The Spectral Energy Distribution of Normal, Starburst and Active Galaxies

We present the results of an extensive literature search of multiwavelength data for a sample of 59 galaxies, consisting of 26 Starbursts, 15 Seyfert 2's, 5 LINER's, 6 normal spirals and 7 normal elliptical galaxies. The data include soft X-ray fluxes, ultraviolet and optical spectra, near, mid/far infrared photometry and radio measurements, selected to match as closely as possible the IUE aperture (10" X 20"). The galaxies are separated into 6 groups with similar characteristics, namely, Ellipticals, Spirals, LINER's, Seyfert 2's, Starbursts of Low and High reddening, for which we create average spectral energy distributions (SED). The individual groups SED's are normalized to the $\lambda$7000\AA flux and compared, looking for similarities and differences among them.The bolometric fluxes of different types of galaxies were calculated integrating their SED's. These values are compared with individual waveband flux densities, in order to determine the wavebands which contribute most to the bolometric flux. Linear regressions were performed between the bolometric and individual band fluxes for each kind of galaxy. These fits can be used in the calculation of the bolometric flux for other objects of similar activity type, but with reduced waveband information. We have also collected multiwavelength data for 4 HII regions, a thermal supernova remnant, and a non-thermal supernova remnant (SNR), which are compared with the Starburst SED's.Comment: 29 pages, 13 postscript figures and 10 tables. To appear in The Astronomical Journa

Slow roll in simple non-canonical inflation

We consider inflation using a class of non-canonical Lagrangians for which the modification to the kinetic term depends on the field, but not its derivatives. We generalize the standard Hubble slow roll expansion to the non-canonical case and derive expressions for observables in terms of the generalized slow roll parameters. We apply the general results to the illustrative case of ``Slinky'' inflation, which has a simple, exactly solvable, non-canonical representation. However, when transformed into a canonical basis, Slinky inflation consists of a field oscillating on a multi-valued potential. We calculate the power spectrum of curvature perturbations for Slinky inflation directly in the non-canonical basis, and show that the spectrum is approximately a power law on large scales, with a ``blue'' power spectrum. On small scales, the power spectrum exhibits strong oscillatory behavior. This is an example of a model in which the widely used solution of Garriga and Mukhanov gives the wrong answer for the power spectrum.Comment: 9 pages, LaTeX, four figures. (V2: minor changes to text. Version submitted to JCAP.

A Hamilton-Jacobi approach to non-slow-roll inflation

I describe a general approach to characterizing cosmological inflation outside the standard slow-roll approximation, based on the Hamilton-Jacobi formulation of scalar field dynamics. The basic idea is to view the equation of state of the scalar field matter as the fundamental dynamical variable, as opposed to the field value or the expansion rate. I discuss how to formulate the equations of motion for scalar and tensor fluctuations in situations where the assumption of slow roll is not valid. I apply the general results to the simple case of inflation from an ``inverted'' polynomial potential, and to the more complicated case of hybrid inflation.Comment: 21 pages, RevTeX (minor revisions to match published version

New Solutions of the Inflationary Flow Equations

The inflationary flow equations are a frequently used method of surveying the space of inflationary models. In these applications the infinite hierarchy of differential equations is truncated in a way which has been shown to be equivalent to restricting the set of models considered to those characterized by polynomial inflaton potentials. This paper explores a different method of solving the flow equations, which does not truncate the hierarchy and in consequence covers a much wider class of models while retaining the practical usability of the standard approach.Comment: References added, and a couple of comment

The Lyth Bound and the End of Inflation

We derive an extended version of the well-known Lyth Bound on the total variation of the inflaton field, incorporating higher order corrections in slow roll. We connect the field variation $\Delta\phi$ to both the spectral index of scalar perturbations and the amplitude of tensor modes. We then investigate the implications of this bound for ``small field'' potentials, where the field rolls off a local maximum of the potential. The total field variation during inflation is {\em generically} of order $m_{\rm Pl}$, even for potentials with a suppressed tensor/scalar ratio. Much of the total field excursion arises in the last e-fold of inflation and in single field models this problem can only be avoided via fine-tuning or the imposition of a symmetry. Finally, we discuss the implications of this result for inflationary model building in string theory and supergravity.Comment: 10 pages, RevTeX, 2 figures (V3: version accepted for publication by JCAP

Cascade Failure in a Phase Model of Power Grids

We propose a phase model to study cascade failure in power grids composed of generators and loads. If the power demand is below a critical value, the model system of power grids maintains the standard frequency by feedback control. On the other hand, if the power demand exceeds the critical value, an electric failure occurs via step out (loss of synchronization) or voltage collapse. The two failures are incorporated as two removal rules of generator nodes and load nodes. We perform direct numerical simulation of the phase model on a scale-free network and compare the results with a mean-field approximation.Comment: 7 pages, 2 figure

General conditions for scale-invariant perturbations in an expanding universe

We investigate the general properties of expanding cosmological models which generate scale-invariant curvature perturbations in the presence of a variable speed of sound. We show that in an expanding universe, generation of a super-Hubble, nearly scale-invariant spectrum of perturbations over a range of wavelengths consistent with observation requires at least one of three conditions: (1) accelerating expansion, (2) a speed of sound faster than the speed of light, or (3) super-Planckian energy density.Comment: 4 pages, RevTe

The scalar bi-spectrum during preheating in single field inflationary models

In single field inflationary models, preheating refers to the phase that immediately follows inflation, but precedes the epoch of reheating. During this phase, the inflaton typically oscillates at the bottom of its potential and gradually transfers its energy to radiation. At the same time, the amplitude of the fields coupled to the inflaton may undergo parametric resonance and, as a consequence, explosive particle production can take place. A priori, these phenomena could lead to an amplification of the super-Hubble scale curvature perturbations which, in turn, would modify the standard inflationary predictions. However, remarkably, it has been shown that, although the Mukhanov-Sasaki variable does undergo narrow parametric instability during preheating, the amplitude of the corresponding super-Hubble curvature perturbations remain constant. Therefore, in single field models, metric preheating does not affect the power spectrum of the large scale perturbations. In this article, we investigate the corresponding effect on the scalar bi-spectrum. Using the Maldacena's formalism, we analytically show that, for modes of cosmological interest, the contributions to the scalar bi-spectrum as the curvature perturbations evolve on super-Hubble scales during preheating is completely negligible. Specifically, we illustrate that, certain terms in the third order action governing the curvature perturbations which may naively be expected to contribute significantly are exactly canceled by other contributions to the bi-spectrum. We corroborate selected analytical results by numerical investigations. We conclude with a brief discussion of the results we have obtained.Comment: v1: 15 pages, 4 figures; v2: 15 pages, 4 figures, discussion and references added, to appear in Phys. Rev.

Second Order General Slow-Roll Power Spectrum

Recent combined results from the Wilkinson Microwave Anisotropy Probe (WMAP) and Sloan Digital Sky Survey (SDSS) provide a remarkable set of data which requires more accurate and general investigation. Here we derive formulae for the power spectrum P(k) of the density perturbations produced during inflation in the general slow-roll approximation with second order corrections. Also, using the result, we derive the power spectrum in the standard slow-roll picture with previously unknown third order corrections.Comment: 11 pages, 1 figure ; A typo in Eq. (38) is fixed ; References expanded and a note adde

Quantum Gravity and Inflation

Using the Ashtekar-Sen variables of loop quantum gravity, a new class of exact solutions to the equations of quantum cosmology is found for gravity coupled to a scalar field, that corresponds to inflating universes. The scalar field, which has an arbitrary potential, is treated as a time variable, reducing the hamiltonian constraint to a time-dependent Schroedinger equation. When reduced to the homogeneous and isotropic case, this is solved exactly by a set of solutions that extend the Kodama state, taking into account the time dependence of the vacuum energy. Each quantum state corresponds to a classical solution of the Hamiltonian-Jacobi equation. The study of the latter shows evidence for an attractor, suggesting a universality in the phenomena of inflation. Finally, wavepackets can be constructed by superposing solutions with different ratios of kinetic to potential scalar field energy, resolving, at least in this case, the issue of normalizability of the Kodama state.Comment: 18 Pages, 2 Figures; major corrections to equations but prior results still hold, updated reference