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apparently, as an artifact generated by squeezing an already strongly inhomogeneous universe into the mathematical corset of a homogeneous solution. On the other hand, the assumption of homogeneity that came along with strong computational simplifications in the theoretical modeling is dropped. Such doubts are, of course, always justified, for predictions merely relying on the availability of simple mathematical solutions are never valid. Simplicity appeals only to our limited and biased minds, not to nature. Solutions of simple enough form can be analyzed in all details, but this comes at the expense of abandoning some properties more difficult to model, yet possibly significant. Whether a model is reliable in all respects can be judged only in a more general setting within the theory used; in general relativity, the required equations easily become so complex that the behavior of their solutions is hardly known. So this proposal, alas, has not yet resulted in completely convincing explanations of dark energy.

It is perhaps consoling to know that accelerated expansion in certain phases is at least possible, though not natural, within general relativity, despite its generally attractive character. In Newtonian gravity, only the mass of matter calls gravitational forces into action, and those forces are purely attractive. In general relativity, by contrast, gravity is caused not only by masses but also by energy, which, according to special relativity, is equivalent to mass by Einstein’s famous formula, as well as to its relative, pressure. Like most differences between Newtonian and Einstein gravity, the role of pressure is once again a consequence of the transformability of space and time. What is primarily relevant for gravity is energy density: some amount of energy located in a certain volume. Since special relativity shows that mass is equivalent to energy, the usual gravitational attraction of masses qualitatively results, as it does in Newtonian physics. But relativistically one can transform space into time intervals by changing one’s state of motion. Just as space and time cannot be viewed independently of each other, but instead form a single object—space-time—energy density cannot be considered a single independent object either; length intervals are used in its definition. After changing the state of motion and partially transforming space in time, the apparently static energy density first takes the form of an energy flow: What to one observer looks like energy located in a region, another one in relative motion would see as energy moving in a certain direction.

The mathematical object describing the energy density is slightly different from that object giving directions in space-time. Space-time directions are called vectors, combining the spatial and temporal shifts. These are four components, corresponding to the four-dimensionality of space-time. Energy density and energy flow—the latter with three components because of its spatial direction—already make four quantities, enough to complete a vector. But the mathematical object describing energy is not a vector; it is a tensor—the so-called stress-energy tensor. A tensor of this kind in a four-dimensional space-time has not four but sixteen components—one might view it as a vector squared, or a matrix.

What are the remaining components of the stress-energy tensor? As the name suggests, these are elastic stresses in matter as well as pressure. Pressure is defined as the negative change of energy divided by the change of the volume enclosing the energy amount. This definition is in accordance with the intuitive behavior of matter under pressure: If one attempts to shrink the volume, one has to work against the pressure, thereby increasing the energy of the enclosed matter. The volume change is negative, the energy change positive; and pressure, defined as the negative ratio of these quantities, is positive. The more energy spent, the larger the pressure. But if the same amount of energy can achieve a larger change in volume, the pressure must be smaller.