Nonlinear Evolution of Anisotropic Cosmological Power

There has been growing interest in the possibility of testing more precisely the assumption of statistical isotropy of primordial density perturbations. If it is to be tested with galaxy surveys at distance scales <~ 10 Mpc, then nonlinear evolution of anisotropic power must be understood. To this end, we calculate the angular dependence of the power spectrum to third order in perturbation theory for a primordial power spectrum with a quadrupole dependence on the wavevector direction. Our results suggest that primordial power anisotropies will be suppressed by <~ 7% in the quasilinear regime. We also show that the skewness in the statistically anisotropic theory differs by no more than 1% from that in the isotropic theory.Comment: 4 pages, 1 figure; accepted for publication in Physical Review Letter

Cosmic Microwave Background Statistics for a Direction-Dependent Primordial Power Spectrum

Statistical isotropy of primordial perturbations is a common assumption in cosmology, but it is an assumption that should be tested. To this end, we develop cosmic microwave background statistics for a primordial power spectrum that depends on the direction, as well as the magnitude, of the Fourier wavevector. We first consider a simple estimator that searches in a model-independent way for anisotropy in the square of the temperature (and/or polarization) fluctuation. We then construct the minimum-variance estimators for the coefficients of a spherical-harmonic expansion of the direction-dependence of the primordial power spectrum. To illustrate, we apply these statistics to an inflation model with a quadrupole dependence of the primordial power spectrum on direction and find that a power quadrupole as small as 2.0% can be detected with the Planck satellite.Comment: Published in Phys. Rev. D; 8 pages; 1 table; Table 1 corrected; references adde

Domain walls in supersymmetric QCD: from weak to strong coupling

We consider domain walls that appear in supersymmetric QCD with Nf < Nc massive flavours. In particular, for 2 Nf < Nc we explicitly construct the domain walls that interpolate between vacua labeled by i and (i+ N_f). We show that these solutions are Bogomol'nyi-Prasad-Sommerfield (BPS) saturated for any value of the mass of the matter fields. This fact allows us to evaluate the large mass limit of these domain walls. We comment on the relevance of these solutions for supersymmetric gluodynamics.Comment: 4 pages, 4 figures, LaTex, uses psfig.st

Functional Approach to Stochastic Inflation

We propose functional approach to the stochastic inflationary universe dynamics. It is based on path integral representation of the solution to the differential equation for the scalar field probability distribution. In the saddle-point approximation scalar field probability distributions of various type are derived and the statistics of the inflationary-history-dependent functionals is developed.Comment: 20 pages, Preprint BROWN-HET-960, uses phyzz

N=2 Sigma Model with Twisted Mass and Superpotential: Central Charges and Solitons

We consider supersymmetric sigma models on the Kahler target spaces, with twisted mass. The Kahler spaces are assumed to have holomorphic Killing vectors. Introduction of a superpotential of a special type is known to be consistent with N=2 superalgebra (Alvarez-Gaume and Freedman). We show that the algebra acquires central charges in the anticommutators {Q_L, Q_L} and {Q_R, Q_R}. These central charges have no parallels, and they can exist only in two dimensions. The central extension of the N=2 superalgebra we found paves the way to a novel phenomenon -- spontaneous breaking of a part of supersymmetry. In the general case 1/2 of supersymmetry is spontaneously broken (the vacuum energy density is positive), while the remaining 1/2 is realized linearly. In the model at hand the standard fermion number is not defined, so that the Witten index as well as the Cecotti-Fendley-Intriligator-Vafa index are useless. We show how to construct an index for counting short multiplets in internal algebraic terms which is well-defined in spite of the absence of the standard fermion number. Finally, we outline derivation of the quantum anomaly in {\bar Q_L, Q_R}.Comment: 21 pages, Latex, 1 eps figure. Two important references adde

Hanbury Brown-Twiss interferometry and second-order correlations of inflaton quanta

The quantum theory of optical coherence is applied to the scrutiny of the statistical properties of the relic inflaton quanta. After adapting the description of the quantized scalar and tensor modes of the geometry to the analysis of intensity correlations, the normalized degrees of first-order and second-order coherence are computed in the concordance paradigm and are shown to encode faithfully the statistical properties of the initial quantum state. The strongly bunched curvature phonons are not only super-Poissonian but also super-chaotic. Testable inequalities are derived in the limit of large angular scales and can be physically interpreted in the light of the tenets of Hanbury Brown-Twiss interferometry. The quantum mechanical results are compared and contrasted with different situations including the one where intensity correlations are the result of a classical stochastic process. The survival of second-order correlations (not necessarily related to the purity of the initial quantum state) is addressed by defining a generalized ensemble where super-Poissonian statistics is an intrinsic property of the density matrix and turns out to be associated with finite volume effects which are expected to vanish in the thermodynamic limit.Comment: 42 pages, 3 included figures; corrected typos; to appear in Physical Review

Cosmological status of Lagrangian theory of density perturbations

We show that hydrodynamical and field approaches in theory of cosmological scalar perturbations are equivalent for a single medium. We also give relations between notations introduced by V. Lukash, J. Bardeen, J. Bardeen et al. and G. Chibisov and V. Mukhanov.Comment: 8 pages, no figures, submitted to Astronomy Report

Exact Results in Gauge Theories: Putting Supersymmetry to Work. The 1999 Sakurai Prize Lecture

Powerful methods based on supersymmetry allow one to find exact solutions to certain problems in strong coupling gauge theories. The inception of some of these methods (holomorphy in the gauge coupling and other chiral parameters, in conjunction with instanton calculations) dates back to the 1980's. I describe the early exact results -- the calculation of the beta function and the gluino condensate -- and their impact on the subsequent developments. A brief discussion of the recent breakthrough discoveries where these results play a role is given.Comment: Based on the talk at the Centennial Meeting of The American Physical Society, March 20-26, Atlanta, GA. LaTex (uses sprocl.sty), 36 pages, 5 eps figures include

Testing of CP, CPT and causality violation with the light propagation in vacuum in presence of the uniform electric and magnetic fields

We have considered the structure of the fundamental symmetry violating part of the photon refractive index in vacuum in the presence of constant electric and magnetic fields. This part of the refractive index can, in principle, contain CPT symmetry breaking terms. Some of the terms violate Lorentz invariance, whereas the others violate locality and causality. Estimates of these effects, using laser experiments are considered.Comment: 12 page

Cosmological Perturbations with Multiple Fluids and Fields

We consider the evolution of perturbed cosmological spacetime with multiple fluids and fields in Einstein gravity. Equations are presented in gauge-ready forms, and are presented in various forms using the curvature (\Phi or \phi_\chi) and isocurvature (S_{(ij)} or \delta \phi_{(ij)}) perturbation variables in the general background with K and \Lambda. We clarify the conditions for conserved curvature and isocurvature perturbations in the large-scale limit. Evolutions of curvature perturbations in many different gauge conditions are analysed extensively. In the multi-field system we present a general solution to the linear order in slow-roll parameters.Comment: 19 pages, 6 figures, revised thoroughly; published version in Class. Quant. Gra