Inflationary Perturbations: the Cosmological Schwinger Effect

This pedagogical review aims at presenting the fundamental aspects of the theory of inflationary cosmological perturbations of quantum-mechanical origin. The analogy with the well-known Schwinger effect is discussed in detail and a systematic comparison of the two physical phenomena is carried out. In particular, it is demonstrated that the two underlying formalisms differ only up to an irrelevant canonical transformation. Hence, the basic physical mechanisms at play are similar in both cases and can be reduced to the quantization of a parametric oscillator leading to particle creation due to the interaction with a classical source: pair production in vacuum is therefore equivalent to the appearance of a growing mode for the cosmological fluctuations. The only difference lies in the nature of the source: an electric field in the case of the Schwinger effect and the gravitational field in the case of inflationary perturbations. Although, in the laboratory, it is notoriously difficult to produce an electric field such that pairs extracted from the vacuum can be detected, the gravitational field in the early universe can be strong enough to lead to observable effects that ultimately reveal themselves as temperature fluctuations in the Cosmic Microwave Background. Finally, the question of how quantum cosmological perturbations can be considered as classical is discussed at the end of the article.Comment: 49 pages, 6 figures, to appear in a LNP volume "Inflationary Cosmology

Beyond CO2-fixation by Rubisco - an interpretation of 13C/12C variations in tree rings from novel intraseasonal studies on broad-leaf trees

Evidence is presented for a very specific, seasonally recurring tri-phase carbon isotope pattern in tree rings of broad-leaf deciduous tree species. It is derived from highly resolved intra-annual measurements of 13C/12C ratios of wood and cellulose from tree rings of Fagus sylvatica, Populus nigra, Quercus petraea and Morus alba. Investigations on δ13C from buds and leaves of Fagus sylvatica revealed a similar tri-phase δ13C pattern. At the very beginning of a growing season, the δ13C trend of tree rings and foliage shows a marked increase of up to 5‰. The maximum δ13C-value of each vegetation period always occurs in young heterotrophic leaves shortly after bud burst and persistently in the early wood of each tree ring, when growth depends on carbon reserves. Thereafter, δ13C profiles represent the autotrophic stage of the leaves, which show different patterns of variation, by and large characterized by a decline. The minimum δ13C-value always shows up in the late wood of each tree ring. At the very end of each tree ring δ13C-values start rising again. This increase in δ13C marks the gradual switch-over to storage-dependent growth and can also be observed in senescent leaves. Seasonal changes of more than 4‰ were measured, whereas contiguous δ13C values rarely differed from each other by more than 0.3‰. This tri-phase pattern cannot be explained by the common model of carbon isotope fractionation during photosynthesis. It appears to be primarily an indication of seasonal changes in down-stream processes of the carbohydrate metabolism. Environmental influences on the carbon isotope fractionation during photosynthesis are presumably of secondary importance and expressed by certain peculiarities showing up during the autotrophic phase, i.e. the mid-section of the seasonal δ13C pattern