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 asymptotically stable solutions 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 behavior, contrary to what is commonly believed. The early-time and intermediate behavior 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 behavior perhaps associated with new physical scenarios of potential importance.

We shall study spatially homogeneous cosmological models containing a self-interacting scalar field with an exponential potential of the form ${\mathrm{V(\phi )=\Lambda e}}^{\mathrm{k\phi }}$ . The asymptotic properties of these models are discussed. In particular, their possible isotropization and inflation are investigated for all values of the parameter $k$ . A particular class of models is analyzed qualitatively using the theory of dynamical systems, illustrating the general asymptotic behavior.

In theories such as teleparallel gravity and its extensions, the frame basis replaces the metric tensor as the primary object of study. A choice of coordinate system, frame basis, and spin-connection must be made to obtain a solution from the field equations of a given teleparallel gravity theory. It is worthwhile to express solutions in an invariant manner in terms of torsion invariants to distinguish between different solutions. In this paper, we discuss the symmetries of teleparallel gravity theories, describe the classification of the torsion tensor and its covariant derivative, and define scalar invariants in terms of the torsion. In particular, we propose a modification of the Cartan–Karlhede algorithm for geometries with torsion (and no curvature or nonmetricity). The algorithm determines the dimension of the symmetry group for a solution and suggests an alternative frame-based approach to calculating symmetries. We prove that the only maximally symmetric solution to any theory of gravitation admitting a non-zero torsion tensor is Minkowski space. As an illustration, we apply the algorithm to six particular exact teleparallel geometries. From these examples, we notice that the symmetry group of the solutions of a teleparallel gravity theory is potentially smaller than their metric-based analogs in general relativity.

We study whether homogeneous cosmological models containing a self-interacting scalar field with an exponential potential [of the form V(φ)=Λ${\mathit{e}}^{\mathit{k}\mathrm{\phi }}$] isotropize. Following Heusler [M. Heusler, Phys. Lett. B 253, 33 (1991)], we show that Bianchi models, other than possibly those of types I, V, VII, or IX, cannot isotropize if ${\mathit{k}}^2$>2. In this case we note that the solutions of Feinstein and Ibáñez [A. Feinstein and J. Ibáñez, Class. Quantum Grav. 10, 93 (1993)], which are neither isotropic nor inflationary, act as stable attractors. When ${\mathit{k}}^2$<2 the cosmic no-hair theorem of Kitada and Maeda [Y. Kitada and K. Maeda, Phys. Rev. D 45, 1416 (1992); Class. Quantum Grav. 10, 703 (1993)] applies and the isotropic power-law inflationary FRW solution is the unique attractor for any initially expanding Bianchi model.