44769698
Designing density fluctuation spectra in inflation.
Scale-invariant (flat) fluctuation spectra are the most natural outcomes of inflation. Nonetheless current large-scale-structure observations seem to indicate more fluctuation power on large scales than flat spectra give. We consider a wide variety of models based on the chaotic inflation paradigm and sketch the effects that varying the expansion rate, structure of the potential surface, and the curvature coupling constants have on the quantum fluctuation spectra. We calculate in detail the quantum generation of fluctuation spectra by numerically solving the linearized perturbation equations for multiple scalar fields, the metric, and the radiation into which the scalars dissipate, following the evolution from inside the horizon through reheating.
123508583
Gauge Invariant Cosmological Perturbations
The physical interpretation of perturbations of homogeneous, isotropic cosmological models in the early Universe, when the perturbation is larger than the particle horizon, is clarified by defining a complete set of gauge-invariant variables. The linearized perturbation equations written in these variables are simpler than the usual versions, and easily accommodate an arbitrary background equation of state, entropy perturbations, and anisotropic pressure perturbations. Particular attention is paid to how a scalar (density) perturbation might be generated by stress perturbations at very early times, when the non-gauge-invariant perturbation in the density itself is ill-defined. The amplitude of the fractional energy density perturbation at the particle horizon cannot be larger, in order of magnitude, than the maximum ratio of the stress perturbation to the background energy density at any earlier time, unless the perturbation is inherent in the initial singularity.
16861778
Distributions of Fourier modes of cosmological density fields.
We discuss the probability distributions of Fourier modes of cosmological density fields using the central limit theorem is it applies to weighted integrals of random fields. It is shown that if the cosmological principle holds in a certain sense, i.e., the Universe approaches homogeneity and isotropy sufficiently rapidly on very large scales, the one-point distribution of each Fourier mode of the density field is Gaussian whether or not the density field itself is Gaussian. Therefore, one-point distributions of the power spectrum obtained from observational data or from simulations are not a good test of whether the density field is Gaussian.
115708597
Can scale invariance be broken in inflation
4258712
Kerr Metric Black Holes
LYNDEN-BELL has suggested1 that a massive collapsed object may lie at the centre of many galaxies, including our own, and that a continuing flux of matter into such a collapsed object, or “black hole”, may be the source of energy for the non-thermal radiation observed to come from some galactic nuclei. The metric used to describe the geometry of space-time in the vicinity of the collapsed object in this and other papers2 on collapsed objects in astrophysics has been the spherically symmetric Schwarz-schild metric, which is valid only if the collapsed object has zero angular momentum. In fact, one would expect any such collapsed object to possess considerable angular momentum, because a great deal of angular momentum must be lost from a typical galactic nucleus to permit collapse inside the gravitational radius in the first place.
5961721
Numerical Tests of Evolution Systems, Gauge Conditions, and Boundary Conditions for 1D Colliding Gravitational Plane Waves
We investigate how the accuracy and stability of numerical relativity simulations of 1D colliding plane waves depends on choices of equation formulations, gauge conditions, boundary conditions, and numerical methods, all in the context of a first-order 3+1 approach to the Einstein equations, with basic variables some combination of first derivatives of the spatial metric and components of the extrinsic curvature tensor. Hyperbolic schemes, specifically variations on schemes proposed by Bona and Masso and Anderson and York, are compared with variations of the Arnowitt-Deser-Misner for- mulation. Modifications of the three basic schemes include raising one index in the metric derivative and extrinsic curvature variables and adding a multiple of the energy constraint to the extrinsic curvature evolution equations. Redundant variables in the Bona-Masso formulation may be reset frequently or allowed to evolve freely. Gauge conditions which simplify the dynamical structure of the system are imposed during each time step, but the lapse and shift are reset periodically to control the evolution of the spacetime slicing and the longitudinal part of the metric. We show that physically correct boundary conditions, satisfying the energy and momentum constraint equations, generically require the presence of some ingoing eigenmodes of the characteristic matrix. Numer- ical methods are developed for the hyperbolic systems based on decomposing flux differences into linear combinations of eigenvectors of the characteristic matrix. These methods are shown to be second-order accurate, and in practice second-order convergent, for smooth solutions, even when the eigenvectors and eigenvalues of the characteristic matrix are spatially varying.
27419591
Hadronic matrix elements and the pi +- pi 0 mass difference.
We estimate the π+-π0 electromagnetic mass difference within the 1/N expansion approach to hadronic matrix elements. Perturbative QCD and a truncated meson theory describe the high- and low-photon-loop-momentum contributions, respectively. The matching between these complementary pictures for strong interactions is discussed.
38514773
Critical surfaces and flat directions in a finite theory.
We discuss the phase structure of an O(N) x O(N)-symmetric model with scalar fields in three-dimensional space-time. The effective potential of the theory is calculated in the large-N limit and stability conditions for the model are given. Spontaneous breaking of scale invariance due to the breakdown of the internal symmetry or to nonperturbative mass generation is observed on a critical surface, in connection with the appearance of flat directions in the effective potential. The ground-state energy of the model remains unchanged under the transition from the scale-invariant phase to the various phases, where scale invariance is spontaneously broken. The critical surface allows for arbitrary ratios between the scales associated with breaking of the internal and scale symmetries.