Once Before Time - Martin Bojowald [78]
In Newtonian physics, mass density causes gravitational forces. In a relativistic description one cannot separate energy density from the energy flow or from pressure and inner tensions. The gravitational force must thus be a consequence of the entire stress-energy tensor, as it indeed appears in Einstein’s equations. Consequently, pressure is relevant for the expansion of the universe; the pressure, not just the density, of all matter contained in the universe contributes to its expansion history. Implications for the possibility of accelerated expansion are immediate: Like mass, the energy density must be positive and can play no role in the direct generation of repulsive forces. Pressure, by contrast, though often positive, can easily take negative values and then cause repulsive gravity—provided it is strong enough to overwhelm the positive energy density. Here we have found one of the main properties of dark energy: strongly negative pressure with positive energy.
Negative pressure is well known to arise in special situations. Negative pressure occurs, for instance, in the transport pipes of trees, caused by water evaporating at the tips of leaves. But what is its role in gravitation? As defined, pressure is characterized by the energy change for some volume change, with a conventional minus sign smuggled in to have a positive value in common situations. In this case, energy decreases when the volume is increased, and matter such as a gas will expand to lower its energy. To prevent this, the gas must be enclosed in a container with sufficiently strong walls. With negative pressure, matter can lower its energy by contracting, and only a pull can prevent this.
This appears to be the role of pressure as long as gravity is ignored. For pressurized matter in a universe, one can again see the idiosyncratic trait of classical gravity, which already obliged us to cope with singularities in gravitational collapse. In that case, an immense piling up results from attractive gravity’s compressing masses and further enhancing gravitational attraction. In general relativity, there is no escaping this unstable situation: After some time, self-destructive gravity ends in a singularity—unless it can be tamed early enough by repulsive forces of quantum gravity.
Gravitational pressure shows a similarly unstable behavior. Now we have, for instance in the homogeneous case of cosmology, matter “enclosed” not in a container but in the entire space of the universe. With positive pressure, matter would have to expand, which would be possible only by an expansion of the whole universe. But positive pressure, like positive energy, implies gravitational attraction, and the cosmic expansion is slowed down. The tendency to expand at positive pressure is counteracted by gravity. If matter under positive pressure is localized in a collapsing piece of space-time, like a burnt-out star, the collapse is accelerated, and at the end of this unstable situation waits the singularity of a black hole.
With negative pressure, the situation is just the opposite, provided it can compensate for positive energy density. Matter in the universe should then contract, which would be possible for a homogeneous matter distribution in the whole cosmos only with contraction of the universe. Gravity reacts adversely by enhancing cosmic expansion, and accelerated expansion results. As observations indicate, the expansion of the universe in the recent past was indeed accelerated. If the homogeneity assumption is justified, one has to expect an immense matter contribution of negative pressure.
Though it presents at least a theoretical characterization, this account is far from being an explanation. To impute sufficient negative pressure active over long cosmic durations