Dark Energy

In some ways, the argument supporting dark energy only really started to be seriously debated in 1998, when scientists discovered the possible accelerated expansion of the universe. This idea was based on the observation of a type of exploding star, i.e. a type-1a supernova, whose distance can be inferred from its apparent brightness.  Basically, what scientists had found was that the more distant supernovae were dimmer than expected, implying that the recessional distance, due to the expansion of the universe, was larger than expected, i.e. the universe was accelerating with respect to some earlier time.

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To put this situation into some historical perspective, at the beginning of the 20th century, most scientists would have probably shared Einstein’s view of a static universe. Only after Hubble’s discovery did most scientists become 'convinced' of the idea of an expanding universe, which was then assumed to be slowing under the effects of gravity. So, the idea that the universe could actually be accelerating required yet another fundamental shift in thinking, because it appears to require an unknown source of energy to explain the acceleration. Although the issue as to what caused the expansion prior to the acceptance of the idea of dark energy might, yet again, be tabled as an open question

In order to account for the observed acceleration, the hypothesis of dark energy was forwarded along with the idea of negative pressure.  Given the amount of acceleration required, it was estimated that the energy-density of dark energy would have to be 6.2E-10 joule/m3. What was subsequently said to add weight to this hypothesis was the fact that the estimated energy density also explained the spatial flatness of the universe in terms of the sum of all the component energy densities adding up to the critical density, i.e. 8.53E-10 joule/m3. However, this said, the exact nature of dark energy is still very speculative. Current ideas suggest that dark energy would have to be homogeneous in distribution and have a net negative pressure in excess of any gravitational effects associated with its energy density. However, possibly the most perplexing attribute is its apparent unchanging energy density under expansion. All other forms of energy density change as a function of expansion, while dark energy remains constant per unit volume. Therefore, while the energy density of dark energy was virtually zero in comparison to all the other energy densities of the earlier universe, its constant energy density grows relative to all other energy densities as a function of the expanding volume - see density graph. Today, dark energy is thought to account for 73% of the critical density. There is also a suggestion in this characteristic of dark energy that the total energy per unit volume of the universe must be increasing in apparent contradiction to the conservation of energy - see energy graph.

Given the level of speculation surrounding dark energy, it should be no surprise that there are still many competing ideas. However, given the somewhat unusual attributes of this form of energy, there is a tendency to look towards quantum theory for an explanation. In physics, zero-point energy is the lowest possible energy that a quantum system may possess as it is considered to be the ground state energy of a system. This idea is backed up by some experimental evidence in the form of the Casimir effect, which can be observed in nano-scale devices. However, in quantum theory, zero-point energy is often thought to be synonymous with the idea of vacuum energy, i.e. the energy within a unit volume of empty space; while in cosmology, this energy might also be discussed in terms of a cosmological constant [Λ]. However, in many respects, dark energy is an idea on which general relativity and quantum theory don’t always see eye to eye. While the actual details behind these opposing `worldviews` is too complex to consider in detail, some insight into the issues may be of some value.

  • If we put cosmology into the general relativity camp, the energy density of the vacuum is essentially determined by the idea of spatial curvature. However, this simply translates into the assertion supporting a spatially flat universe, i.e. k=0, where all known energy density components must add up to the critical density. On the basis of the ΛCDM model, the present-day dark energy or vacuum energy density corresponds to 73% of the critical density, i.e. 6.2E-10 joule/m3. As stated, this also seems to account for the observed acceleration.

  •  However, various flavours of quantum theory can come up with very different answers. For example, if we define the zero-point energy in terms of harmonic oscillators with energy E=hf/2 and simply add up all the possible harmonic oscillations based on the assumption that spacetime is a continuum; the vacuum energy density would be infinite. Even if we modify the previous assumption to only include those oscillations with a wavelength greater than the Planck length, i.e. ~10-35 meters, the answer is finite, but still enormous in comparison to the observed dark energy estimates.

There are several other permutations along this line, but the bottom line, at present, seems to be that only the energy density estimate associated with the cosmological definition of dark energy makes any sense, although acknowledging that lack of support from quantum theory, at this time. However, within the confines of the concordance model, we shall assume that dark energy does have negative pressure as defined by the equation of state [ω=-1]. While we might initially perceive negative pressure in terms of a region of lower pressure, i.e. a vacuum that would suck things from a region of higher pressure, dark energy is said to act more like anti-gravity. However, the justification for some of these statements will be deferred to the discussion entitled ‘Interpreting Friedmann in which the equation of state for each energy density will be derived.