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

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

The Hubble rate in averaged cosmology

The calculation of the averaged Hubble expansion rate in an averaged perturbed Friedmann-Lemaitre-Robertson-Walker cosmology leads to small corrections to the background value of the expansion rate, which could be important for measuring the Hubble constant from local observations. It also predicts an intrinsic variance associated with the finite scale of any measurement of H_0, the Hubble rate today. Both the mean Hubble rate and its variance depend on both the definition of the Hubble rate and the spatial surface on which the average is performed. We quantitatively study different definitions of the averaged Hubble rate encountered in the literature by consistently calculating the backreaction effect at second order in perturbation theory, and compare the results. We employ for the first time a recently developed gauge-invariant definition of an averaged scalar. We also discuss the variance of the Hubble rate for the different definitions.Comment: 12 pages, 25 figures, references added, clarity improved, frame switching subtlety fixed, results unchanged, v3 minor typos fixe

Cu(II) 4-phenoxybenzoate dimers and monomer coordinated by pyridines: synthesis and crystal structures

The complexes [Cu(PhOBz)2(dPy)]2 (PhOBz = 4-phenoxybenzoate; dPy = pyridine (1), 3-phenylpyridine (2), 4-benzylpyridine (3) and 4-phenylpyridine (4) and the complex [Cu(PhOBz)2(4-Phpy)2(H2O)] (5) were prepared and fully characterized. X-ray crystal structures of the five complexes have been determined. Complexes 1-4 consist of binuclear units where both Cu(II) are linked by four syn-syn carboxylate bridges, showing a paddle-wheel unit. The compound 5 is mononuclear and the metal center is coordinated to two PhOBz in monodentate form, two 4-Phpy ligands and one H2O molecule with slightly distorted square pyramidal geometry. Finally, the magnetic properties of compounds 3 and 5 have also been studied, confirming the different strength interactions between Cu(II) cations

Isopropyl 2-[2-(2,6-dichloro­anilino)phen­yl]acetate

In the title compound, C17H17Cl2NO2, the NH group exhibits an intra­molecular hydrogen bond to the carbonyl O atom and no inter­molecular hydrogen bonding, in contrast with previous studies. The dihedral angle between the two benzene rings is 58.57 (5)°. The ester group is planar, the greatest deviation from planarity being 0.0135 (11) Å for the ether O atom

Constraints on scalar-tensor theories of gravity from observations

In spite of their original discrepancy, both dark energy and modified theory of gravity can be parameterized by the effective equation of state (EOS) $\omega$ for the expansion history of the Universe. A useful model independent approach to the EOS of them can be given by so-called Chevallier-Polarski-Linder (CPL) parametrization where two parameters of it ($\omega_{0}$ and $\omega_{a}$) can be constrained by the geometrical observations which suffer from degeneracies between models. The linear growth of large scale structure is usually used to remove these degeneracies. This growth can be described by the growth index parameter $\gamma$ and it can be parameterized by $\gamma_{0} + \gamma_{a} (1 - a)$ in general. We use the scalar-tensor theories of gravity (STG) and show that the discernment between models is possible only when $\gamma_a$ is not negligible. We show that the linear density perturbation of the matter component as a function of redshift severely constrains the viable subclasses of STG in terms of $\omega$ and $\gamma$. From this method, we can rule out or prove the viable STG in future observations. When we use $Z(\phi) =1$, $F$ shows the convex shape of evolution in a viable STG model. The viable STG models with $Z(\phi) = 1$ are not distinguishable from dark energy models when we strongly limit the solar system constraint.Comment: 19 pages, 20 figures, 2 tables, submitted to JCA

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

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

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