Cosmological solutions of massive gravity on de Sitter

In the framework of the recently proposed models of massive gravity, defined with respect to a de Sitter reference metric, we obtain new homogeneous and isotropic solutions for arbitrary cosmological matter and arbitrary spatial curvature. These solutions can be classified into three branches. In the first two, the massive gravity terms behave like a cosmological constant. In the third branch, the massive gravity effects can be described by a time evolving effective fluid with rather remarkable features, including the property to behave as a cosmological constant at late time.Comment: 6 pages, 1 figure; discussion extended, a few references added, improved analysis in Section

Is there an imprint of Planck scale physics on inflationary cosmology?

We study the effects of the trans-Planckian dispersion relation on the spectrum of the primordial density perturbations during inflation. In contrast to the earlier analyses, we do not assume any specific form of the dispersion relation and allow the initial state of the field to be arbitrary. We obtain the spectrum of vacuum fluctuations of the quantum field by considering a scalar field satisfying the linear wave equation with higher spatial derivative terms propagating in the de Sitter space-time. We show that the power spectrum does not strongly depend on the dispersion relation and that the form of the dispersion relation does not play a significant role in obtaining the corrections to the scale invariant spectrum. We also show that the signatures of the deviations from the flat scale-invariant spectrum from the CMBR observations due to quantum gravitational effects cannot be differentiated from the standard inflationary scenario with an arbitrary initial state.Comment: 6 pages, uses RevTex4; References added; Final versio

Collective character of spin excitations in a system of Mn2+^{2+} spins coupled to a two-dimensional electron gas

We have studied the low energy spin excitations in n-type CdMnTe based dilute magnetic semiconductor quantum wells. For magnetic fields for which the energies for the excitation of free carriers and Mn spins are almost identical an anomalously large Knight shift is observed. Our findings suggests the existence of a magnetic field induced ferromagnetic order in these structures, which is in agreement with recent theoretical predictions [J. K{\"o}nig and A. H. MacDonald, submitted Phys. Rev. Lett. (2002)]Comment: 4 figure

Mitochondrial DNA depletion syndrome presenting with ataxia and external ophthalmoplegia: Case report

The mitochondrial DNA depletion syndromes are autosomal recessive disorders characterized by decreased mitochondrial DNA copy number in affected tissues.Mutations in 2 genes involved in deoxyribonucleotide metabolism, the deoxyguanosine kinase gene and the thymidine kinase 2 gene, had been related to this syndrome. This study aims to describe the clinical, histochemical, biochemical and molecular diagnosis of one Egyptian pediatric patient with the myopathic form of mitochondrial depletion syndrome. The patient presented to Cairo University Pediatric Hospital with the clinical suspicion of mitochondrial encephalomyopathy. Histochemical and biochemical studies of the respiratory chain complexes were performed on the muscle biopsy specimen from the patient. Molecular diagnosis was done by quantitative radioactive Southern blot and sequencing analysis of the whole coding regions of the TK2 gene. Histochemical staining revealed cytochrome oxidase negative fibers and increased staining for succinate dehydrogenase. The activity of complex I was not detected and complex IV activity was about 46%of age matched controls. Southern blot analysis showed reduction of the mitochondrial/nuclear DNA ratio, the degree of depletion was around 30% of aged-matched controls. Sequencing analysis of the TK2 gene revealed no sequence variation. Targeted molecular diagnosis based on the biochemical analysis of the respiratory chain enzymes makes the molecular evaluation of mitochondrial disorders much easier. Involvement of other nuclear genes rather than TK2 gene in the pathogenesis of the myopathic form of mitochondrial depletion syndrome should be considered.Keywords: Mitochondrial; Nuclear; Sequencing; Depletion; Mutation

Wigner's DD-matrix elements for SU(3)SU(3) - A Generating Function Approach

A generating function for the Wigner's $D$-matrix elements of $SU(3)$ is derived. From this an explicit expression for the individual matrix elements is obtained in a closed form.Comment: RevTex 3.0, 22 pages, no figure

Massive Gravity Theories and limits of Ghost-free Bigravity models

We construct a class of theories which extend New Massive Gravity to higher orders in curvature in any dimension. The lagrangians arise as limits of a new class of bimetric theories of Lovelock gravity, which are unitary theories free from the Boulware-Deser ghost. These Lovelock bigravity models represent the most general non-chiral ghost-free theories of an interacting massless and massive spin-two field in any dimension. The scaling limit is taken in such a way that unitarity is explicitly broken, but the Boulware-Deser ghost remains absent. This automatically implies the existence of a holographic $c$-theorem for these theories. We also show that the Born-Infeld extension of New Massive Gravity falls into our class of models demonstrating that this theory is also free of the Boulware-Deser ghost. These results extend existing connections between New Massive Gravity, bigravity theories, Galileon theories and holographic $c$-theorems.Comment: 11+5 page