Cosmological Scaling Solutions for Multiple Scalar Fields
  The general k-essence Lagrangian for the existence of cosmological scaling
solutions is derived in the presence of multiple scalar fields coupled to a
barotropic perfect fluid. In addition to the scaling fixed point associated
with the dynamics during the radiation and matter eras, we also obtain a
scalar-field dominated solution relevant to dark energy and discuss the
stability of them in the two-field set-up. We apply our general results to a
model of two canonical fields with coupled exponential potentials arising in
string theory. Depending on model parameters and initial conditions, we show
that the scaling matter-dominated epochs followed by an attractor with cosmic
acceleration can be realized with/without the couplings to scalar fields. The
different types of scaling solutions can be distinguished from each other by
the evolution of the dark energy equation of state from high-redshifts to
today.
