Beta Phase: Square45 is currently in beta testing. Expect some features or content to be incomplete or missing.
45

Equation of State of Dark Energy

w = \frac{p}{e}\_\rho, relating the pressure (p) of dark energy to its energy density (\rho), determining its effect on the universe's expansion.
📜

The statement of the theorem

Define the equation of state parameter ww for dark energy as the ratio of its pressure pp to its energy density ρ\rho: \nw=pρw = \frac{p}{\rho} \nThis parameter governs the evolution of the energy density ρ\rho via the continuity equation:\nρ˙+3a˙a(+ρ+p)=0\dot{\rho} + 3\frac{\dot{a}}{a}(+\rho + p) = 0 \nFor a constant ww, the density evolves as ρ(a)=ρ0a−3(1+w)\rho(a) = \rho_0 a^{-3(1+w)}.