A viable form of the metric Teleparallel F(T) theory of gravity

Unlike F(R) gravity, pure metric F(T) gravity in the vacuum dominated era, ends up with an imaginary action and is therefore not feasible. This eerie situation may only be circumvented by associating a scalar field, which can also drive inflation in the very early universe. We show that, despite diverse claims, F(T) theory admits Noether symmetry only in the pressure-less dust era in the form F(T) proportional to the nth power of T, n being odd integers. A suitable form of F(T), admitting a viable Friedmann-like radiation dominated era, together with early deceleration and late-time accelerated expansion in the pressure-less dust era, has been proposed.Comment: 12 pages, 0 figure

Viability of Noether symmetry of F(R) theory of gravity

Canonization of F(R) theory of gravity to explore Noether symmetry is performed treating R - 6(\frac{\ddot a}{a} + \frac{\dot a^2}{a^2} + \frac{k}{a^2}) = 0 as a constraint of the theory in Robertson-Walker space-time, which implies that R is taken as an auxiliary variable. Although it yields correct field equations, Noether symmetry does not allow linear term in the action, and as such does not produce a viable cosmological model. Here, we show that this technique of exploring Noether symmetry does not allow even a non-linear form of F(R), if the configuration space is enlarged by including a scalar field in addition, or taking anisotropic models into account. Surprisingly enough, it does not reproduce the symmetry that already exists in the literature (A. K. Sanyal, B. Modak, C. Rubano and E. Piedipalumbo, Gen.Relativ.Grav.37, 407 (2005), arXiv:astro-ph/0310610) for scalar tensor theory of gravity in the presence of R^2 term. Thus, R can not be treated as an auxiliary variable and hence Noether symmetry of arbitrary form of F(R) theory of gravity remains obscure. However, there exists in general, a conserved current for F(R) theory of gravity in the presence of a non-minimally coupled scalar-tensor theory (A. K. Sanyal, Phys.Lett.B624, 81 (2005), arXiv:hep-th/0504021 and Mod.Phys.Lett.A25, 2667 (2010), arXiv:0910.2385 [astro-ph.CO]). Here, we briefly expatiate the non-Noether conserved current and cite an example to reveal its importance in finding cosmological solution for such an action, taking F(R) \propto R^{3/2}.Comment: 16 pages, 1 figure. appears in Int J Theoretical Phys (2012

Revisiting Noether gauge symmetry for F(R) theory of gravity

Noether gauge symmetry for F(R) theory of gravity has been explored recently. The fallacy is that, even after setting gauge to vanish, the form of F(R) \propto R^n (where n \neq 1, is arbitrary) obtained in the process, has been claimed to be an outcome of gauge Noether symmetry. On the contrary, earlier works proved that any nonlinear form other than F(R) \propto R^3/2 is obscure. Here, we show that, setting gauge term zero, Noether equations are satisfied only for n = 2, which again does not satisfy the field equations. Thus, as noticed earlier, the only admissible form that Noether symmetry is F(R) \propto R^3/2 . Noether symmetry with non-zero gauge has also been studied explicitly here, to show that it does not produce anything new.Comment: 9 pages, To appear in Astrophysics Space Scienc

Cardiac involvement in Beagle-based canine X-linked muscular dystrophy in Japan (CXMD(J)): electrocardiographic, echocardiographic, and morphologic studies

BACKGROUND: Cardiac mortality in Duchenne muscular dystrophy (DMD) has recently become important, because risk of respiratory failure has been reduced due to widespread use of the respirator. The cardiac involvement is characterized by distinctive electrocardiographic abnormalities or dilated cardiomyopathy, but the pathogenesis has remained obscure. In research on DMD, Golden retriever-based muscular dystrophy (GRMD) has attracted much attention as an animal model because it resembles DMD, but GRMD is very difficult to maintain because of their severe phenotypes. We therefore established a line of dogs with Beagle-based canine X-linked muscular dystrophy in Japan (CXMD(J)) and examined the cardiac involvement. METHODS: The cardiac phenotypes of eight CXMD(J )and four normal male dogs 2 to 21 months of age were evaluated using electrocardiography, echocardiography, and histopathological examinations. RESULTS: Increases in the heart rate and decreases in PQ interval compared to a normal littermate were detected in two littermate CXMD(J )dogs at 15 months of age or older. Distinct deep Q-waves and increase in Q/R ratios in leads II, III, and aVF were detected by 6–7 months of age in all CXMD(J )dogs. In the echocardiogram, one of eight of CXMD(J )dogs showed a hyperechoic lesion in the left ventricular posterior wall at 5 months of age, but the rest had not by 6–7 months of age. The left ventricular function in the echocardiogram indicated no abnormality in all CXMD(J )dogs by 6–7 months of age. Histopathology revealed myocardial fibrosis, especially in the left ventricular posterobasal wall, in three of eight CXMD(J )dogs by 21 months of age. CONCLUSION: Cardiac involvement in CXMD(J )dogs is milder and has slower progression than that described in GRMD dogs. The distinct deep Q-waves have been ascribed to myocardial fibrosis in the posterobasal region of the left ventricle, but our data showed that they precede the lesion on echocardiogram and histopathology. These findings imply that studies of CXMD(J )may reveal not only another causative mechanism of the deep Q-waves but also more information on the pathogenesis in the dystrophin-deficient heart