
Quintessence is a hypothetical form of dark energy characterized by a dynamic scalar field driving cosmic acceleration.Quintessence is a hypothetical form of dark energy with variable density, described by a scalar field. Unlike Einstein's cosmological constant (Λ), which is unchanging, quintessence can evolve in time and space. The equation of state of such energy is characterized by the parameter w = p/ρ (ratio of pressure to density), which for quintessence lies in the range -1 < w < -1/3. When w = -1, it is indistinguishable from Λ, and values close to -1/3 lead to a slowdown of the acceleration. Observations have not yet confirmed deviations of w from -1, but allow for subtle dynamics.
After the discovery of the accelerated expansion of the Universe in 1998 by groups led by Saul Perlmutter, Adam Riess, and Brian Schmidt, the question arose about the nature of dark energy. Although the cosmological constant was the simplest explanation, theorists including Paul Steinhardt and Robert Caldwell proposed models of a dynamic scalar field — quintessence. The term became established in the literature as a contrast to the static Λ. The idea is supported by attempts to link dark energy with the inflationary field in the early Universe.
The dynamics of quintessence obey the Klein-Gordon equation in an expanding Universe: ϕ̈ + 3Hϕ̇ + dV/dϕ = 0, where H is the Hubble parameter. The braking due to expansion causes the field to roll slowly, preserving the potential energy, which dominates and creates negative pressure. The energy density and pressure of the field: ρ_ϕ = ϕ̇²/2 + V(ϕ), p_ϕ = ϕ̇²/2 - V(ϕ). When V(ϕ) ≫ ϕ̇², we get p_ϕ ≈ -ρ_ϕ, which leads to acceleration. Quintessence models must solve the fifth force problem, since field variations could manifest in laboratory experiments, so it is usually assumed that the field interacts very weakly with matter.
Helps understand why the Universe is expanding at an accelerating rate and predict its ultimate fate — whether it will be a Big Rip or eternal cooling.
The name 'fifth element energy' refers to the ancient Greek notion that the heavens consist of a special substance — ether, or quintessence. Modern physics may be bringing this idea back on scientific grounds.
| c_s | variable | sound speed — sound speed metre per second |
| P | variable | pressure of the scalar field — pressure pascal |
| X | variable | kinetic term, -1/2 (∂φ)^2 — kinetic energy density joule per cubic metre |
| P_X | variable | partial derivative of P with respect to X — partial derivative |
| P_XX | variable | second partial derivative of P with respect to X — second partial derivative |






















