Non-Abelian Born-Infeld cosmology

Abstract

We investigate homogeneous and isotropic cosmological solutions supported by the SU͑2͒ gauge field governed by the Born-Infeld Lagrangian. In the framework of the Friedmann-Robertson-Walker cosmology with or without the cosmological constant , we derive dynamical systems that give a rather complete description of the space of solutions. For ϭ0 the effective equation of state (p) is shown to interpolate between pϭϪ/3 in the regime of the strong field and pϭ/3 for the weak field. Correspondingly, the universe starts with zero acceleration and gradually enters the decelerating regime, asymptotically approaching the Tolman solution.

Born-Infeld corrections to Coulombian interactions

“…The renewed interest in Born-Infeld theory can be traced to its emergence in the study of strings and branes: loop calculations for open superstrings lead to a Born-Infeld type low energy action [11,12,13]. Nowadays Born-Infeld-like Lagrangians have been proposed for quintessential matter models and inflation [14], and also for alternative theories of gravity [15]. Born-Infeld charges coupled with gravity have been investigated in attempts to remove geometrical singularities of charged black holes [16].…”

Non-Abelian Brane Cosmology

“…In the opposite limit ε ≪ λ one finds the hot matter state equation p = ε/3, in fact in this limit the scale invariance of the action is restored. The dynamics of the gauge field w in the usual FRW model is then expressible in terms of the Jacobi elliptic functions [3]. Remarkably, the space-time evolution can be separated from that of the gauge field.…”

“…In the context of the FRW cosmology this means that the equation of state will be different from p = ε/3 found in the latter case for isotropic and homogeneous configurations [4]. In the model with the ordinary trace (4) the energy density is [3] …”

“…The universe contracts to the minimal radius a = |C|, bounces and reexpands. The situation is qualitatively similar, though not precisely the same in the model with symmetrized trace (3). One has to solve the full system of equations consisting of one derived from the action (3) for the gauge field and the equation (11) for the metric.…”

“…The computation of the reduced action is straightforward for the "ordinary trace" prescription [3]. For the symmetrized trace one has to expand the square root into powers of the matrix-valued F µν , to perform symmetrization in the generator products, to take the trace, and then to attempt a resummation.…”