Quintessence (physics)

Quintessence models dark energy through an evolving scalar field. For a homogeneous canonical field in natural units,A positive potential dominating the kinetic term gives negative pressure. The Friedmann acceleration equation requires $w=p_{\varphi }/{\rho }_{\varphi }<-1/3$ for scalar-dominated accelerated expansion. A nonnegative canonical kinetic term prevents $w<-1$ when ${\rho }_{\varphi }>0$.

Unlike a strict cosmological constant, the field can evolve, so $w$ need not remain $-1$. This is a model class, not an identified substance.^[ref]

A homogeneous scalar with $V=m^2{\varphi }^2/2$ obeys $\ddot{\varphi }+3H\dot{\varphi }+m^2\varphi =0$. If it is to provide potential-dominated dark energy today rather than rapidly oscillating matter, $m\lesssim H_0\sim 10^{-33}\mathrm{eV}$ is required. Its present density gives ${\varphi }_0\simeq \sqrt{6{\Omega }_X}{M}_{\mathrm{Pl}}{H}_0/m$. Taking $m\sim H_0$ gives a Planck-scale field; a much smaller mass requires a larger field value, so density alone does not fix a unique mass.

// Target: cosmology.bigb

A flat universe dominated by a canonical homogeneous scalar field with constant equation-of-state parameter $w>-1$ has $\rho ={\rho }_0(a/a_0{)}^{-3(1+w)}$ and ${\dot{\varphi }}^2=(1+w)\rho$. The positive rolling branch gives the displayed relation and $V(\varphi )=(1-w){\rho }_0\exp [-\sqrt{24\pi G(1+w)}(\varphi -{\varphi }_0)]/2$. The opposite rolling branch reverses the exponential slope. For $w=-1$ the field is constant; $w<-1$ cannot be realized by a real scalar with this positive kinetic term. An exponential slope $\lambda \sqrt{8\pi G}$ yields $w={\lambda }^2/3-1$, with accelerating nonphantom expansion when $0<{\lambda }^2<2$.

For $w=-2/3$, zero cosmological constant, and negative curvature, $a(t)=\sqrt{\beta }t+\gamma t^2/4$ with density and curvature parameters $\gamma ,\beta >0$.

For $w=-2/3$, a quintessence-dominated scale factor grows quadratically and $tH$ approaches two.