between objects shrinks or grows as the various geodesics converge or diverge. Because this expansion is caused by relative changes in the distance-defining metric, this expansion (and the resultant movement apart of objects) is not restricted by the speed of light upper bound of special relativity. Two reference frames that are globally separated can be moving apart faster than light without violating special relativity, although whenever two reference frames diverge from each other faster than the speed of light, there will be observable effects associated with such situations including the existence of various cosmological horizons. Theory and observations suggest that very early in the history of the universe, there was an inflationary phase where the metric changed very rapidly, and that the remaining time-dependence of this metric is what we observe as the so-called Hubble expansion, the moving apart of all gravitationally unbound objects in the universe. The expanding universe is therefore a fundamental feature of the universe we inhabit – a universe fundamentally different from the static universe Albert Einstein first considered when he developed his gravitational theory. Comoving coordinates In expanding space, proper distances are dynamical quantities that change with time. An easy way to correct for this is to use comoving coordinates, which remove this feature and allow for a characterization of different locations in the universe without having to characterize the physics associated with metric expansion. In comoving coordinates, the distances between all objects are fixed and the instantaneous dynamics of matter and light are determined by the normal physics of gravity and electromagnetic radiation. Any time-evolution however must be accounted for by taking into account the Hubble law expansion in the appropriate equations in addition to any other effects that may be operating (gravity, dark energy, or curvature, for example). Cosmological simulations that run through significant fractions of the universe's history therefore must include such effects in order to make applicable predictions for observational cosmology. Understanding the expansion of the universe Measurement of expansion and change of rate of expansion In principle, the expansion of the universe could be measured by taking a standard ruler and measuring the distance between two cosmologically distant points, waiting a certain time, and then measuring the distance again, but in practice, standard rulers are not easy to find on cosmological scales and the timescales over which a measurable expansion would be visible are too great to be observable even