On the degree of scale invariance of inflationary perturbations

Many, if not most, inflationary models predict the power-law index of the spectrum of density perturbations is close to one, though not precisely equal to one, |n-1| \sim O(0.1), implying that the spectrum of density perturbations is nearly, but not exactly, scale invariant. Some models allow n to be significantly less than one (n \sim 0.7); a spectral index significantly greater than one is more difficult to achieve. We show that n \approx 1 is a consequence of the slow-roll conditions for inflation and ``naturalness,'' and thus is a generic prediction of inflation. We discuss what is required to deviate significantly from scale invariance, and then show, by explicit construction, the existence of smooth potentials that satisfy all the conditions for successful inflation and give $n$ as large as 2.Comment: 7 pages, 2 figures, submitted to Phys. Rev.

Dark Energy and the quietness of the Local Hubble Flow

The linearity and quietness of the Local ($< 10 Mpc$) Hubble Flow (LHF) in view of the very clumpy local universe is a long standing puzzle in standard and in open CDM cosmogony. The question addressed in this paper is whether the antigravity component of the recently discovered dark energy can cool the velocity flow enough to provide a solution to this puzzle. We calculate the growth of matter fluctuations in a flat universe containing a fraction $\Omega_X(t_0)$ of dark energy obeying the time independent equation of state $p_X = w \rho_X$. We find that dark energy can indeed cool the LHF. However the dark energy parameter values required to make the predicted velocity dispersion consistent with the observed value $v_{rms}\simeq 40km/sec$ have been ruled out by other observational tests constraining the dark energy parameters $w$ and $\Omega_X$. Therefore despite the claims of recent qualitative studies dark energy with time independent equation of state can not by itself explain the quietness and linearity of the Local Hubble Flow.Comment: 4 pages, 3 figures, accepted in Phys. Rev. D. Minor corrections, one figure adde

Convergence of the expansion of the Laplace-Borel integral in perturbative QCD improved by conformal mapping

The optimal conformal mapping of the Borel plane was recently used to accelerate the convergence of the perturbation expansions in QCD. In this work we discuss the relevance of the method for the calculation of the Laplace-Borel integral expressing formally the QCD Green functions. We define an optimal expansion of the Laplace-Borel integral in the principal value prescription and establish conditions under which the expansion is convergent.Comment: 10 pages, no figure

Protogalactic Extension of the Parker Bound

We extend the Parker bound on the galactic flux $\cal F$ of magnetic monopoles. By requiring that a small initial seed field must survive the collapse of the protogalaxy, before any regenerative dynamo effects become significant, we develop a stronger bound. The survival and continued growth of an initial galactic seed field $\leq 10^{-9}$G demand that ${\cal F} \leq 5 \times 10^{-21} (m/10^{17} {GeV}) {cm}^{-2} {sec}^{-1} {sr}^{-1}$. For a given monopole mass, this bound is four and a half orders of magnitude more stringent than the previous `extended Parker bound', but is more speculative as it depends on assumptions about the behavior of magnetic fields during protogalactic collapse. For monopoles which do not overclose the Universe ($\Omega_m <1$), the maximum flux allowed is now $8 \times 10^{-19}$ cm^{-2} s^{-1} sr^{-1}, a factor of 150 lower than the maximum flux allowed by the extended Parker bound.Comment: 9 pages, 1 eps figur

Introduction to Magnetic Monopoles

One of the most basic properties of magnetism is that a magnet always has two poles, north and south, which cannot be separated into isolated poles, i.e., magnetic monopoles. However, there are strong theoretical arguments why magnetic monopoles should exist. In spite of extensive searches they have not been found, but they have nevertheless played a central role in our understanding of physics at the most fundamental level.Comment: 22 pages, 7 figures. To be published in Contemporary Physic

CBR Anisotropy and the Running of the Scalar Spectral Index

Accurate ($\lesssim 1\%$) predictions for the anisotropy of the Cosmic Background Radiation (CBR) are essential for using future high-resolution ($\lesssim 1^\circ$) CBR maps to test cosmological models. In many inflationary models the variation (``running'') of the spectral index of the spectrum of density perturbations is a significant effect and leads to changes of around 1\% to 10\% in the CBR power spectrum. We propose a general method for taking running into account which uses the derivative of the spectral index ($dn/d\ln k$). Conversely, high-resolution CBR maps may be able to determine $dn/d\ln k$, giving important information about the inflationary potential.Comment: Discussion of calculation clarified; error corrected which reduces estimated effect for chaotic inflatio

Duality Invariance of Cosmological Perturbation Spectra

I show that cosmological perturbation spectra produced from quantum fluctuations in massless or self-interacting scalar fields during an inflationary era remain invariant under a two parameter family of transformations of the homogeneous background fields. This relates slow-roll inflation models to solutions which may be far from the usual slow-roll limit. For example, a scale-invariant spectrum of perturbations in a minimally coupled, massless field can be produced by an exponential expansion with $a\propto e^{Ht}$, or by a collapsing universe with $a\propto (-t)^{2/3}$.Comment: 5 pages, Latex with Revtex. Hamiltonian formulation added and discussion expanded. Version to appear in Phys Rev

The cosmic gravitational wave background in a cyclic universe

Inflation predicts a primordial gravitational wave spectrum that is slightly ``red,'' i.e., nearly scale-invariant with slowly increasing power at longer wavelengths. In this paper, we compute both the amplitude and spectral form of the primordial tensor spectrum predicted by cyclic/ekpyrotic models. The spectrum is blue and exponentially suppressed compared to inflation on long wavelengths. The strongest observational constraint emerges from the requirement that the energy density in gravitational waves should not exceed around 10 per cent of the energy density at the time of nucleosynthesis.Comment: 4 pages, 3 figuer

Nonperturbative Effects from the Resummation of Perturbation Theory

Using the general argument in Borel resummation of perturbation theory that links the divergent perturbation theory to the nonperturbative effect we argue that the nonperturbative effect associated with the perturbation theory should have a branch cut only along the positive real axis in the complex coupling plane. The component in the weak coupling expansion of the nonperturbative amplitude, which usually includes the leading term in the weak coupling expansion, that gives rise to the branch cut can be calculated in principle from the perturbation theory combined with some exactly calculable properties of the nonperturbative effect. The realization of this mechanism is demonstrated in the double well potential and the two-dimensional O(N) nonlinear sigma model. In these models the leading term in weak coupling of the nonperturbative effect can be obtained with good accuracy from the first terms of the perturbation theory. Applying this mechanism to the infrared renormalon induced nonperturbative effect in QCD, we suggest some of the QCD condensate effects can be calculated in principle from the perturbation theory.Comment: 21 Pages, 1 Figure; To appear in Phys Rev