A rule of thumb for cosmological backreaction

In the context of second order perturbation theory, cosmological backreaction is seen to rescale both time and the scale factor. The issue of the homogeneous limit of long-wavelength perturbations is addressed and backreaction is quantified in terms of a gauge-invariant metric function that is the true physical degree of freedom in the homogeneous limit. The time integral of this metric function controls whether backreaction hastens or delays the expansion of the universe. As an example, late time acceleration of the universe is shown to be inconsistent with a perturbative approach. Any tendency to accelerate the expansion requires negative non-adiabatic pressure fluctuations.