Extended Birkhoff's Theorem in the f(T) Gravity

The f(T) theory, a generally modified teleparallel gravity, has been proposed as an alternative gravity model to account for the dark energy phenomena. Following our previous work [Xin-he Meng and Ying-bin Wang, EPJC(2011), arXiv:1107.0629v1], we prove that the Birkhoff's theorem holds in a more general context, specifically with the off diagonal tetrad case, in this communication letter. Then, we discuss respectively the results of the external vacuum and internal gravitational field in the f(T) gravity framework, as well as the extended meaning of this theorem. We also investigate the validity of the Birkhoff's theorem in the frame of f(T) gravity via conformal transformation by regarding the Brans-Dicke-like scalar as effective matter, and study the equivalence between both Einstein frame and Jordan frame.Comment: 7 pages, 1 figure, submitted to EPJ-C. arXiv admin note: substantial text overlap with arXiv:1107.062

Birkhoff's Theorem in f(T) Gravity up to the Perturbative Order

f(T) gravity, a generally modified teleparallel gravity, has become very popular in recent times as it is able to reproduce the unification of inflation and late-time acceleration without the need of a dark energy component or an inflation field. In this present work, we investigate specifically the range of validity of Birkhoff's theorem with the general tetrad field via perturbative approach. At zero order, Birkhoff's theorem is valid and the solution is the well known Schwarzschild-(A)dS metric. Then considering the special case of the diagonal tetrad field, we present a new spherically symmetric solution in the frame of f(T) gravity up to the perturbative order. The results with the diagonal tetrad field satisfy the physical equivalence between the Jordan and the so-called Einstein frames, which are realized via conformal transformation, at least up to the first perturbative order.Comment: 8 pages, no figure. Final version, accepted for publication in EPJ

Birkhoff's theorem in the f(T) gravity

Generalized from the so-called teleparallel gravity which is exactly equivalent to general relativity, the $f(T)$ gravity has been proposed as an alternative gravity model to account for the dark energy phenomena. In this letter we prove that the external vacuum gravitational field for a spherically symmetric distribution of source matter in the $f(T)$ gravity framework must be static and the conclusion is independent of the radial distribution and spherically symmetric motion of the source matter that is, whether it is in motion or static. As a consequence, the Birkhoff's theorem is valid in the general $f(T)$ theory. We also discuss its application in the de Sitter space-time evolution phase as preferred to by the nowadays dark energy observations.Comment: 5p

Standard Model baryogenesis through four-fermion operators in braneworlds

We study a new baryogenesis scenario in a class of braneworld models with low fundamental scale, which typically have difficulty with baryogenesis. The scenario is characterized by its minimal nature: the field content is that of the Standard Model and all interactions consistent with the gauge symmetry are admitted. Baryon number is violated via a dimension-6 proton decay operator, suppressed today by the mechanism of quark-lepton separation in extra dimensions; we assume that this operator was unsuppressed in the early Universe due to a time-dependent quark-lepton separation. The source of CP violation is the CKM matrix, in combination with the dimension-6 operators. We find that almost independently of cosmology, sufficient baryogenesis is nearly impossible in such a scenario if the fundamental scale is above 100 TeV, as required by an unsuppressed neutron-antineutron oscillation operator. The only exception producing sufficient baryon asymmetry is a scenario involving out-of-equilibrium c quarks interacting with equilibrium b quarks.Comment: 39 pages, 5 figures v2: typos, presentational changes, references and acknowledgments adde

QCD ghost f(T)-gravity model

Within the framework of modified teleparallel gravity, we reconstruct a f(T) model corresponding to the QCD ghost dark energy scenario. For a spatially flat FRW universe containing only the pressureless matter, we obtain the time evolution of the torsion scalar T (or the Hubble parameter). Then, we calculate the effective torsion equation of state parameter of the QCD ghost f(T)-gravity model as well as the deceleration parameter of the universe. Furthermore, we fit the model parameters by using the latest observational data including SNeIa, CMB and BAO data. We also check the viability of our model using a cosmographic analysis approach. Moreover, we investigate the validity of the generalized second law (GSL) of gravitational thermodynamics for our model. Finally, we point out the growth rate of matter density perturbation. We conclude that in QCD ghost f(T)-gravity model, the universe begins a matter dominated phase and approaches a de Sitter regime at late times, as expected. Also this model is consistent with current data, passes the cosmographic test, satisfies the GSL and fits the data of the growth factor well as the LCDM model.Comment: 19 pages, 9 figures, 2 tables. arXiv admin note: substantial text overlap with arXiv:1111.726

The torsion of a finite quasigroup quandle is annihilated by its order

We prove that if Q is a finite quasigroup quandle, then |Q| annihilates the torsion of its homology. It is a classical result in reduced homology of finite groups that the order of a group annihilates its homology. From the very beginning of the rack homology (between 1990 and 1995) the analogous result was suspected. The first general results in this direction were obtained independently about 2001 by R.A.Litherland and S.Nelson, and P.Etingof and M.Grana. In Litherland-Nelson paper it is proven that if (Q;*) is a finite homogeneous rack (this includes quasigroup racks) then the torsion of homology is annihilated by |Q|^n. In Etingof-Grana paper it is proven that if (X;A) is a finite rack and N=|G^0_Q| is the order of a group of inner automorphisms of Q, then only primes which can appear in the torsion of homology are those dividing N (the case of connected Alexander quandles was proven before by T.Mochizuki). The result of Litherland-Nelson is generalized by Niebrzydowski and Przytycki and in particular, they prove that the torsion part of the homology of the dihedral quandle R_3 is annihilated by 3. In Niebrzydowski-Przytycki paper it is conjectured that for a finite quasigroup quandle, torsion of its homology is annihilated by the order of the quandle. The conjecture is proved by T.Nosaka for finite Alexander quasigroup quandles. In this paper we prove the conjecture in full generality. For this version, we rewrote the Section 3 totally and introduced the concept of the precubic homotopy. In Section 2, the main addition is Corollary 2.2 which summarizes identities observed in the proof of the main theorem as we use it later in Section 3.Comment: 13 pages, 1 figure; accepted for publication in Journal of Pure and Applied Algebr

The Vega debris disc: A view from Herschel

We present five band imaging of the Vega debris disc obtained using the Herschel Space Observatory. These data span a wavelength range of 70-500 mu m with full-width half-maximum angular resolutions of 5.6-36.9 ''. The disc is well resolved in all bands, with the ring structure visible at 70 and 160 mu m. Radial profiles of the disc surface brightness are produced, and a disc radius of 11 '' (similar to 85AU) is determined. The disc is seen to have a smooth structure thoughout the entire wavelength range, suggesting that the disc is in a steady state, rather than being an ephemeral structure caused by the recent collision of two large planetesimals

The 3C cooperation model applied to the classical requirement analysis

Aspects related to the users' cooperative work are not considered in the traditional approach of software engineering, since the user is viewed independently of his/her workplace environment or group, with the individual model generalized to the study of collective behavior of all users. This work proposes a process for software requirements to address issues involving cooperative work in information systems that provide distributed coordination in the users' actions and the communication among them occurs indirectly through the data entered while using the software. To achieve this goal, this research uses ergonomics, the 3C cooperation model, awareness and software engineering concepts. Action-research is used as a research methodology applied in three cycles during the development of a corporate workflow system in a technological research company. This article discusses the third cycle, which corresponds to the process that deals with the refinement of the cooperative work requirements with the software in actual use in the workplace, where the inclusion of a computer system changes the users' workplace, from the face to face interaction to the interaction mediated by the software. The results showed that the highest degree of users' awareness about their activities and other system users contribute to a decrease in their errors and in the inappropriate use of the system