Newtonian and Post-Newtonian approximations of the k = 0 Friedmann Robertson Walker Cosmology

In a previous paper we derived a post-Newtonian approximation to cosmology which, in contrast to former Newtonian and post-Newtonian cosmological theories, has a well-posed initial value problem. In this paper, this new post-Newtonian theory is compared with the fully general relativistic theory, in the context of the k = 0 Friedmann Robertson Walker cosmologies. It is found that the post-Newtonian theory reproduces the results of its general relativistic counterpart, whilst the Newtonian theory does not.Comment: 11 pages, Latex, corrected typo

On the Significance of the Weyl Curvature in a Relativistic Cosmological Model

The Weyl curvature includes the Newtonian field and an additional field, the so-called anti-Newtonian. In this paper, we use the Bianchi and Ricci identities to provide a set of constraints and propagations for the Weyl fields. The temporal evolutions of propagations manifest explicit solutions of gravitational waves. We see that models with purely Newtonian field are inconsistent with relativistic models and obstruct sounding solutions. Therefore, both fields are necessary for the nonlocal nature and radiative solutions of gravitation.Comment: 15 pages, incorporating proof correction

Can noncommutativity resolve the Big-Bang singularity?

A possible way to resolve the singularities of general relativity is proposed based on the assumption that the description of space-time using commuting coordinates is not valid above a certain fundamental scale. Beyond that scale it is assumed that the space-time has noncommutative structure leading in turn to a resolution of the singularity. As a first attempt towards realizing the above programme a modification of the Kasner metric is constructed which is commutative only at large time scales. At small time scales, near the singularity, the commutation relations among the space coordinates diverge. We interpret this result as meaning that the singularity has been completely delocalized.Comment: Latex, 13 pages, 2 figures, accepted for publication in EPJ

On Shear-Free perturbations of FLRW Universes

A surprising exact result for the Einstein Field Equations is that if pressure-free matter is moving in a shear-free way, then it must be either expansion-free or rotation-free. It has been suggested this result is also true for any barotropic perfect fluid, but a proof has remained elusive. We consider the case of barotropic perfect fluid solutions linearized about a Robertson-Walker geometry, and prove that the result remains true except for the case of a specific highly non-linear equation of state. We argue that this equation of state is non-physical, and hence the result is true in the linearized case for all physically realistic barotropic perfect fluids. This result, which is not true in Newtonian cosmology, demonstrates that the linearized solutions, believed to result in standard local Newtonian theory, do not always give the usual behaviour of Newtonian solutions

Post-Newtonian extension of the Newton-Cartan theory

The theory obtained as a singular limit of General Relativity, if the reciprocal velocity of light is assumed to tend to zero, is known to be not exactly the Newton-Cartan theory, but a slight extension of this theory. It involves not only a Coriolis force field, which is natural in this theory (although not original Newtonian), but also a scalar field which governs the relation between Newtons time and relativistic proper time. Both fields are or can be reduced to harmonic functions, and must therefore be constants, if suitable global conditions are imposed. We assume this reduction of Newton-Cartan to Newton`s original theory as starting point and ask for a consistent post-Newtonian extension and for possible differences to usual post-Minkowskian approximation methods, as developed, for example, by Chandrasekhar. It is shown, that both post-Newtonian frameworks are formally equivalent, as far as the field equations and the equations of motion for a hydrodynamical fluid are concerned.Comment: 13 pages, LaTex, to appear in Class. Quantum Gra

Tachyonic potential in Bianchi type-I universe

Motivated from recent string theoretic results, a tachyonic potential is constructed for a spatially homogeneous and anisotropic background cosmology.Comment: 5 pages,LATEX,Typos in the text corrected, more references adde

Newtonian nonlinear hydrodynamics and magnetohydrodynamics

We use covariant methods to analyse the nonlinear evolution of self-gravitating, non-relativistic media. The formalism is first applied to imperfect fluids, aiming at the kinematic effects of viscosity, before extended to inhomogeneous magnetised environments. The nonlinear electrodynamic formulae are derived and successively applied to electrically resistive and to highly conductive fluids. By nature, the covariant equations isolate the magnetic effects on the kinematics and the dynamics of the medium, combining mathematical transparency and physical clarity. Employing the Newtonian analogue of the relativistic 1+3 covariant treatment, also facilitates the direct comparison with the earlier relativistic studies and helps to identify the differences in an unambiguous way. The purpose of this work is to set the framework and take a first step towards the detailed analytical study of complex nonlinear systems, like non-relativistic astrophysical plasmas and collapsing protogalactic clouds.Comment: Typos corrected, references added and updated (MNRAS in press

Cosmological Models with Shear and Rotation

Cosmological models involving shear and rotation are considered, first in the General Relat ivistic and then in the Newtonian framework with the aim of investigating singularities in them by using numerical and analytical techniques. The dynamics of these rotating models ar e studied. It is shown that singularities are unavoidable in such models and that the centr ifugal force arising due to rotation can never overcome the gravitational and shearing forc e over a length of time.Comment: 17 pages, 6 figures Journal Ref: J. Astrophys. Astr. (1999) 20, 79-8

NORMA-Gene: A simple and robust method for qPCR normalization based on target gene data

<p>Abstract</p> <p>Background</p> <p>Normalization of target gene expression, measured by real-time quantitative PCR (qPCR), is a requirement for reducing experimental bias and thereby improving data quality. The currently used normalization approach is based on using one or more reference genes. Yet, this approach extends the experimental work load and suffers from assumptions that may be difficult to meet and to validate.</p> <p>Results</p> <p>We developed a data driven normalization algorithm (NORMA-Gene). An analysis of the performance of NORMA-Gene compared to reference gene normalization on artificially generated data-sets showed that the NORMA-Gene normalization yielded more precise results under a large range of parameters tested. Furthermore, when tested on three very different real qPCR data-sets NORMA-Gene was shown to be best at reducing variance due to experimental bias in all three data-sets compared to normalization based on the use of reference gene(s).</p> <p>Conclusions</p> <p>Here we present the NORMA-Gene algorithm that is applicable to all biological and biomedical qPCR studies, especially those that are based on a limited number of assayed genes. The method is based on a data-driven normalization and is useful for as little as five target genes comprising the data-set. NORMA-Gene does not require the identification and validation of reference genes allowing researchers to focus their efforts on studying target genes of biological relevance.</p

The Cosmic No-Hair Theorem and the Nonlinear Stability of Homogeneous Newtonian Cosmological Models

The validity of the cosmic no-hair theorem is investigated in the context of Newtonian cosmology with a perfect fluid matter model and a positive cosmological constant. It is shown that if the initial data for an expanding cosmological model of this type is subjected to a small perturbation then the corresponding solution exists globally in the future and the perturbation decays in a way which can be described precisely. It is emphasized that no linearization of the equations or special symmetry assumptions are needed. The result can also be interpreted as a proof of the nonlinear stability of the homogeneous models. In order to prove the theorem we write the general solution as the sum of a homogeneous background and a perturbation. As a by-product of the analysis it is found that there is an invariant sense in which an inhomogeneous model can be regarded as a perturbation of a unique homogeneous model. A method is given for associating uniquely to each Newtonian cosmological model with compact spatial sections a spatially homogeneous model which incorporates its large-scale dynamics. This procedure appears very natural in the Newton-Cartan theory which we take as the starting point for Newtonian cosmology.Comment: 16 pages, MPA-AR-94-