Integrability of anisotropic and homogeneous Universes in scalar-tensor theory of gravitation

In this paper, we develop a method based on the analysis of the Kovalewski exponents to study the integrability of anisotropic and homogeneous Universes. The formalism is developed in scalar-tensor gravity, the general relativistic case appearing as a special case of this larger framework. Then, depending on the rationality of the Kovalewski exponents, the different models, both in the vacuum and in presence of a barotropic matter fluid, are classified, and their integrability is discussed.Comment: 16 pages, no figure, accepted in CQ

New bioconjugated rhenium carbonyls by transmetalation reaction with zinc derivatives

The transmetallation reaction between zinc dithiocarbamates and rhenium carbonyls has been used as a new strategy to link biomolecules to transition metals. The zinc(II) dithiocarbamate of isonipecotic acid (1) and the succinimidyl ester derivative (2) were prepared by straight forward procedures and were fully characterized by spectroscopic and X-ray diffraction methods, showing in both cases the presence of dinuclear complexes. Complex 2 reacted with all the primary and secondary amines studied (glycine methyl ester, β-alanine methyl ester, 1-(2-methoxyphenyl)piperazine and D-(+)-glucosamine) through the activated succinimidyl ester group, linking the metallic fragment with the biomolecule by the formation of a peptidic bond, and leading to the respective bioconjugated zinc complexes 3-6. In all cases, these zinc complexes could be isolated from the reaction medium by simple precipitation. These results evidence the potential of complex 2 to be used as a synthon to link the zinc dithiocarbamate fragment to biomolecules that contain an amine group. Complexes 3-6 were characterized by the usual spectroscopic methods and all data agree with the proposed structures, which do not contain significant interactions between the zinc fragment and the functional groups of these biomolecules. The transmetallation reaction between the zinc complexes 3-6 and the rhenium carbonyl [ReBr₃(CO)₃]²⁻ led to the expected rhenium dithiocarbamates 7-10 with no change in the organic dithiocarbamate fragments, confirming the viability of this reaction as a tool for linking biomolecules to transition elements. All complexes were characterized by spectroscopic methods and the crystal structure of 8 was studied by X-ray diffraction analysis. All data demonstrated that the biomolecule is positioned far away from the fac-{Re(CO)₃} fragment and the octahedral coordination around the metal is completed by the functionalized dithiocarbamate and a phosphine ligand. Finally, the analysis by ESI-MS spectrometry of the reaction between the zinc complex 4 and a water solution of [Re(H₂O)₃(CO)₃]+ at a very low concentration (10 ppm) showed that the transmetallation reaction took place even though the solubility of the zinc complex in water medium was as low as 0.66 ppm. This preliminary result supports the viability of this approach for the preparation of rhenium and technetium target specific radiopharmaceuticals since the preparation of these compounds are always performed in water medium

Averaging inhomogeneities in scalar-tensor cosmology

The backreaction of inhomogeneities on the cosmic dynamics is studied in the context of scalar-tensor gravity. Due to terms of indefinite sign in the non-canonical effective energy tensor of the Brans-Dicke-like scalar field, extra contributions to the cosmic acceleration can arise. Brans-Dicke and metric f(R) gravity are presented as specific examples. Certain representation problems of the formalism peculiar to these theories are pointed out.Comment: Comments and references added. 14 page

Triple-Decker Pentalene Complex of Iron and Cobalt

In [1(1,2,3,3a,6a-ƞ)-1,4-dihydropentalenyl][µ-1](1,2,3,3a,-6a-ƞ):2(3a,4,5,6,6a-ƞ)-pentalene][2(ƞ5)-pentamethylcyclopentadienyl]cobaltiron, [CoFe(C8H7)Cp*(C8H6)] (Cp*=C10H15), the Cp*-Co and (C8H7)-Fe moieties reside on opposite sides of the fused bridging pentalene ring system

Triple-Decker [Cp*Fe(C8H6)Fe(C8H7)]

The title compound [2(1,2,3,3a,6a-ƞ)pentalene]-[l(ƞ5)-pentamethylcyclopentadienyl]diiron, [Fe2(C8H7)-(C10H15)(C8H6)], has a metallocenic structure with the two pentalene ligands adopting an eclipsed conformation. In the central pentalene ligand, all the peripheral bonds are of similar length whereas the bridge bond is longer; there are two significantly different Fe-C distances, i.e. a mean value of 2.121(3)A for the Fe-Cbridge distances and a mean value of 2.028(3)A for the distances from the Fe atoms to all other Catoms. In the terminal pentalene ligand, the C-C and C-Fe distances in the ring bonded to the Fe atom are all similar

(2-{[2-(diphenyl-phosphino)phen-yl]thio}-phen-yl)diphenyl-phosphine sulfide

In the title compound, CHPS, the dihedral angle between the central benzene rings is 66.95 (13)°. In the crystal, molecules are linked via C-H⋯π and π-π inter­actions [shortest centroid-centroid distance between benzene rings = 3.897 (2) Å]

Cosmology Without Averaging

We construct cosmological models consisting of large numbers of identical, regularly spaced masses. These models do not rely on any averaging procedures, or on the existence of a global Friedmann-Robertson-Walker (FRW) background. They are solutions of Einstein's equations up to higher order corrections in a perturbative expansion, and have large-scale dynamics that are well modelled by the Friedmann equation. We find that the existence of arbitrarily large density contrasts does not change either the magnitude or scale of the background expansion, at least when masses are regularly arranged, and up to the prescribed level of accuracy. We also find that while the local space-time geometry inside each cell can be described as linearly perturbed FRW, one could argue that a more natural description is that of perturbed Minkowski space (in which case the scalar perturbations are simply Newtonian potentials). We expect these models to be of use for understanding and testing ideas about averaging in cosmology, as well as clarifying the relationship between global cosmological dynamics and the static space-times associated with isolated masses.Comment: 24 pages, 3 figures. Corrected and expande

Cosmological Backreaction from Perturbations

We reformulate the averaged Einstein equations in a form suitable for use with Newtonian gauge linear perturbation theory and track the size of the modifications to standard Robertson-Walker evolution on the largest scales as a function of redshift for both Einstein de-Sitter and Lambda CDM cosmologies. In both cases the effective energy density arising from linear perturbations is of the order of 10^-5 the matter density, as would be expected, with an effective equation of state w ~ -1/19. Employing a modified Halofit code to extend our results to quasilinear scales, we find that, while larger, the deviations from Robertson-Walker behaviour remain of the order of 10^-5.Comment: 15 pages, 8 figures; replaced by version accepted by JCA

LTB solutions in Newtonian gauge: from strong to weak fields

Lemaitre-Tolman-Bondi (LTB) solutions are used frequently to describe the collapse or expansion of spherically symmetric inhomogeneous mass distributions in the Universe. These exact solutions are obtained in the synchronous gauge where nonlinear dynamics (with respect to the FLRW background) induce large deviations from the FLRW metric. In this paper we show explicitly that this is a gauge artefact (for realistic sub-horizon inhomogeneities). We write down the nonlinear gauge transformation from synchronous to Newtonian gauge for a general LTB solution using the fact that the peculiar velocities are small. In the latter gauge we recover the solution in the form of a weakly perturbed FLRW metric that is assumed in standard cosmology. Furthermore we show how to obtain the LTB solutions directly in Newtonian gauge and illustrate how the Newtonian approximation remains valid in the nonlinear regime where cosmological perturbation theory breaks down. Finally we discuss the implications of our results for the backreaction scenario.Comment: 17 page

Covariant coarse-graining of inhomogeneous dust flow in General Relativity

A new definition of coarse-grained quantities describing the dust flow in General Relativity is proposed. It assigns the coarse--grained expansion, shear and vorticity to finite-size comoving domains of fluid in a covariant, coordinate-independent manner. The coarse--grained quantities are all quasi-local functionals, depending only on the geometry of the boundary of the considered domain. They can be thought of as relativistic generalizations of simple volume averages of local quantities in a flat space. The procedure is based on the isometric embedding theorem for S^2 surfaces and thus requires the boundary of the domain in question to have spherical topology and positive scalar curvature. We prove that in the limit of infinitesimally small volume the proposed quantities reproduce the local expansion, shear and vorticity. In case of irrotational flow we derive the time evolution for the coarse-grained quantities and show that its structure is very similar to the evolution equation for their local counterparts. Additional terms appearing in it may serve as a measure of the backreacton of small-scale inhomogeneities of the flow on the large-scale motion of the fluid inside the domain and therefore the result may be interesting in the context of the cosmological backreaction problem. We also consider the application of the proposed coarse-graining procedure to a number of known exact solutions of Einstein equations with dust and show that it yields reasonable results.Comment: 17 pages, 5 figures. Version accepted in Classical and Quantum Gravity