radius of the geometry.] This formalism is particularly well suited to properly consider strings in the context of quantum black holes and cosmology. As an illustration we apply it to de Sitter spacetime and find the mass spectrum and vertex operator. The lower mass states are the same as in flat space up to corrections of order g2 whereas heavy states deviate significantly from the linear Regge trajectories. We find a maximum (very large) value of order 1g2 for the quantum number N and spin J of particles. The critical dimension for bosonic strings is found to be 25 in de Sitter spacetime.

Classical and quantum strings near spacetime singularities: gravitational plane waves with arbitrary polarization

We study the classical and quantum dynamics of strings near spacetime singularities. We deal with singular gravitational plane waves of arbitrary polarization and arbitrary profile functions W1(U) and W2(U), whose behaviour for U to 0 is W1(U)= alpha 1/ mod U mod ( beta 1), W2(U)= alpha 2/ mod U mod ( beta 2) (U being a null variable). In these spacetimes, the string dynamics is exactly (and explicitly) solvable even at the spacetime singularities. The string behaviour depends crucially on whether both parameters beta 1 and beta 2 are smaller or larger than two. When beta 1>or=2 and/or beta 2>or=2, the string does not cross the singularity U = 0 but goes off to infinity in a given direction alpha depending on the polarization of the gravitational wave. The string time evolution is fully determined by the spacetime geometry, whereas the overall sigma -dependence is fixed by the initial string state. The proper length at fixed tau to 0 (U to 0) stretches infinitely. For beta 1 0 region. In this case, outgoing operators make sense and we find the explicit transformation relating in and out operators. For the quantum string states, this implies spin polarization rotations and particle transmutations. The expectation values of the outgoing mass and mode number operators are computed and the excitation of the string modes after the crossing of the spacetime singularity is analysed.

String Quantization in Accelerated Frames and Black Holes

Abstract We quantize a closed bosonic string in a light-cone gauge in Rindler (uniformly accelerated) space-time and apply it to the Schwarzschild-Kruskal manifold. Inertial and accelerated particle states of the string associated to positive frequency modes with respect to the inertial and Rindler times respectively, are defined. There is a stretching effect of the string due to the presence of an event horizon. We explicitly solve the dynamical constraints leaving as physical degrees of freedom only those transverse to the acceleration. Different mass formulae are introduced depending on whether the centre of mass of the string has uniform speed or uniform acceleration. The expectation value of the Rindler (Schwarzschild) number-mode operator in the string around state (tachyon) results equal to a thermal spectrum at the Hawking-Unruh temperature T s = α /2 π (∼ M Pl ( M Pl / M ) 1/( D −3 ), where M is the black hole mass). We find T 0 = M ′/2 π where M ′ is the accelerated ground state string mass and T 0 the temperature T s in dimensionless frequency units. Correlation functions of string coordinates and vertex operators and their Fourier transforms in accelerated time (string response functions) are computed and their thermal properties analyzed.

Generation of gravitational waves by generic sources in de Sitter space-time

We study the generation of gravitational radiation by sources moving in the de Sitter background. Exploiting the maximal symmetry and the conformal flatness of de Sitter space-time we prove that the derivation of this gravitational radiation can be done along the same lines as in Minkowski space-time. A gauge is chosen in which all the physical and unphysical modes of the graviton are those of a minimally coupled massless scalar field in de Sitter space-time and a massless field in Minkowski space-time. The graviton retarded Greens function and the Schwinger commutator function are computed in this gauge using Quantum Field Theory techniques. We obtain closed formulae for the spectral decomposition in frequencies of the linaearized gravitational field produced by the source, in terms of a suitable spectral decomposition of the source energy-momentum tensor. This spectral decomposition is dictated by the free (sourceless) gravitational wave modes in the de Sitter background

The Fractal Structure of the Universe: A New Field Theory Approach

While the universe becomes more and more homogeneous at large scales, statistical analysis of galaxy catalogs have revealed a fractal structure at small scales (λ < 100 h-1 Mpc), with a fractal dimension D = 1.5-2. We study the thermodynamics of a self-gravitating system using the theory of critical phenomena and finite-size scaling, and we show that gravity provides a dynamical mechanism for producing this fractal structure. We develop a field theoretical approach for computing the galaxy distribution, assuming them to be in quasi-isothermal equilibrium. Only a limited (although large) range of scales is involved, between a short-distance cutoff, below which other physics intervene, and a large-distance cutoff, beyond which the thermodynamic equilibrium is not satisfied. The galaxy ensemble can be considered at critical conditions, with large density fluctuations developing at any scale. From the theory of critical phenomena, we derive the two independent critical exponents ν and η and predict the fractal dimension D = 1/ν to be either 1.585 or 2, depending on whether the long-range behavior is governed by the Ising or the mean-field fixed points, respectively. Both set of values are compatible with present observations. In addition, we predict the scaling behavior of the gravitational potential to be r-(1+η)/2; that is, r-0.5 for mean field or r-0.519 for the Ising fixed point. The theory allows us to compute the 3 and higher density correlators without any assumption or Ansatz. We find that the N-point density scales as r when r1 ri, 2 ≤ i ≤N. There are no free parameters in this theory.

The Effective Theory of Inflation in the Standard Model of the Universe and the CMB+LSS data analysis

Inflation is part of the Standard Model of the Universe supported by CMB and large scale structure LSS datasets. This review presents new developments of inflation in three main chapters. (I): The effective theory of inflation a la Ginsburg-Landau (GL): the inflaton potential is a polynomial with universal form making explicit the inflation energy scale M, the Planck mass and the inflation e-folds number N ~ 60. The slow-roll expansion becomes a systematic 1/N expansion and the inflaton couplings are naturally small as powers of (M/M_{Pl})^2. The spectral index (n_s - 1) and the ratio of tensor/scalar fluctuations r are O(1/N), the running index is O(1/N^2). M ~ 0.7 10^{16} GeV is completely determined by the scalar adiabatic fluctuations amplitude. (II): A Monte Carlo Markov Chains (MCMC) analysis of the CMB+LSS data (including WMAP5) with our analytic theoretical results yields: a lower bound for r (new inflation): r > 0.023 (95%CL), r > 0.046 (68%CL); the preferred inflation potential is a double well, even function of the field yielding as most probable values n_s ~ 0.964, r ~ 0.051. This value for r is within reach of forthcoming CMB observations. Slow-roll inflation is generically preceded by a short fast-roll stage which leads to a suppression of the CMB quadrupoles. MCMC analysis of the WMAP+SDSS data shows that fast-roll fits the TT, TE and EE modes well reproducing the quadrupole suppression and fixes the total number of efolds of inflation to be N_{total} ~ 64. (III) Quantum loop corrections are very small and controlled by powers of (H /M_{Pl})^2 ~ 10^{-9} which validates the effective theory of inflation. We show how powerful is the GL theory of inflation in predicting observables.

Quantum string dynamics in the conformal invariant SL(2,R) WZWN background: Anti-de Sitter space with torsion

We consider classical and quantum strings in the conformally invariant background corresponding to the SL(2,R) WZWN model. This background is locally anti-de Sitter spacetime with non-vanishing torsion. Conformal invariance is expressed as the torsion being parallelized. The precise effect of the conformal invariance on the dynamics of both circular and generic classical strings is extracted. In particular, the conformal invariance gives rise to a repulsive interaction of the string with the background which precisely cancels the dominant attractive term arising from gravity. We perform both semi-classical and canonical string-quantization, in order to see the effect of the conformal invariance of the background on the string mass spectrum. Both approaches yield that the high-mass states are governed by m sim HN (N,`large integer), where m is the string mass and H is the Hubble constant. It follows that the level spacing grows proportionally to N: d(m^2 alpha)/dN sim N, while the entropy goes like: S sim sqrt{m}. Moreover, it follows that there is no Hagedorn temperature,so that the partition function is well defined at any positive temperature. All results are compared with the analogue results in Anti- de Sitter spacetime, which is a non conformal invariant background. Conformal invariance simplifies the mathematics of the problem but the physics remains mainly unchanged. Differences between conformal and non-conformal backgrounds only appear in the intermediate region of the string spectrum, but these differences are minor. For low and high masses, the string mass spectra in conformal and non-conformal backgrounds are identical. Interestingly enough, conformal invariance fixes the value of the spacetime curvature to be -69/(26 alpha).

CONSTANT SURFACE GRAVITY AND DENSITY PROFILE OF DARK MATTER

Cumulative observational evidence confirms that the surface gravity of dark matter (DM) halos μ0 D = r0ρ0, where r0 and ρ0 are the halo core radius and central density, respectively, is nearly constant and independent of galaxy luminosity for a high number of galactic systems (spirals, dwarf irregular and spheroidals, elliptics) spanning over 14 magnitudes in luminosity and of different Hubble types. Remarkably, its numerical value, μ0D ≃140M⊙/pc2 = (18.6 MeV)3, is approximately the same (up to a factor of 2) in all these systems. First, we present the physical consequences of the independence of μ0D from r0: the energy scales as the volume , while the mass and the entropy scale as the surface and the surface times log r0, respectively. Namely, the entropy scales similarly to the black hole entropy but with a much smaller coefficient. Second, we compute the surface gravity and the density profile for small scales from first principles and the evolution of primordial density fluctuations from the end of inflation till today using the linearized Boltzmann–Vlasov equation. The density profile ρlin(r) obtained in this way decreases as r-1-ns/2 for intermediate scales, where ns≃0.964 is the primordial spectral index. This scaling is in remarkable agreement with the empirical behavior found observationally and in N-body simulations: r-1.6±0.4. The observed value of μ0D indicates that the DM particle mass m is on the keV scale. The theoretically derived density profiles ρlin(r) turn to be cored for m on the keV scale and they are cusped for m on the GeV scale or beyond. We consider both fermions and bosons as DM particles decoupling either ultrarelativistically or nonrelativistically. Our results do not use any particle physics model and vary slightly with the statistics of the DM particle.

Classical splitting of fundamental strings.

We find exact solutions of the string equations of motion and constraints describing the classical splitting of a string in two. We show that for the same Cauchy data the strings that split have a smaller action than the string without splitting. This phenomenon is already present in flat space-time. The mass, energy, and momentum carried out by the strings are computed. We show that the splitting solution describes a natural decay process of one string of mass M into two strings with a smaller total mass and some kinetic energy. The standard nonsplitting solution is contained as a particular case. We also describe the splitting of a closed string in the background of a singular gravitational plane wave, and show how the presence of the strong gravitational field increases (and amplifies by an overall factor) the negative difference between the action of the splitting and nonsplitting solutions.

Exact string solutions in 2+1-dimensional de Sitter spacetime

Exact and explicit string solutions propagating in 2+1 dimensional de Sitter spacetime are presented and physically analized. (In this case the string equations reduce to a sinh-Gordon model.) Strings generically tend to inflate or either to collapse. The world-sheet time τ interpolates between the cosmic (τ→±∞) and conformal (τ→0) times. For τ→0, the typical string instability is found, while for τ→±∞, a new string behavior appears. In that regime, the string expands (or contracts) but not with the same rate as the universe does. The string constraints select periodic solutions of the sinh-Gordon equation associated to the lower boundary of the allowed zone, therefore excluding elliptic solutions.