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there are several independent ways to determine the global cosmological parameters that describe the current state of the universe . it is important to have several complementary and independent methods that yield consistent results since any given method could be plagued by unknown systematic errors . a particularly useful way to determine global cosmological parameters is through measurements of the coordinate distance to high - redshift sources . this method is particularly useful because the coordinate distance depends only upon global cosmological parameters , and is independent of the clustering properties of the mass - energy components that control the expansion rate of the universe , as long as each component is homogeneous and isotropic on very large scales . the coordinate distance is also independent of whether different components cluster differently , known as biasing , and on whether the dark matter is cold , warm , or hot ( though it does depend on the equation of state of each component ) . two cosmological tools that are particularly sensitive to the coordinate distance as a function of redshift are friib radio galaxies , which provide a modified standard yardstick ( daly 1994 , 2002a ; guerra 1997 ; guerra & daly 1998 [ gd98 ] ; guerra , daly , & wan 2000 [ gdw00 ] ) , and type ia supernovae , which provide a modified standard candle ( e.g. riess et al . 1998 , perlmutter et al . . some aspects of the methods are compared in [ compare ] . the coordinate distance to a source at a given redshift depends on the present value of the mean mass - energy density of each component , and on the redshift evolution of the mass - energy density of each component . non - relativistic matter , including baryonic matter and clustered dark matter , have a mean mass - energy density that evolves as @xmath5 . there is a contribution from radiation and neutrinos left over from the big bang , currently negligible , which has an energy - density that evolves as @xmath6 . there may also be a cosmological constant , which constant energy density , and so evolves as @xmath7 . the redshift evolution of the mean mass - energy density of a component depends on the equation of state @xmath8 of the component . there could exist a dynamical vaccum energy density called quintessence ( caldwell , dave , & steinhardt 1998 ) . quintessence would have an equation of state @xmath1 such that the density evolves as @xmath9 , where @xmath10 ( see turner & white 1997 ; bludman & roos 2001 , wang et al . 2000 ; or the appendix of this paper ) . for example , pressure - less dust ( i.e. , non - relativistic matter ) is described by @xmath11 and @xmath12 ; a relativistic fluid is described by @xmath13 and @xmath14 , and a cosmological constant is described by @xmath15 and @xmath16 . two components of the universe are known to exist with certainty : there is a non - relativistic component ( including baryons and clustered dark matter ) , with zero - redshift , normalized mean mass - energy density @xmath2 , and a primordial relativistic component that is negligible for the epochs of interest here ( including microwave background photons and neutrinos ) . there must be at least one more component , which remains to be determined . this third component could be a cosmological constant , quintessence , space curvature , or something else . in the simplest case , there is only one additional component that is significant and has a measurable impact over the redshift interval where the coordinate distance is used to constrain cosmological parameters and the properties of the unknown component .    here , the determination of the coordinate distances to 20 radio galaxies with redshifts between zero and two are used to constrain the equation of state and current mean mass - energy density of quintessence assuming a spatially flat universe as indicated by measurements of the microwave background radiation ( de bernardis et al . 2000 , balbi et al . 2000 ) . the radio galaxy method is briefly reviewed in  [ radgals ] . constraints on cosmological parameters and the equation of state of quintessence obtained using friib radio galaxies as a modified standard yardstick are presented in  [ quint ] . the supernovae and radio galaxy methods and results are compared in detail in  [ compare ] . the relation between beam power and total energy for friib radio jets is discussed in  [ beta ] . here it is shown that the underlying hypotheses of the radio galaxy method is consistent with current models of large - scale jet production in agn . the results are summarized in  [ summary ] . the use of friib radio galaxies as a modified standard yardstic to determine global cosmological parameters has been presented in detail elsewhere ; see daly ( 1994 , 2002a ) , gd98 , and gdw00 . radio images of the 20 sources used here can be found in leahy , muxlow , & stephens ( 1989 ) , liu , pooley , & riley ( 1992 ) , and gdw00 . the radio galaxy method is based on the following premises . first , it is assumed that the forward region of the radio bridge of an friib source represents a strong shock front , and the equations of strong shock physics are applied at this boundary . second , it is assumed that there is a power - law relation between the average beam power of the source @xmath17 and the total lifetime of the outflow @xmath18 : @xmath19 ( see  [ beta ] ) . third , it is assumed that , at a given redshift , the sources studied will have an average source size similar to that of the parent population of friib sources at the same redshift , where the source size is defined as the separation between the radio hot spots . all of these points are discussed in detail in previous work ( e.g. daly 2002a , b ; gdw00 ) . in addition , in its simplest interpretation , the model works in a straight - forward way if the radio power of a given friib radio galaxy does not decrease monotonically and measurably with time . there is substantial evidence that this is the case for radio galaxies that fall into the friib category , as do all of the radio galaxies considered here ( daly 2002b ) . for example , neeser et al . ( 1995 ) find that there is no correlation between radio size and radio power . the low frequency radio surface brightness of these sources can be explained using adiabatic expansion alone if the radio powers of the sources are roughly time - independent ( wellman , daly , & wan 1997 ) . gopal - krishna , kulkarni , & wiita ( 1996 ) find that a roughly constant radio power followed by an exponential drop in radio power would explain the relative sizes of radio galaxies and radio loud quasars in the context of the orientation unified model . and , it is shown in  [ beta ] that the beam power is independent of core - hot spot separation , which would not be expected if the radio power of a given source decreases with time . thus , there is no empirical evidence that the radio power of a given friib radio galaxy decreases with time , and substantial evidence that it is roughly constant over the lifetime of a given source , followed by a precipitous drop . the mach numbers of friib radio galaxies are about 2.5 to 10 ( wellman , daly , & wan 1997 ) , implying overpressures of 10 to 200 , so the lobe will rapidly expand and drop in radio power when the beam power shuts off , as suggested by neeser et al . some authors ( e.g. , blundell , rawlings , & willcot 1999 ) have studied large heterogeneous samples that include sources with all types of radio structure and power and both radio loud quasars and radio galaxies . to explain the properties of this heterogenous sample , a model is proposed that allows for the decrease in the radio power of a given source as a function of time . there is , however , no evidence that this applies to the select subset of sources ( the most powerful frii radio galaxies ) studied here , and substantial evidence that the radio powers of friib radio galaxies do not monotonically decline over the lifetime of a given source . since friib radio galaxies form a remarkably homogenous population , and all the sources at a given redshift are quite similar , the average size of a given source @xmath20 will equal the average size of the full population @xmath21 of friib radio galaxies with similar redshifts . the dependence of @xmath20 and @xmath21 on the coordinate distance , and hence on cosmological parameters , is quite different , and @xmath22 since @xmath23 ( see gd98 eq . 6 ) . by construction , the ratio @xmath24 should be a constant , independent of redshift . because the model is based upon a comparison of individual source characteristics with the characteristics of the parent population at the same redshift , selection effects , such as radio power selection effects , are unlikely to affect the constraints placed on cosmological parameters . all of the sources for which values of @xmath20 are determined belong to the parent population . the sources for which @xmath20 is determined are subject to selection effects that are identical to those of the parent population , used to determine @xmath21 . thus , this method is one of the few methods that is unlikely to be affected by observational selection effects . equation ( 1 ) allows constraints to be placed on the model parameter @xmath4 , and the cosmological parameters that enter into the determination of the coordinate distance . recent measurements of the cosmic microwave background anisotropy suggest that the universe has zero space curvature ( de bernardis et al . 2000 , balbi et al . 2000 ) . here , a universe with zero space curvature ( @xmath25 ) and quintessence is considered . the coordinate distance to a source at redshift @xmath26 in a spatially flat universe is @xmath27 where @xmath28 . the coordinate distance is obtained by substituting this into eq . [ eqcoor1 ] and solving for @xmath29 ( see , for example , turner & white 1997 ; bludman & roos 2001 ; the appendix of this paper ) . the equation of state @xmath1 of quintessence is assumed to be time - independent over the redshift interval from zero to two ( wang et al . thus , the mean mass - energy density of quintessence will evolve as @xmath9 , where @xmath30 . for a present value of the normalized mass - energy density of quintessence @xmath0 , and that of non - relativistic matter @xmath2 , we have @xmath31 at @xmath32 , since space curvature is taken to be zero . this implicitly assumes that there is only one unidentified component , @xmath0 , that contributes significantly over the redshift interval where the coordinate distance will be determined . the minimization of the chi - squared of @xmath33 constant leads to constraints on @xmath2 , @xmath1,and the model parameter @xmath4 . the one and two - dimensional confidence intervals have been determined in the usual way ( see , for example , press , teukolsky , & flannery 1992 ) . figure 1 shows the 68% , 90% , and 95% one - dimensional confidence contours in the @xmath3 plane . at 90% confidence , @xmath2 is less than about 0.5 for any value of @xmath1 . a cosmological constant , represented by @xmath15 is clearly consistent with the radio data . this figure differs slightly from the two - dimensional confidence intervals presented in figure 2 of daly & guerra 2001 . at 68 % confidence , @xmath34 , and @xmath35 . at 90 % confidence , @xmath36 and @xmath37 . note , some models for the dark energy invoke mechanisms that behave like quintessence with w less than -1 ( e.g.frampton 2002 ) . the fifty - four supernovae identified by perlmutter et al . ( 1999 ) and used to obtain their `` primary fit '' c have been similarly fitted , and imply strong contraints on @xmath2 , though the supernovae do not place a lower bound on w , as shown in figure 2 . as described by turner & white ( 1997 ) and presented in some detail in the appendix , the expansion rate of the universe is accelerating at the present epoch if @xmath38 this line is drawn on the @xmath3 plane ( see figures 1 and 2 ) ; points below the line represent solutions for which the universe is currently accelerating , while those above the line represent solutions for which the universe is currently decelerating . radio galaxies alone ( fig 1 ) indicate that the expansion of the universe is accelerating ( @xmath39 ) ; this is an 84% confidence result . it is very important to consider whether significant covariance exists between the different parameters determined by the fit . figure 3 shows the 68% , 95% , and 99% one - dimensional confidence contours in the @xmath40 plane . clearly , there is no covariance between the equation of state @xmath1 of quintessence and the model parameter @xmath4 : @xmath1 and @xmath4 are independent . figure 4 shows the 68% , 95% , and 99% one - dimensional confidence contours in the @xmath41 plane . clearly the two parameters are independent . the data suggest that @xmath42 independent of the cosmological parameters @xmath2 , @xmath0 , or the equation of state @xmath1 of quintessence . the observation of the acceleration of the universe through measurements of the coordinate distance to high redshift sources is so important that it needs to be independently verified using different methods . in 4 , it was shown that the radio galaxy method alone indicates at about 84% confidence that the universe is accelerating in its expansion at the present epoch if the universe has zero space curvature . the supernovae teams report similar results at stronger confidence levels ( riess et al . 1998 , perlmutter et al . 1999 ) , as illustrated in figure 2 . it is important to consider the similarities and differences between the methods to insure that the results of each are independent , and to compare the quantities that are actually determined in each method . the two methods are compared in table 1 . the two methods are similar is their dependence on the coordinate distance , and in the sense that both provide a modified standard rather than an absolute standard . they are somewhat similar in their redshift interval of coverage , and in the number of sources studied . the radio galaxy and supernova methods differ in the way the `` modification '' relation is derived ; one is empirical and one is based on physical arguments . they also differ in that the radio galaxy method is not normalized at zero redshift , and is independent of the properties of local sources and of the local distance scale ; in fact , nearly identical results obtain when the low redshift bin is excluded from the analysis ( gdw00 ) . the supernova relation is derived at low redshift . thus , the radio galaxy method provides independent verification of the supernova results . current constraints on cosmological parameters determined using the radio galaxy method are consistent with those obtained using the supernova method . clearly , any selection effects , or unknown systematic errors , must be completely different for these two methods . the supernova method involves short - lived optical events , and the radio galaxy method involves much more long - lived radio agn events . the methods are derived in vastly different ways , and are normalized differently . however , similar constraints obtain , suggesting each method is reliable . it is interesting to compare the constraints placed on cosmological parameters assuming that three main terms control the expansion of the universe at the present epoch : non - relativistic matter with contribution @xmath2 , a cosmological constant with contribution @xmath43 , and space curvature . figures 5 and 6 show constraints placed by the microwave background radiation ( bond et al . 2000 ) , and the high - redshift supernovae project ( riess et al . 1998 ) ; the results obtained by the supernovae cosmology project ( perlmutter et al . 1999 ) are similar and are presented by daly & guerra ( 2001 ) . each method carves out a different part of parameter space because each method covers a different redshift range with the supernovae being at the lowest redshift , the radio galaxies at higher redshift , and the microwave background radiation at still higher redshift . the three methods are thus complementary in their redshift coverage . the radio galaxy and supernovae methods are independent of the initial power spectrum of density fluctuations , and hence are independent of the index of the primordial fluctuation spectrum . these methods are also independent of the hubble constant , and of the baryon fraction . the radio galaxy and supernovae methods depend only on the global cosmological parameters @xmath2 and @xmath43 allowing for space curvature , or @xmath2 and @xmath1 allowing for quintessence , where @xmath44 , and assuming zero space curvature . they are therefore particularly important to study since most other methods depend on several other parameters such as the initial spectrum of fluctuations , the hubble constant , and/or the baryon fraction . the application of the radio galaxy cosmology method indicates that @xmath42 irrespective of cosmological model , as discussed here for quintessence , by gdw00 in cosmologies that include space curvature , and summarized by daly ( 2002a ) . the total energy released over the lifetime of the friib in the form of a highly collimated outflow is @xmath45 assuming that @xmath17 is roughly constant over the lifetime of a given source , which is supported by lack of correlation between @xmath17 and the hotspot to core distances in these sources ( see wan , daly , & guerra 2000 ; guerra & daly 2001 ) . values of @xmath17 and @xmath18 are obtained independently , using different aspects of the radio data for a given source . two values are determined for each source , one on each side of each source . an indicator of possible problems with the model assumptions or selection biases is whether the beam powers , total source lifetimes , or total energies depend strongly on the distance of the radio hot spot from the location of the agn . each of these quantities is plotted as a function of hot spot distance from the agn in figures 7 , 8 , and 9 . there are 40 data points on each figure , two for each of the 20 radio galaxies studied here . it is interesting to note that the total energy processed through large - scale jets has a rather small range , from @xmath46 to @xmath47 , though it does increase systematically with redshift , as shown in figure 10 .    because @xmath19 and @xmath45 , the relation between beam power and energy released by an friib is @xmath48 , where @xmath49 to 3 for @xmath50 to 2.0 . in terms of the total lifetime of the source , @xmath51 for values of @xmath4 of 1.5 , 1.75 , and 2.0 respectively . clearly , @xmath4 remains far from the limiting cases of @xmath4 = 0 or 3 . blandford ( 1990 ) gives a summary of the energy and beam power of outflows associated with the electromagnetic extraction of the spin energy of a rotating black hole . the beam power and total energy available are @xmath52 and @xmath53 for @xmath54 , where @xmath55 is the mass of the black hole , @xmath56 is the mass in units of @xmath57 , @xmath58 is the spin angular momentum @xmath59 per unit mass @xmath55 : @xmath60 , c is the speed of light , @xmath61 is the gravitational radius @xmath62 , @xmath63 is the magnetic field strength , and @xmath64 is the magnetic field strength in units of @xmath65 g ( blandford 1990 ) . empirically , @xmath66 with @xmath67 . this is consistent with equations ( 4 ) and ( 5 ) when the magnetic field strength satisfies @xmath68 this is particularly simple when @xmath50 ; in this case @xmath69 . for the cases @xmath70 and 2 , the empirical constraint is consistent with equations ( 4 ) and ( 5 ) when @xmath71 and @xmath72 respectively . typical values for the beam power , total energy processed by a jet , and lifetime are @xmath73 , @xmath74 , and @xmath75 yr ( see figures 7 , 8 , and 9 ) . equations [ ljeq ] and [ estareq ] imply a total source lifetime of @xmath76 , indicating a lifetime of about @xmath77 yr for @xmath78 . this is satisfied for @xmath79 , and @xmath80 . in this case , the beam power is @xmath81 for @xmath82 , and the total energy is @xmath83 . these values for @xmath56 , @xmath64 , and @xmath84 seem quite reasonable . the scaling between variables required by the empirically determine relation between total energy and beam power are discussed above . type iib radio galaxies and type ia supernovae are particularly important methods to develop to constrain the global cosmological parameters @xmath2 , @xmath43 , and space curvature , or @xmath2 , @xmath0 , and the equation of state of quintessence @xmath1 . these methods depend only upon the properties of global cosmological parameters , and are independent of other factors such as the index of the primordial power spectrum , the hubble constant , the baryon fraction , the properties of the dark matter that clusters around galaxies and clusters of galaxies , any biasing of dark relative to luminous matter , etc . the radio galaxy and supernova methods are completely independent and have completely different potential systematic errors , as discussed in [ compare ] . radio galaxies may be used to constrain the mass - energy density and equation of state of quintessence . these results are presented here assuming a spatially flat universe , which is supported by recent measurements of fluctuations of the cosmic microwave background . radio galaxies alone suggest that the universe is accelerating in its expansion at present ( see s [ quint ] ) , consistent with results obtained by the supernovae teams , indicating that both methods are working well and probably are not plagued by unknown systematic errors . the implications for models of energy extraction for the cases of an outflow related to accretion and the eddington luminosity , and electromagnetic energy extraction of rotational energy are considered . if the outflow is produced by the electromagnetic extraction of energy from a rotating black hole , then the magnetic field strength must be related to the spin angular momentum of the rotating black hole @xmath59 , the mass of the black hole @xmath55 , and the gravitational radius of the black hole @xmath61 , as described in  5 . the relation is particularly simple if @xmath85 , and implies that the magnetic field strength satisfies @xmath69 , where @xmath86 . we are grateful to lin wan and greg wellman who have contributed significantly our studies of radio galaxies . we also thank megan donahue , paddy leahy , chris odea , adam riess , max tegmark , and an anonymous referee for helpful comments . this work was supported in part by a national young investigator award ast-0096077 from the national science foundation , and by penn state university . research at rowan university was supported in part by the college of liberal arts and sciences and national science foundation grant ast-9905652 . balbi , a. et al . 2000 , apj , 545 , l1    begelman , m. c. , blandford , r. d. , & rees , m. j. 1984 , rev . phys . , 56 , 255    blandford , r. d. 1990 , in active galactic nuclei , ed . t. j. l. courvoisier & m. mayor , springer - verlag , 161    bludman , s. , & roos , m. 2001 , apj , 547 , 77    blundell , k. m. , rawlings , s. , & willott , c. j. 1999 , aj , 117 , 677    bond et al . 2000 , preprint ( astro - ph/0011378 )    caldwell , r. r. , dave , r. , & steinhardt , p. j. 1998 , phys . , 80 , 1582    daly , r. a. 1994 , apj , 426 , 38    daly , r. a. 2002a , to appear in `` the dark universe : matter , energy , and gravity , '' in press ( available at www.bk.psu.edu/faculty/daly )    daly , r. a. 2002b , to appear in `` lifecycles of radio galaxies , '' in press ( available at www.bk.psu.edu/faculty/daly )    daly , r. a. , & guerra , e. j. 2001 , in iau symposium no . 201 : new cosmological data and the values of the fundamental parameters , ed . a. lasenby , a. w. jones , & a. wilkinson ( san francisco : asp conference series ) , in press    de bernardis , p. et al . 2000 , nature , 404 , 995    fanaroff , b. l. , & riley , j. m. 1974 , mnras , 167 , 31p    frampton , p. h. 2002 , in the coral gables conference proceeding    gopal - krishna , kulkarni , v. k. , & wiita , p. j. 1996 , apj , 463 , l1    guerra , e. j. 1997 , phd thesis , princeton university    guerra , e. j. , & daly , r. a. 1998 , apj , 493 , 536 ( gd98 )    guerra , e. j. & daly , r. a. 2001 , in particles and fields in radio galaxies , ed . r. laing & k. blundell , ( san francisco : asp conference series ) , in press . guerra , e. j. , daly , r. a. , & wan , l. 2000 , apj , 544 , 659 ( gdw00 )    leahy , j. p. , muxlow , t. w. , & stephens , p. w. 1989 , mnras , 239 , 401    liu , r. , poole , g. , & riley , j. m. 1992 , mnras , 257 , 545    neeser , m. j. , eales , s. a. , law - green , j. d. , leahy , j. p. , & rawlings , s. 1995 , apj , 451 , 76    perlmutter et al .  1999 , apj , 517 , 565    press , w. h. , teukolsky , s. a. , & flannery , b. p 1992 , numerical recipes in c , cambridge university press    riess et al . 1998 , aj , 116 , 1009    turner & white 1997 , phys . d , 56 , 4439    wan , l. , daly , r. a. , & guerra , e. j. 2000 , apj , 544 , 671    wang , l. , caldwell , r. r. , ostriker , j. p. , & steinhardt , p. j. 2000 , apj , 530 , 17    wellman , g. f. , daly , r. a. , & wan , l. 1997 , apj , 480 , 79    crrrrrrrrrrr type snia & type friib + @xmath87 & @xmath88 + @xmath89 & @xmath90 + @xmath91 sources&20 sources ( 70 in parent pop . ) + modified standard candle & modified standard yardstick + light curve @xmath92 peak luminosity&radio bridge @xmath92 average length + empirical relation & physical relation + written in terms of observables&written in terms of physical variables + model parameter determined at @xmath32 & model parameter not determined at @xmath32 + may depend on local distance scale & independent of local distance scale + universe is accelerating & @xmath2 is low + & universe is acclelerating if k=0 + some theoretical understanding & good theoretical understanding + well tested empirically&needs more empirical testing + the deceleration parameter is defined to be @xmath93 evaluated at z=0 , where @xmath58 is the cosmic scale factor . this may also be written @xmath94 , where quantities evaluated at z=0 have a subscript o , and @xmath95 . it is straight - forward to show that ( e.g. peebles [ 1993 ] eq . 5.15 ) @xmath96 where @xmath97 is the pressure , @xmath98 is the mean mass - energy density , @xmath99 is the equation of state of @xmath100 component , @xmath101 , and the quintessence or cosmological constant term is included in the summation .    for each component , mass - energy conservation implies @xmath102 ( e.g. peebles [ 1993 ] eqs . 5.16 ) . by definition , the equation of state is @xmath103 , so the eq . [ conseq ] implies @xmath104 when the equation of state @xmath99 is time independent , the solution to this equation is @xmath105 , where @xmath106 . thus , a component with equation of state @xmath99 and present mean mass - energy density @xmath107 will have a mean mass - energy density at redshift @xmath26 of @xmath108 , where @xmath109 .    when @xmath25 , @xmath110 where @xmath111 . it follows that @xmath112 . for @xmath25 , @xmath113 where @xmath114 is the critical density at redshift zero . thus , @xmath115 for @xmath25 . the deceleration parameter @xmath116 then becomes @xmath117 where @xmath118 and equations [ acceq ] and [ hnot ] have been used . the universe is accelerating rather than decelerating when @xmath119 . this can only occur if @xmath120 , or @xmath121 , which is a necessary but not sufficient condition to have an accelerating universe at the present epoch . if there are only two significant types of mass - energy controlling the expansion rate of the universe at the present epoch , quintessence and non - relativistic matter , then the deceleration parameter is @xmath122 . the universe will be accelerating in its expansion when @xmath123 which follows since @xmath124 . thus , a curve can be drawn on the @xmath3 plane ; points below the curve represent solutions for which the universe is currently accelerating , while those above the curve represent solutions for which the universe is currently decelerating ( e.g. see figure 1 ) . for example , this curve is shown on figure 1 , which illustrates the constraints obtained using radio galaxies alone , and is discussed in more detail below . note that radio galaxies alone place interesting constraints on @xmath2 and @xmath1 , and these results are consistent with those obtained using other methods ( e.g wang et al . 2000 ) . the coordinate distance to a source at redshift @xmath26 follows from the equation @xmath125 ( weinberg 1972 ) . for a spatially flat universe , the left hand side of the equation reduces to the coordinate distance @xmath126 . equations [ eqadot ] and [ hnot ] imply that @xmath127 or @xmath128 following the notation of peebles ( 1993 ) , this reads @xmath129 , where @xmath130 thus , the coordinate distance to a source at redshift @xmath26 in a spatially flat universe is ( see equation [ eqcoor ] ) @xmath27    a spatially flat universe has @xmath131 . the components that must be included in equation [ eqeofz ] are those that contribute from redshift zero out to the redshift that the coordinate distance is being determined . two components are considered here : non - relativistic matter with normalized mean mass - energy density at @xmath32 of @xmath2 , and quintessence with normalized mean mass - energy density at @xmath32 of @xmath0 . thus , @xmath132 , and equation [ eqeofz ] becomes @xmath28 . the coordinate distance is obtained by substituting this into eq . [ eqcoor1 ] and solving for @xmath29 .
friib radio galaxies provide a modified standard yardstick that allows constraints to be placed on global cosmological parameters . 
 this modified standard yardstick is analogous to the modified standard candle provided by type ia supernovae . 
 the radio galaxy and supernova methods provide a measure of the coordinate distance to high - redshift sources , and the coordinate distance is a function of global cosmological parameters . 
 a sample of 20 friib radio galaxies with redshifts between zero and two 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 @xmath0 , the equation of state of the quintessence @xmath1 , and the current mean mass - energy density of non - relativistic matter @xmath2 ; zero space curvature is assumed . 
 radio galaxies alone indicate that the 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 @xmath3 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 @xmath2 must be less than about 0.5 and the equation of state @xmath1 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 @xmath4 , which describes a relation between the beam power of the 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 .