Simple expressions for second order density perturbations in standard cosmology

In this paper we present four simple expressions for the relativistic first and second order fractional density perturbations for $\Lambda$CDM cosmologies in different gauges: the Poisson, uniform curvature, total matter and synchronous gauges. A distinctive feature of our approach is the use of a canonical set of quadratic differential expressions involving an arbitrary spatial function, the so-called comoving curvature perturbation, to describe the spatial dependence, which enables us to unify, simplify and extend previous seemingly disparate results. The simple structure of the expressions makes the evolution of the density perturbations completely transparent and clearly displays the effect of the cosmological constant on the dynamics, namely that it stabilizes the perturbations. We expect that the results will be useful in applications, for example, studying the effects of primordial non-Gaussianity on the large scale structure of the universe.Comment: 9 pages; some simplifications and notational change

Cosmological Perturbation Theory Revisited

Increasingly accurate observations are driving theoretical cosmology toward the use of more sophisticated descriptions of matter and the study of nonlinear perturbations of FL cosmologies, whose governing equations are notoriously complicated. Our goal in this paper is to formulate the governing equations for linear perturbation theory in a particularly simple and concise form in order to facilitate the extension to nonlinear perturbations. Our approach has several novel features. We show that the use of so-called intrinsic gauge invariants has two advantages. It naturally leads to: (i) a physically motivated choice of a gauge invariant associated with the matter density, and (ii) two distinct and complementary ways of formulating the evolution equations for scalar perturbations, associated with the work of Bardeen and of Kodama and Sasaki. In the first case the perturbed Einstein tensor gives rise to a second order (in time) linear differential operator, and in the second case to a pair of coupled first order (in time) linear differential operators. These operators are of fundamental importance in cosmological perturbation theory, since they provide the leading order terms in the governing equations for nonlinear perturbations.Comment: 29 pages, no figures, minor revision

The Impact of Early Career Experiences on Youth’s Proactive Work Socialization Behavior

Little is known about the impact of individual characteristics, historical factors, and situational characteristics on youth\u27s proactive work socialization behavior (career planning, skill development, consultation, and networking). Data from a longitudinal cross-national study (Belgium, England, Israel, Italy, the Netherlands and Spain) on career starters from two occupational groups, are used to test the hypothesized impact of predictor sets. Results confirm the positive impact of early career experience on the skill development proactive behavior; the dominant impact of the broader socioeconomic political and cultural country context on all four aspects of proactive behavior; and the sporadic effect of occupation, gender, and educational history on some proactive behavior dimensions