Trispectrum versus Bispectrum in Single-Field Inflation

In the standard slow-roll inflationary cosmology, quantum fluctuations in a single field, the inflaton, generate approximately Gaussian primordial density perturbations. At present, the bispectrum and trispectrum of the density perturbations have not been observed and the probability distribution for these perturbations is consistent with Gaussianity. However, Planck satellite data will bring a new level of precision to bear on this issue, and it is possible that evidence for non-Gaussian effects in the primordial distribution will be discovered. One possibility is that a trispectrum will be observed without evidence for a non-zero bispectrum. It is not difficult for this to occur in inflationary models where quantum fluctuations in a field other than the inflaton contribute to the density perturbations. A natural question to ask is whether such an observation would rule out the standard scenarios. We explore this issue and find that it is possible to construct single-field models in which inflaton-generated primordial density perturbations have an observable trispectrum, but a bispectrum that is too small to be observed by the Planck satellite. However, an awkward fine tuning seems to be unavoidable.Comment: 15 pages, 3 figures; journal versio

Studies on the reactivity of a tertiary allylic alcohol in an acetophenonic series, a model for natural products synthesis

The synthesis of benzopyranic simplified analogues of dibenzopyranic natural compounds is described, together with the access to a precursor of a new furobenzopyranic natural product. These natural products have anti-cancer activity. The 1,3-diacetoxy-2-acetyl-4-(3-hydroxy-3-methylbut-1-enyl)benzene synthone is used as a common precursor to these structures

Dynamics of a lattice Universe : the dust approximation in cosmology

We find a solution to Einstein field equations for a regular toroidal lattice of size L with equal masses M at the centre of each cell; this solution is exact at order M/L. Such a solution is convenient to study the dynamics of an assembly of galaxy-like objects. We find that the solution is expanding (or contracting) in exactly the same way as the solution of a Friedman–Lemaître–Robertson–Walker Universe with dust having the same average density as our model. This points towards the absence of backreaction in a Universe filled with an infinite number of objects, and this validates the fluid approximation, as far as dynamics is concerned, and at the level of approximation considered in this work

Novel Cytotoxic 4-Phenylfuranocoumarins from Calophyllum dispar

Eight new 4-phenylfuranocoumarins (1−8) have been isolated from the stem bark and the fruits of Calophyllum dispar, together with three known coumarins. The structures of 1−8 were established by means of spectroscopic analysis, including extensive 2D NMR studies. Some of these furanocoumarins exhibited significant cytotoxic activity against KB cells