  Fanaroff-Riley type IIb (FR IIb) radio galaxies provide a modified standard
yardstick that allows constraints to be placed on global cosmological
parameters. A sample of 20 FR IIb radio galaxies with redshifts between 0 and 2
are compared with the parent population of 70 radio galaxies to determine the
coordinate distance to each source. The coordinate-distance determinations are
used to constrain the current mean mass-energy density of quintessence
$\Omega_q$, the equation of state of the quintessence w, and the current mean
mass-energy density of nonrelativistic matter $\Omega_m$; zero space curvature
is assumed. Radio galaxies alone indicate that the universe is currently
accelerating in its expansion (with 84% confidence); most of the allowed
parameter space falls within the accelerating universe region on the
$\Omega_m$-w plane. This provides verification of the acceleration of the
universe indicated by high-redshift supernovae and suggests that neither method
is plagued by systematic errors. It is found that $\Omega_m$ must be less than
about 0.5 and the equation of state w of the quintessence must lie between
-0.25 and -2.5 at about 90% confidence. Fits of the radio galaxy data constrain
the model parameter $\beta$, which describes a relation between the beam power
of the active galactic nucleus (AGN) and the total energy expelled through
large-scale jets. It is shown that the empirically determined model parameter
is consistent with models in which the outflow results from the electromagnetic
extraction of rotational energy from the central compact object. A specific
relation between the strength of the magnetic field near the AGN and the spin
angular momentum per unit mass of the central compact object is predicted.
