Narrow Results

We consider the model of modified gravity with dynamical torsion. This model was previously found to have promising stability properties about various backgrounds. Here, we study the stability of linear perturbations about the self-accelerating solution. We apply the (3+1)-decomposition and consider the scalar sector of perturbations. We find that the number of degrees of freedom is equal to 2, which is the same as in Minkowski background. However, there is at least one instability in the scalar sector, if the value of background torsion is large enough. This does not rule out the possibility of stable self-acceleration with torsion of the order of the effective cosmological constant.

We consider the model of modified gravity with dynamical torsion. This model was found to have promising stability properties about various backgrounds. The model admits a self-accelerating solution. We have shown previously that if the parameters are adjusted in such a way that the torsion is much greater than the effective cosmological constant, the self-accelerating solution is unstable: there are exponentially growing modes. Here, we study the scalar perturbations in the case when the torsion is of the order of the effective cosmological constant. We find that there are no exponential instabilities.

We develop a new description of curved manifolds that represent a topological phase for the usual Levi-Civita connection and a dynamical phase for the torsion, being the only part of the connection that generates curvature. The holonomy group structure of such manifolds is studied, and different expressions of the torsion in terms of gauge fields are considered with the purpose to describe different dynamical scenarios. Additionally some models of torsion interacting with fermions are constructed; specifically a four-dimensional model that mimics an usual fermion-gauge fields system is considered; this model undergoes parity symmetry breaking with a dynamical background. Since these manifolds represent new gravitational backgrounds, we speculate on possible applications in the study of qualitative and quantitative aspects of the gauge/gravity duality.