The dark energy that appears to produce the accelerating expansion of the universe can be characterized by an equation of state p = w \rho with w < -1 / 3 .
A number of observational tests have been proposed to study the value or redshift dependence of w , including SN Ia distances , the Sunyaev-Zel ’ dovich effect , cluster abundances , strong and weak gravitational lensing , galaxy and quasar clustering , galaxy ages , the Ly \alpha forest , and cosmic microwave background anisotropies .
The proposed observational tests based on these phenomena measure either the distance-redshift relation d ( z ) , the Hubble parameter H ( z ) , the age of the universe t ( z ) , the linear growth factor D _ { 1 } ( z ) , or some combination of these quantities .
We compute the evolution of these four observables , and of the combination H ( z ) d ( z ) that enters the Alcock-Paczyznski anisotropy test , in models with constant w , in quintessence models with some simple forms of the potential V ( \phi ) , and in toy models that allow more radical time variations of w .
Measurement of any of these quantities to precision of a few percent is generally sufficient to discriminate between w = -1 and w = -2 / 3 .
However , the time-dependence predicted in quintessence models is extremely difficult to discern because the quintessence component is dynamically unimportant at the redshifts where w departs substantially from its low- z value .
Even for the toy models that allow substantial changes in w at low redshift , there is always a constant- w model that produces very similar evolution of all of the observables simultaneously .
We conclude that measurement of the effective equation of state of the dark energy may be achieved by several independent routes in the next few years , but that detecting time-variation in this equation of state will prove very difficult except in specialized cases .