Abstract
Vacuum energy corresponds to negative pressure, so its equation of state is P = w ρ, with w negative. In the Einstein equation that gives the acceleration of expansion, the term intervenes as - (ρ +3P), so to ensure an acceleration of expansion, w must - 1/3. The dark energy problem can be solved in two ways, depending on whether we add the extra term to the right or subtract it from the left of Einstein's equation. By modifying the term on the right comprising the energy-impulse tensor, we add a term to matter, quintessence, or K-essence, tachyons, Chaplygin gases, or coupled models, etc., to the Einstein equation. By modifying the term on the left, we modify gravity, for example with f(R) modified gravity theories (R the Ricci), tensor-scalar models, brane world, massive gravity, inhomogeneities, etc. (w - 1 possible). There are sometimes overlaps between the two types of solution. Quintessence theories add a scalar field, spin 0; in field theory, the only one in the Standard Model is the Higgs field, whose interaction gives mass to particles. The scalar field should have a low mass (10-33 eV) and therefore slope gently down to its minimum.
A number of possibilities have been envisaged, such as the cosmon, which couples with neutrinos. Since neutrinos are more strongly coupled to the cosmon than to gravity, neutrino mass could increase over time, and neutrinos could become non-relativistic 5 billion years ago. There's also the theory of chameleons, which are particles whose mass varies with the environment': their effective mass increases with density. They therefore have a very high mass in the solar system, with a short range (1 mm). On large scales, they have low mass and a much greater range (> kpc). So these particles escape detection as a fifth force. Galileon theory uses the Vainshtein shielding mechanism, which suppresses the fifth force within a certain radius in the vicinity of massive sources. Generic quintessence models are studied (either thawing or freezing, depending on their behavior as a function of cosmic time).
