Teleparallel Theories of Gravity: Illuminating a Fully Invariant Approach

Teleparallel gravity and its popular generalization $f(T)$ gravity can be formulated as fully invariant (under both coordinate transformations and local Lorentz transformations) theories of gravity. Several misconceptions about teleparallel gravity and its generalizations can be found in the literature, especially regarding their local Lorentz invariance. We describe how these misunderstandings may have arisen and attempt to clarify the situation. In particular, the central point of confusion in the literature appears to be related to the inertial spin connection in teleparallel gravity models. While inertial spin connections are commonplace in special relativity, and not something inherent to teleparallel gravity, the role of the inertial spin connection in removing the spurious inertial effects within a given frame of reference is emphasized here. The careful consideration of the inertial spin connection leads to the construction of a fully invariant theory of teleparallel gravity and its generalizations. Indeed, it is the nature of the spin connection that differentiates the relationship between what have been called good tetrads and bad tetrads and clearly shows that, in principle, any tetrad can be utilized. The field equations for the fully invariant formulation of teleparallel gravity and its generalizations are presented and a number of examples using different assumptions on the frame and spin connection are displayed to illustrate the covariant procedure. Various modified teleparallel gravity models are also briefly reviewed.Comment: v2: 72 pages, revised version, references added, matches published versio

Scalar Field Cosmologies with Barotropic Matter: Models of Bianchi class B

We investigate in detail the qualitative behaviour of the class of Bianchi type B spatially homogeneous cosmological models in which the matter content is composed of two non-interacting components; the first component is described by a barotropic fluid having a gamma-law equation of state, whilst the second is a non-interacting scalar field (phi) with an exponential potential V=Lambda exp(k phi). In particular, we study the asymptotic properties of the models both at early and late times, paying particular attention on whether the models isotropize (and inflate) to the future, and we discuss the genericity of the cosmological scaling solutions.Comment: 18 pages, 1 figure, uses revtex and epsf to insert figur

The stability of cosmological scaling solutions

We study the stability of cosmological scaling solutions within the class of spatially homogeneous cosmological models with a perfect fluid subject to the equation of state p_gamma=(gamma-1) rho_gamma (where gamma is a constant satisfying 0 < gamma < 2) and a scalar field with an exponential potential. The scaling solutions, which are spatially flat isotropic models in which the scalar field energy density tracks that of the perfect fluid, are of physical interest. For example, in these models a significant fraction of the current energy density of the Universe may be contained in the scalar field whose dynamical effects mimic cold dark matter. It is known that the scaling solutions are late-time attractors (i.e., stable) in the subclass of flat isotropic models. We find that the scaling solutions are stable (to shear and curvature perturbations) in generic anisotropic Bianchi models when gamma < 2/3. However, when gamma > 2/3, and particularly for realistic matter with gamma >= 1, the scaling solutions are unstable; essentially they are unstable to curvature perturbations, although they are stable to shear perturbations. We briefly discuss the physical consequences of these results.Comment: AMSTeX, 7 pages, re-submitted to Phys Rev Let

Dynamics of Generalized Assisted Inflation

We study the dynamics of multiple scalar fields and a barotropic fluid in an FLRW-universe. The scalar potential is a sum of exponentials. All critical points are constructed and these include scaling and de Sitter solutions. A stability analysis of the critical points is performed for generalized assisted inflation, which is an extension of assisted inflation where the fields mutually interact. Effects in generalized assisted inflation which differ from assisted inflation are emphasized. One such a difference is that an (inflationary) attractor can exist if some of the exponential terms in the potential are negative.Comment: 27 page

Bibliography

Regular use of beta2-agonists might result in increased bronchial hyper-responsiveness (BHR) and decreased forced expiratory volume in 1 sec (FEV1). It has been suggested that these possible detrimental effects are not a real deterioration of the disease, but that it might be only a transient (rebound) effect shortly after discontinuing this regular use. Moreover, these effects are thought to occur especially during short-acting and not during long-acting beta2-agonists use. The aim of this study was to invest gate whether a rebound effect (a pharmacological deterioration effect diminishing after several hours) in FEV1 and PC20 (concentration of histamine causing a 20% fall in FEV1 with regard to baseline) occurred after cessation of regular use of beta2-agonists, and whether this occurred both after short-acting and long-acting beta2-agonists. Allergic asthmatic patients (n = 134) were randomly allocated to the use of a short-acting (salbutamol), a long-acting beta2-agonist (formoterol) or placebo for 12 weeks (double-blind, double-dummy). No other asthma medication was allowed, including inhaled corticosteroids. At the start and every 4 weeks later FEV and PC20 were measured, each time at least 12 h after the last doses of study medication, which is in the possible rebound period. To investigate whether a (transient) rebound effect occurred, parameters were additionally measured at least 72 h later after discontinuation of the study medication. After 12 weeks of short-acting beta2-agonist use, a drop was seen in FEV1 from 85.6 (+/- 2.21)% predicted to 78.8 (+/- 2.9)% predicted, measured 15 h (median) after the last doses of medication. This was significantly different compared to placebo. When measured 168 h (median) later FEV1 recovered to 85.5 (+/- 2.4)% predicted, comparable to baseline. PC20 decreased with -1.17 (+/- 0.44) doubling dose after 12 weeks of short-acting beta2-agonist use, measured 15 h after the last doses of medication, which was significantly different compared to placebo. However, 168 h later PC20 recovered slightly with +0.55 (+/- 0.34) doubling dose, but this value was still lower compared to placebo. In contrast, during long-acting beta2-agonist and placebo use no significant changes were seen. In conclusion, the use of short-acting beta2-agonists resulted in a transient (rebound) effect in FEV while the effects on PC20 may point to a real deterioration of the disease. Long-acting beta2-agonist and placebo use showed no changes.We conclude that a mono-therapy of short-acting and not of long-acting beta2-agonists might have deleterious effects in asthma

Self-similar spherically symmetric cosmological models with a perfect fluid and a scalar field

Self-similar, spherically symmetric cosmological models with a perfect fluid and a scalar field with an exponential potential are investigated. New variables are defined which lead to a compact state space, and dynamical systems methods are utilised to analyse the models. Due to the existence of monotone functions global dynamical results can be deduced. In particular, all of the future and past attractors for these models are obtained and the global results are discussed. The essential physical results are that initially expanding models always evolve away from a massless scalar field model with an initial singularity and, depending on the parameters of the models, either recollapse to a second singularity or expand forever towards a flat power-law inflationary model. The special cases in which there is no barotropic fluid and in which the scalar field is massless are considered in more detail in order to illustrate the asymptotic results. Some phase portraits are presented and the intermediate dynamics and hence the physical properties of the models are discussed.Comment: 31 pages, 4 figure

The Dynamics of Multi-Scalar Field Cosmological Models and Assisted Inflation

We investigate the dynamical properties of a class of spatially homogeneous and isotropic cosmological models containing a barotropic perfect fluid and multiple scalar fields with independent exponential potentials. We show that the assisted inflationary scaling solution is the global late-time attractor for the parameter values for which the model is inflationary, even when curvature and barotropic matter are included. For all other parameter values the multi-field curvature scaling solution is the global late-time attractor (in these solutions asymptotically the curvature is not dynamically negligible). Consequently, we find that in general all of the scalar fields in multi-field models with exponential potentials are non-negligible in late-time behaviour, contrary to what is commonly believed. The early-time and intermediate behaviour of the models is also studied. In particular, n-scalar field models are investigated and the structure of the saddle equilibrium points corresponding to inflationary m-field scaling solutions and non-inflationary m-field matter scaling solutions are also studied (where m<n), leading to interesting transient dynamical behaviour with new physical scenarios of potential importance.Comment: 27 pages, uses REVTeX Added an appendix illustrating some of the details needed to compute the stability of the assisted inflationary solutio