Effective anisotropic stresses of the relic gravitons
  The effective anisotropic stresses induced by the scalar modes of the
geometry depend on the coordinate system so that the comparison of the
competing results is ultimately determined by the evolution of the pivotal
variables in each particular gauge. After arguing that the only reasonable
physical coordinate systems for this problem are the ones where the gauge
freedom is completely fixed (like the longitudinal and the uniform curvature
gauges), we propose a novel gauge-invariant strategy for the comparison of
gauge-dependent results. Instead of employing the pivotal variables of a given
coordinate system, the effective anisotropic stress is solely expressed in
terms of the gravitating normal modes of the plasma and in terms of their
conformal time derivatives. The new approach is explicitly gauge-invariant and
when the wavelengths of the normal modes are either shorter or larger than the
sound horizon, the physical limits of the anisotropic stresses are determined
without relying on the specific details of the background evolution. The
relevance of the proposed strategy is discussed in the general situation where
the scalar anisotropic stress and the non-adiabatic pressure fluctuations are
simultaneously present. We finally argue that the anisotropic stress can be
most efficiently obtained from the second-order effective action of the
curvature inhomogeneities.
