I use the formalism of Thomas Buchert in taking account of back-reaction in the evolution of Einstein's equations, but take the extra essential step of asking how our own measurements are related to volume average ones. One crucial insight is that gravitational energy, and clock rates, are defined with respect to a notion of infinity. I specifically develop the notion of finite infinity, as suggested qualitatively by George Ellis in 1984. Bound systems where space is not expanding, including all galaxies, live within finite infinity, but volume average positions in freely expanding space lie beyond it - there is a difference in gravitational energy and spatial curvature between the two locations. The differences were initially miniscule but are large today. Taking account of the initial conditions set by primordial inflation at the time of last scattering, when the cosmic microwave background was laid down, a quantitative model of the universe is developed. It appears to be observationally viable.

Relative to bound system observers, ideal observers at volume average positions in voids will measure an older age of the universe, a lower mean temperature for the cosmic microwave background, and a smaller angular anisotropy scale. These differences can be systematically quantified. On account of the variance in clock rates volume average observers in voids infer no apparent "cosmic acceleration", but observers such as ourselves in bound systems do. Apparent acceleration begins when the void volume fraction reaches 59%, at a redshift of order z=0.5 to 1.0 (depending on whether one uses the CMB or supernovae as an estimator).

The mystery of dark energy is explained purely in Einstein's theory, through a deeper understanding of those parts of general relativity, which Einstein himself recognised as being difficult: the understanding of gravitational energy, given that space itself is dynamical and may contain energy and momentum.