Evolution of Cosmological Perturbations in the Long Wavelength Limit

The relation between the long wavelength limit of solutions to the cosmological perturbation equations and the perturbations of solutions to the exactly homogeneous background equations is investigated for scalar perturbations on spatially flat cosmological models. It is shown that a homogeneous perturbation coincides with the long wavelength limit of some inhomogeneous perturbation only when the former satisfies an additional condition corresponding to the momentum constraint if the matter consists only of scalar fields. In contrast, no such constraint appears if the fundamental variables describing the matter contain a vector field as in the case of a fluid. Further, as a byproduct of this general analysis, it is shown that there exist two universal exact solutions to the perturbation equations in the long wavelength limit, which are expressed only in terms of the background quantities. They represent adiabatic growing and decaying modes, and correspond to the well-known exact solutions for perfect fluid systems and scalar field systems.Comment: 16 pages, no figure, submitted to PR

Evolution of Cosmological Perturbations in the Universe dominated by Multiple Scalar Fields

By efforts of several authors, it is recently established that the dynamical behavior of the cosmological perturbation on superhorizon scales is well approximated in terms of that in the long wavelength limit, and the latter can be constructed from the evolution of corresponding exactly homogeneous universe. Using these facts, we investigate the evolution of the cosmological perturbation on superhorizon scales in the universe dominated by oscillating multiple scalar fields which are generally interacting with each other, and the ratio of whose masses is incommensurable. Since the scalar fields oscillate rapidly around the local minimum of the potential, we use the action angle variables. We found that this problem can be formulated as the canonical perturbation theory in which the perturbed part appearing as the result of the expansion of the universe and the interaction of the scalar fields is bounded by the negative power ot time. We show that by constructing the canonical transformations properly, the transformed hamiltonian becomes simple enough to be solved. As the result of the invetigation using the long wavelength limit and the canonical perturbation theory, under the sufficiently general conditions, we prove that for the adiabatic growing mode the Bardeen parameter stays constant and that for all the other modes the Bardeen parameter decays. From the viewpoint of the ergodic theory, it is discussed that as for the Bardeen parameter, the sigularities appear probabilistically. This analysis serves the understanding of the evolution of the cosmological perturbations on superhorizon scales during reheating.Comment: 31 Pages; Latex, No figure

Lack of an Association or an Inverse Association Between Low-Density-Lipoprotein Cholesterol and Mortality in the Elderly: A Systematic Review

OBJECTIVE: It is well known that total cholesterol becomes less of a risk factor or not at all for all-cause and cardiovascular (CV) mortality with increasing age, but as little is known as to whether low-density lipoprotein cholesterol (LDL-C), one component of total cholesterol, is associated with mortality in the elderly, we decided to investigate this issue. SETTING, PARTICIPANTS AND OUTCOME MEASURES: We sought PubMed for cohort studies, where LDL-C had been investigated as a risk factor for all-cause and/or CV mortality in individuals ≥60 years from the general population. RESULTS: We identified 19 cohort studies including 30 cohorts with a total of 68 094 elderly people, where all-cause mortality was recorded in 28 cohorts and CV mortality in 9 cohorts. Inverse association between all-cause mortality and LDL-C was seen in 16 cohorts (in 14 with statistical significance) representing 92% of the number of participants, where this association was recorded. In the rest, no association was found. In two cohorts, CV mortality was highest in the lowest LDL-C quartile and with statistical significance; in seven cohorts, no association was found. CONCLUSIONS: High LDL-C is inversely associated with mortality in most people over 60 years. This finding is inconsistent with the cholesterol hypothesis (ie, that cholesterol, particularly LDL-C, is inherently atherogenic). Since elderly people with high LDL-C live as long or longer than those with low LDL-C, our analysis provides reason to question the validity of the cholesterol hypothesis. Moreover, our study provides the rationale for a re-evaluation of guidelines recommending pharmacological reduction of LDL-C in the elderly as a component of cardiovascular disease prevention strategies

An adaptogenic role for omega-3 fatty acids in stress; a randomised placebo controlled double blind intervention study (pilot) [ISRCTN22569553]

BACKGROUND: There is evidence for an adaptive role of the omega -3 fatty acid, docosahexaenoic acid (DHA) during stress. Mechanisms of action may involve regulation of stress mediators, such as the catecholamines and proinflammatory cytokines. Prevention of stress-induced aggression and hostility were demonstrated in a series of clinical trials. This study investigates whether perceived stress is ameliorated by DHA in stressed university staff. METHODS: Subjects that scored ≥ 17 on the Perceived Stress Scale were randomised into a 6-week pilot intervention study. The diet reactive group was supplemented with 6 g of fish oil containing 1.5 g per day DHA, while the placebo group was supplemented with 6 g a day of olive oil. The groups were compared with each other and a wider cross sectional study population that did not receive either active or placebo intervention. RESULTS: There was a significant reduction in perceived stress in both the fish oil and the placebo group from baseline. There was also a significant between-group difference between the fish oil group and the no-treatment controls in the rate of stress reduction (p < 0.05). However, there was not a significant between-group difference between the fish oil and the placebo group, nor the placebo group and the control group. These results are discussed in the context of several methodological limitations. The significant stress reductions in both the fish oil and the placebo group are considered in view of statistical regression, an effect likely to have been exaggerated by the time course of the study, a large placebo effect and the possibility of an active effect from the placebo. CONCLUSION: There were significant differences (p < 0.05) in the fish oil group compared with no-treatment controls. This effect was not demonstrated in the placebo group. As a pilot study, it was not sufficiently powered to find the difference between the fish oil group and the placebo group significant. Further work needs to be undertaken to conclusively demonstrate these data trends. However, the findings from this research support the literature in finding a protective or 'adaptogenic' role for omega-3 fatty acids in stress

Bubble fluctuations in Ω<1\Omega<1 inflation

In the context of the open inflationary universe, we calculate the amplitude of quantum fluctuations which deform the bubble shape. These give rise to scalar field fluctuations in the open Friedman-Robertson-Walker universe which is contained inside the bubble. One can transform to a new gauge in which matter looks perfectly smooth, and then the perturbations behave as tensor modes (gravitational waves of very long wavelength). For $(1-\Omega)<<1$, where $\Omega$ is the density parameter, the microwave temperature anisotropies produced by these modes are of order $\delta T/T\sim H(R_0\mu l)^{-1/2} (1-\Omega)^{l/2}$. Here, $H$ is the expansion rate during inflation, $R_0$ is the intrinsic radius of the bubble at the time of nucleation, $\mu$ is the bubble wall tension and $l$ labels the different multipoles ($l>1$). The gravitational backreaction of the bubble has been ignored. In this approximation, $G\mu R_0<<1$, and the new effect can be much larger than the one due to ordinary gravitational waves generated during inflation (unless, of course, $\Omega$ gets too close to one, in which case the new effect disappears).Comment: 17 pages, 3 figs, LaTeX, epsfig.sty, available at ftp://ftp.ifae.es/preprint/ft/uabft387.p

Quantized gravitational waves in the Milne universe

The quantization of gravitational waves in the Milne universe is discussed. The relation between positive frequency functions of the gravitational waves in the Milne universe and those in the Minkowski universe is clarified. Implications to the one-bubble open inflation scenario are also discussed.Comment: 26 pages, 1 figure, revtex. submitted to Phys. Rev. D1

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

Metric perturbations at reheating: the use of spherical symmetry

We consider decay of the inflaton with a quartic potential coupled to other fields, including gravity, but restricted to spherical symmetry. We describe analytically an early, quasilinear regime, during which inflaton fluctuations and the metric functions are driven by nonlinear effects of the decay products. We present a detailed study of the leading nonlinear effects in this regime. Results of the quasilinear approximation, in its domain of applicability, are found to be consistent with those of fully nonlinear lattice studies. We discuss how these results may be promoted to the full three dimensions.Comment: 18 pages, revtex, 2 figure

Complete power spectrum for an induced gravity open inflation model

We study the phenomenological constraints on a recently proposed model of open inflation in the context of induced gravity. The main interest of this model is the relatively small number of parameters, which may be constrained by many different types of observation. We evaluate the complete spectrum of density perturbations, which contains continuum sub-curvature modes, a discrete super curvature mode, and a mode associated with fluctuations in the bubble wall. From these, we compute the angular power spectrum of temperature fluctuations in the microwave background, and derive bounds on the parameters of the model so that the predicted spectrum is compatible with the observed anisotropy of the microwave background and with large-scale structure observations. We analyze the matter era and the approach of the model to general relativity. The model passes all existing constraints.Comment: 12 pages RevTeX file with four figures incorporated (uses RevTeX and epsf). Also available by e-mailing ARL, or by WWW at http://star-www.maps.susx.ac.uk/papers/early_papers.html Only change is additional reference

Primordial Gravitational Waves From Open Inflation

We calculate the spectrum of gravitational waves generated during inflation in open $(\Omega _0<1)$ inflationary models. In such models an initial epoch of old inflation solves the horizon and flatness problems, and during this first epoch of inflation the quantum state of the graviton field rapidly approaches the Bunch-Davies vacuum. Then old inflation ends by the nucleation of a single bubble, inside of which there is a shortened epoch of slow-roll inflation giving $\Omega _0<1$ today. In this paper we re-express the Bunch-Davies vacuum for the graviton field in terms of the hyperbolic modes inside the bubble and propagate these modes forward in time into the present era. We derive the expression for the contribution from these gravity waves to the cosmic microwave background anisotropy including the effect of a finite energy difference across the bubble wall.Comment: 40 pages, TEX with phyzzx macro, 5 figure