Dark energy

Dark energy is a smooth component with sufficiently negative pressure to drive accelerated cosmic expansion.

A propagating adiabatic fluid with the constant closure $p=w\rho$ has $c_s^2=dp/d\rho =w$. For $-1<w<0$, a short-wavelength Fourier perturbation obeys ${\omega }^2\simeq w{k}_{\mathrm{phys}}^2<0$, producing gradient growth. This does not exclude a negative-pressure perfect-fluid stress tensor with nonadiabatic pressure response, or a canonical scalar with rest-frame sound speed one. A cosmological constant has no independent propagating fluid density mode.

// Target: cosmology.bigb

Dynamical dark energy has an energy density or equation-of-state parameter that changes with cosmic time, unlike a cosmological constant.

For $P_{\mathrm{DE}}=w(z){\rho }_{\mathrm{DE}}$, the continuity equation gives

The Chevallier-Polarski-Linder parametrization models dynamical dark energy by $w(a)=w_0+w_a(1-a)$, equivalently $w(z)=w_0+w_{a}z/(1+z)$.

The cosmological constant $\Lambda$ is the constant term proportional to the metric in the Einstein field equations. Interpreted as vacuum energy, it has $P_{\Lambda }=-{\rho }_{\Lambda }$, so its energy density is constant during expansion.

Nonrelativistic matter dilutes as $a^{-3}$, while a cosmological constant has constant energy density. The ratio of vacuum energy density to matter density consequently scales as $a^3$, so comparable contributions occur during a limited epoch. The cosmic coincidence problem asks why observers find these very different components comparable near their own epoch. This timing puzzle is distinct from the cosmological constant problem, which concerns the tiny absolute vacuum-energy scale.

The cosmological constant problem is the unexplained smallness of the gravitationally observable vacuum energy compared with the contributions expected from quantum field theory. In units with $\hslash =c=1$, an ultraviolet cutoff ${\Lambda }_{\mathrm{UV}}$ generically gives contributions of order ${\Lambda }_{\mathrm{UV}}^4$, whereas the observed dark-energy density is of order $10^{-47}{\mathrm{GeV}}^4$. The Einstein equation depends on the sum of a bare cosmological constant and these contributions; subtracting a constant from a nongravitational Hamiltonian does not remove its gravitational effect. Exact global supersymmetry gives zero energy to a supersymmetric vacuum, but supersymmetry breaking generally reintroduces a much larger positive scale.