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there is now a substantial amount of observational evidence that the universe is dominated by a dark component which is causing its expansion rate to accelerate . the analysis of the cosmic microwave background ( cmb ) anisotropy power spectra @xcite combined with results from large scale structure ( lss ) surveys @xcite strongly suggest that about @xmath4 of the energy in the universe is in an exotic form of matter which we refer to as dark energy ( de ) . measurements of the luminosity distance to supernova type ia ( snia ) independently confirm these conclusions by showing that high redshift supernovae are dimmer than in a matter dominated universe @xcite .    further evidence , which has recently become available , is the detection of the integrated sachs - wolfe ( isw ) effect using the cmb / lss cross - correlation @xcite . this evidence is complementary in nature to the snia data . rather than probing the overall expansion of the universe , it detects the slow down in the growth of density perturbations that occurs when the universe ceases to be matter dominated . cmb photons traveling to us from the surface of last scattering blueshift and redshift as they fall into and climb out of gravitational potentials along their paths . during matter domination , the large scale potentials remain constant in time , hence the blueshift and the redshift exactly cancel each other out . however , any deviation from a constant total equation of state results in a time variation of the potentials and a net change in the photon energy . this is observed as an additional cmb temperature anisotropy , which is the isw effect @xcite . detecting the isw effect from measurements of cmb temperature anisotropy alone is not feasible because the signal is hard to separate from the primordial anisotropy from the last scattering surface . to circumvent this , it was proposed to correlate the cmb temperature maps with the local distribution of matter @xcite . the cross - correlation arises from cmb anisotropies produced after the cosmic structures were formed . on large angular scales the cross - correlation signal is dominated by the isw effect , while at small angles an additional contribution comes from the sunyaev - zeldovich effect @xcite . the cosmological constant @xmath5 is the simplest model of dark energy that provides a satisfactory fit to the existing data . despite the success of the concordance @xmath5 cold dark matter scenario ( @xmath5cdm ) , it is difficult to explain why the cosmological constant value is so extremely small compared to the expectations of particle physics without involving anthropic selection @xcite . on the other hand , the observations are also consistent with an evolving dark energy , such as quintessence models where the dark energy originates from a scalar field @xcite . establishing whether the dark energy is constant or evolving is one of the main challenges for modern cosmology . in the friedmann - robertson - walker ( frw ) universe the evolution of dark energy is completely determined by its equation of state , which is defined as the ratio of pressure to energy density : @xmath6 . for scalar field quintessence , the sound speed is unity and @xmath1 determines the clustering properties of de . depending on the model @xmath1 can be constant or change with time . models with @xmath7 correspond to evolving de , while @xmath8 corresponds to @xmath5 .    the time dependence of the dark energy equation has been constrained by fitting various forms of @xmath0 to the snia data , often in combination with cmb and the lss measurements @xcite . however the data are not accurate enough to distinguish between the cosmological constant and many forms of dynamical dark energy . moreover degeneracies between dark energy parameters strongly limit the possibility to test whether @xmath1 is constant or not . as we shall describe in this paper , the cmb / lss correlation can provide another probe of the evolution of @xmath0 . the sensitivity of the cross - correlation to the dark energy evolution has previously been investigated in @xcite . in this paper we study constraints expected from correlating surveys such as des and lsst with the cmb data . we introduce a novel way of parameterizing @xmath0 that has the average @xmath2 ( eq . ( [ def : aver ] ) ) as an explicit parameter . this helps to separate information contained in the estimate of the distance to last scattering from that in the isw contribution . we then proceed to show that the cross - correlation , in the absence of errors , is more sensitive to the details of the high redshift evolution of @xmath0 than other available observables . this sensitivity , however , is off - set by large statistical errors due to a large primordial contribution to the cmb signal . we forecast the expected uncertainties in de parameters ( using two different models ) extracted from cmb / lss correlation that will be possible in the next five years ( wmap / des ) and in the next ten years ( planck / lsst ) . we also calculate corresponding constraints from the sne data ( snls in short term and snap in long term ) . we find that in long term , cross - correlation can provide competitive constraints on the evolution of @xmath0 . the paper is organized as follows . in section [ theory ] we discuss the dark energy modeling and the details of the calculations . section [ sec : exp ] describes the observations considered in the paper . in section [ results ] we discuss some advantages of including the cross correlation information and give the resulting parameter constraints . finally in section [ conc ] we present our conclusions . many models of dark energy have been proposed : cosmological constant ( @xmath5 ) , quintessence , k - essence , tangled defects , etc . for simplicity , we will focus on quintessence based models where the dark energy arises from a scalar field currently slow - rolling down a potential , which is effectively inflation occurring at late times . perturbations in the dark energy are easily incorporated in such models , and the sound speed is typically of order the speed of light .    the shape of the potential , which determines the evolution of the dark energy , is generally a free function . this makes it difficult to predict the time dependence of the de equation of state , so one is potentially left with constraining a completely arbitrary function of redshift . the problem must be simplified by considering some parameterization of the function @xmath0 . several parameterizations have been suggested in a vast literature , but any resulting constraints are very sensitive to the choice of parameterization . for instance it was shown in @xcite that fitting a constant @xmath1 will tend to favor lower negative values if the de equation of state is time dependent . even two - parameter taylor expansions are too simplistic , resulting in a strong dependence on the assumed priors and generally biased against dynamical models @xcite . one of the most popular two - parameter formulae is the linear change in the scale factor @xmath9 @xcite given by , w(a)=w_0+(a-1)_w  , [ lin ] [ w : linder ]    where @xmath10 and @xmath11 being the value at some early time , such as the radiation - matter equality . from eq . ( [ lin ] ) it appears evident that with two parameters one can fix the value of the equation of state today and at high redshift , but the time evolution between the two extremes can not be changed ( i.e. @xmath12 ) . as consequence of this , a linear expansion can not allow for rapid variation in the equation of state and particularly in the case of quintessence , for which @xmath13 , this bias will tend to favor small values of @xmath14 . despite these potential problems , eq . ( [ lin ] ) has become a common tool of testing the capability of future experiments to constrain de models ( see @xcite ) . due to its wide use in the literature , we will consider this parameterization here to help the comparison of our results with previous works . we shall refer to it as model  i.    in order to avoid the pitfalls introduced by the taylor expansion we also consider a phenomenological approach and model @xmath0 according to some minimal requirements , which are : 1 ) the form of @xmath0 depends on a minimal number of parameters which are of simple physical interpretation , 2 ) the parameterization is not biased against any particular time behavior and can account for both rapid ( large ) or slow ( small ) variation of the equation of state , 3 ) the parameterization reproduces the evolution of several proposed models of de such as quintessence . in this regard , a general formula constructed to follow these guidelines was proposed in @xcite and is usually referred to as the `` kink '' model @xcite .    within the class of the kink models we consider a unique new parameterization . we start with the functional form w(z)= +  tanh  , [ def : tanh ] which describes a transition from @xmath15 for @xmath16 , to @xmath17 for @xmath18 , with parameters @xmath19 and @xmath20 describing the width and the central redshift of the transition . the novelty is in using the average equation of state ( @xmath2 ) as an explicit parameter , where @xmath21 is defined as [ def : aver ]  . here @xmath22 is the scale factor ( @xmath23 today ) , @xmath24 is the scale factor at the surface of last scattering and @xmath25 is the ratio of the de energy density to the critical density . it is well known @xcite that on small scales the cmb temperature anisotropy spectra are insensitive to the details of @xmath0 except for its average value as defined in eq . ( [ def : aver ] ) . specifying @xmath2 roughly fixes the distance to the last scattering surface @xcite , which determines positions of the acoustic peaks in the cmb temperature anisotropy spectrum . the cmb temperature data , combined with a prior knowledge of @xmath26 and under the assumption that the universe is flat , is capable of constraining the value of @xmath2 with a very high accuracy . by explicitly specifying @xmath2 we preserve the information that would be obtained from fitting a constant @xmath1 to the cmb , while still allowing for a varying @xmath0 . hence , a direct control on the value @xmath2 allows us to reduce the four dimensional parameter space to a much smaller observationally allowed region , which corresponds to a narrow range of possible values of @xmath2 . note that for @xmath2 close to @xmath27 , as favored by the data , most choices of @xmath28 would lead to @xmath0 changing between @xmath27 and @xmath29 , where @xmath30 . also note that in a large class of quintessence models either @xmath15 or @xmath17 is @xmath27 . this is the case when the scalar field is initially in a slow - roll regime ( @xmath31 ) as in , , the doomsday model @xcite . similarly for tracker models , where the quintessence field starts tracking the background component and evolves at late time settling to a minimum of its potential ( i.  e. @xmath32 ) @xcite . hence , fixing the value of either @xmath17 or @xmath15 to @xmath27 is physically and observationally motivated and allows us to reduce the number of parameters in eq . ( [ def : tanh ] ) from four to three . thus , instead of using the four parameters of eq . ( [ def : tanh ] ) , @xmath15 , @xmath17 , @xmath20 and @xmath19 , we use three parameters : @xmath2 , @xmath28 and @xmath19 . here , @xmath20 is chosen to reproduce the desired value of @xmath2 . ( alternatively , we could explicitly specify @xmath20 and use eq . ( [ def : aver ] ) to find the corresponding value of @xmath19 . ) since we are primarily interested in determining whether @xmath0 is varying or constant , @xmath28 is the main parameter of interest . the role of the third parameter , @xmath20 or @xmath19 , is only to allow for sufficient freedom in the ansatz . in this paper , we will stay with the choice of @xmath2 , @xmath28 and @xmath19 and refer to this parameterization as our model  ii . representative plots of @xmath0 versus @xmath3 for model  i and model  ii are shown in fig . [ fig : eos ] .      the cmb temperature anisotropy due to the isw effect can be written as @xmath33 - \dot{\psi}\left[(\eta_0-\eta ) \hat{\bf n},\eta \right ] \right ) , \label{def : dt_isw}\ ] ] where @xmath34 is a direction on the sky , @xmath35 is the conformal time , @xmath36 is some initial time far into the matter era , @xmath37 is the time today , @xmath38 and @xmath39 are the gravitational potentials in the newtonian gauge , and the dot denotes differentiation with respect to @xmath35 .    the isw temperature anisotropy can be correlated with the distribution of galaxies on the sky using , @xmath40 where @xmath41 is the overdensity of galaxies in the direction @xmath34 , @xmath42 is the number of galaxies in the pixel corresponding to the direction @xmath34 , and @xmath43 is the mean number of galaxies per pixel . we assume here that we sample galaxies in a fixed redshift region , characterized by a normalized galaxy selection function , @xmath44 . for simplicity , we initially consider a single selection function , but below we consider correlations arising between different redshift bins as well . the galaxy number overdensity @xmath41 is assumed to be tracing the cold dark matter ( cdm ) density contrast @xmath45 via @xmath46 where @xmath47 is the linear galaxy bias , which is possibly redshift dependent . the cdm density contrast can be written as an integral over conformal time , @xmath48 where @xmath49 is the three - dimensional density contrast and is directly related to the gravitational potentials . we are interested in calculating the cross - correlation function @xmath50 where the angular brackets denote ensemble averaging and @xmath51 is the angle between directions @xmath52 and @xmath53 . calculations are often simplified when @xmath54 is decomposed into a legendre series , @xmath55 the coefficients @xmath56 can be evaluated using @xcite : @xmath57 where @xmath58 is the wave - number , @xmath59 is the primordial curvature power spectrum , and functions @xmath60 and @xmath61 are defined as @xmath62 ) \nonumber \\   & \times & ( c_{\phi \psi } \dot{\phi}(k,\eta ) - \dot{\psi}(k,\eta))\label{tisw }   \nonumber \\ m_\ell(k ) & = & b_g c_{\delta \psi } \int_{\eta_k}^{\eta_0 } d\eta \ j_\ell(k[\eta-\eta_0])\nonumber \\   & \times & \dot{z } w_g(z(\eta ) ) \delta ( k,\eta ) \label{mlk}\ . \label{delta_isw}\end{aligned}\ ] ] in the above , the integration starts at an early time @xmath63 , when a given mode @xmath58 is well - outside the horizon , @xmath64 are the spherical bessel functions , @xmath65 , @xmath66 and @xmath67 are the evolution functions defined in @xcite along with the numerical coefficients @xmath68 and @xmath69 : @xmath70 where @xmath71 and @xmath72 and @xmath73 are the photon and relativistic neutrino densities .    above we have considered the correlations between the cmb and a sample of galaxies defined by a single galaxy selection function . future surveys will enable us to separate galaxies into many redshift slices with photometric redshift slices ( bins ) , and we can consider separate correlations with each of the slices , @xmath74 . we calculate these as above using the different selection functions , @xmath75 , each of which has a corresponding weighting function @xmath76 . for each bin , we consider a different possible bias factor @xmath77 , but as we discuss in section [ sec : bias ] , these can be determined sufficiently well by the observations of the galaxy - galaxy correlation functions . the galaxy - galaxy correlations are evaluated in a similar way . we have many correlation functions @xmath78 , corresponding to correlations between all possible redshift bins labeled by indices @xmath79 . similarly to eq . ( [ eval : x_l ] ) , the legendre coefficients of these correlations are given by @xmath80    the full cmb auto - correlation @xmath81 contains the primary anisotropy from the last scattering surface as well as contributions from the isw , the sz and other effects : @xmath82 the uncorrelated anisotropies from the last scattering surface dominate the noise in the cross correlation detection . the isw contribution dominates the galaxy - cmb cross - correlation on large scales ( where the signal is strongest ) , while the sz effect is anti - correlated at wmap frequencies and affects only the small angular scales @xcite . in principle the sz signal can be eliminated by smoothing the cmb maps on scales smaller than the typical angular size of a cluster (  @xmath83 ) , therefore we will not include the sz in our analysis . we evaluate the cmb / lss correlation coefficients @xmath84 , as well as all other relevant spectra , using an appropriately modified version of cmbfast @xcite . for all models , we assume a flat universe with adiabatic initial conditions for all particle species , including the quintessence . we use the usual fisher method @xcite for parameter estimation forecasts to study the potential of the cmb / lss cross - correlation for dark energy constraints . we assume that the universe has evolved from adiabatic initial conditions with a nearly scale - invariant spectrum of density fluctuation , negligible tensor component and no massive neutrinos . it is also assumed to be flat with a quintessence field parameterized by @xmath0 . in addition to the dark energy parameters @xmath85,@xmath14 ] of model  i or [ @xmath2,@xmath28,@xmath19 ] of model  ii , our parameter space @xmath88 includes the matter fraction of total energy density @xmath89 , the hubble parameter @xmath90 , the baryon density @xmath91 , the reionization optical depth @xmath92 , the scalar spectral index @xmath93 and the amplitude of the initial power spectrum @xmath94 . in total , we have @xmath95 parameters for model  i and @xmath96 parameters for model  ii . in addition , for the sne analysis , we account for @xmath97  the intrinsic supernova magnitude . cross - correlation parameters also include the bias factors for each photometric bin , as described in section [ sec : bias ] . the cross - correlation fisher matrix can be written as f^x_,=f_sky _ = _ min^_x _ i , j x^i_p _ cov^-1 ( x_^i x_^j ) x^j_p_. [ fisher : x ] here @xmath98 , as well as the partial derivatives , are evaluated at the fiducial values ( see sec .  [ sec : fid ] ) . the sky fraction , @xmath99 , is the smallest of the cmb and the galaxy survey sky coverage fractions . we used @xmath100 as the summation limit , although most of the contribution comes from @xmath101 . the smallest value of @xmath102 can be approximately determined from @xmath103 . the covariance matrix @xmath104 is given by ( x_^i x_^j ) = ( ^tt_^(i , j ) _ + x^i_x^j_)/(2 + 1 )  , [ cov : x ] where @xmath105 and @xmath106 are defined in eqns . ( [ cmb : noise ] ) and ( [ galaxy : noise ] ) and include the contributions from the noise . note that the contribution to the @xmath81 from the surface of last scattering is much larger than that from the isw effect , while @xmath107 is not sensitive to the last scattering physics at all . this results in a very large variance in @xmath107 that significantly impairs its potential for parameter estimation . for cmb measurements , the fisher information matrix is given by f^_,=f_sky_=2^ _ _ a , b ^a_p _ ^-1(^a_^b _ ) ^b_p _ , [ fisher : cmb ] with the covariance matrices for @xmath108 given explicitly in @xcite . in the above , @xmath109 was taken to be @xmath110 for wmap and @xmath111 for planck , safely above the maximum @xmath102 allowed by the angular resolution of each experiment . the partial derivatives and the covariance matrix are evaluated at a fiducial choice of parameters that is specified in the next subsection . the quantity directly measured from sne observations is their redshift - dependent magnitude m(z ) = m + 5 + 25 [ def : mz ] where @xmath97 is the intrinsic supernova magnitude and @xmath112 the luminosity distance ( in mpc ) . the luminosity distance is defined as [ lumdis ] d_l(z)=(1+z ) _ 0^z dz h(z )  , where @xmath113 is the hubble parameter with a current value of @xmath26 . the information matrix for sne observations is f^_,= _ i^n 1(z_i)^2 m(z_i)p _ m(z_i)p_. [ fisher : sne ] where the summation is over the redshift bins and @xmath114 is the value given by eq . ( [ sigma_m ] ) at the midpoint of the @xmath115-th bin . given the fisher matrix , the lower bound on the uncertainty in determination of a parameter @xmath116 is given by p_i c_ii = ( f^-1)_ii  , where @xmath117 is the error matrix . one can forecast constraints from a combination of measurements by adding the individual fisher matrices . for example , cross - correlation measurements can be combined with measurements of the cmb spectra by planck as f^planck+x_,=f^planck_,+ f^x _ ,  . forecasts obtained using fisher analysis are sensitive to the choice of the fiducial model . we will consider the same fiducial models for the two dark energy parameterizations discussed above and plotted in fig . [ fig : eos ] . the fiducial parameters for model  i were taken to be @xmath118 and @xmath119 . for model  ii we chose @xmath120 , @xmath121 and @xmath122 . we take all other cosmological parameters to be the same for both models . we have set the hubble parameter @xmath123 , baryon density @xmath124 , total matter density @xmath125 , spectral index @xmath126 , optical depth @xmath127 and the amplitude of scalar fluctuations @xmath128 ( as defined in @xcite . ) all of current data is consistent with @xmath129 at @xmath130 level @xcite . both , model  i and model  ii , have the same weighted average @xmath131 . this assures that these two models have nearly identical cmb spectra as shown in fig . [ fig : cmb ] .    in fig . [ fig : pk ] we compare the matter power spectra predicted by the two models . plotted are the linear cdm spectra at @xmath132 . the bias , non - linear effects and the redshift space distortion would modify the three spectra in a similar way . while one can not compare these linear spectra to the data without accounting for the above - mentioned corrections , we include the sdss data points @xcite to illustrate the uncertainty in the current determination of @xmath133 . models i and ii are also consistent with current estimates of the change in luminosity distance @xmath134 obtained from the snia measurements . in fig . [ fig : lumin ] we plot the percent difference in @xmath135 between the model with constant @xmath136 and models i and model  ii . the differences between the models are of order @xmath137% , well below the current level uncertainty and comparable to the projected accuracy of snap . hence , present data can not distinguish between @xmath129 and our models i and ii and both are perfectly consistent with all available observations . we are interested in forecasting the errors in dark energy parameters that can be extracted from cmb / lss correlation studies and compare them to those expected from the luminosity distance measurements . we make short- ( less than 5 years ) and long- ( ten years ) term predictions based on the ongoing and planned cmb , galaxy and sne observations .    for our short term predictions we assume the 4-year cmb temperature and polarization data from wmap @xcite , the expected galaxy counts from the dark energy survey ( des ) @xcite , and the sne from the nearby supernova factory ( nsnf ) @xcite and the supernovae legacy survey ( snls ) @xcite . in addition , we impose a gaussian prior on the value of @xmath90 corresponding to a @xmath130 uncertainty of @xmath138 from the hubble space telescope s key project ( hstkp ) @xcite .    for the long term predictions we assume the 14 months cmb temperature and polarization data by planck satellite @xcite , the galaxy catalogues by the large synoptic survey telescope ( lsst ) @xcite , and the sne from the supernovae acceleration probe ( snap ) @xcite complemented by those from the nsnf . to describe the distribution of galaxies from a given survey , we take the total galaxy number density to have the following redshift dependence @xcite : @xmath139 where @xmath140 is a parameter that is adjusted to reproduce the expected median redshift of the survey . the galaxies are further divided into photometric redshift bins , i.  e. @xmath141 following reference @xcite , we assume that the photometric redshift errors are gaussian distributed , and that their rms fluctuations increase with redshift as @xmath142 . the bins sizes are chosen to increase proportionally to the errors . the resulting photometric redshift distributions are given by , @xmath143 , \label{eq : erfc}\ ] ] where erfc is the complementary error function . for a given photometric redshift bin , the normalized selection function is given by @xmath144 where @xmath145 is the total number of galaxies in the @xmath115-th bin . the poisson noise is uncorrelated between bins and contributes only to the galaxy angular auto - correlation as @xmath146 where @xmath147 is the kronecker delta and @xmath148 is the galaxy number per solid angle in the @xmath115-th bin . the observed correlation @xmath106 is the sum of the signal and the poisson noise : [ galaxy : noise ] ^(i , j)_^(i , j)_+ n^(i , j ) _    the dark energy survey ( des ) is designed to probe the redshift range @xmath149 with an approximate 1-@xmath150 error of @xmath151 in photometric redshift . this roughly corresponds to four bins ( see fig . [ fig : des ] ) and a median redshift of @xmath152 . the total expected number of galaxies is approximately @xmath153 million in a @xmath154 sq . area on the sky , or @xmath155 . the proposed lsst survey is expected to cover up to @xmath156 sq . deg . of the sky and catalogue over a billion galaxies out to @xmath157 . we consider two cases : the conservative scenario case with @xmath158 and @xmath159 photometric redshift bins out to @xmath160 , and the desired case with @xmath161 and @xmath162 photometric redshift bins out to @xmath157 . for both cases we assume @xmath163 gal@xmath164arcmin@xmath165 . the assumed galaxy number distributions for the two cases are shown in figs . [ fig : lsst_cons ] and [ fig : lsst_goal ] . in what follows , we will refer to the two lsst cases as `` _ conservative _ '' and `` _ goal _ '' . the photometric redshift errors used in our analysis should be seen as the optimistic values for the respective experiments . for a discussion of potential sources of systematic errors in photo - z estimates the reader is referred to @xcite . the latest expected values for the sensitivity and the resolution parameters of the 4-year wmap and 14 months planck missions are available in @xcite . to make comparison with previous results easier , we opted to use similar , although somewhat different , parameters employed in @xcite for the three highest frequency channels of wmap and the lowest three planck hfi channels . we have checked that using the exact parameters given in @xcite would lead to an insignificant modification of our results . the relevant parameters are listed in table  [ tab : wmap ] .    . the relevant parameters of wmap @xcite and planck @xcite . we use the three highest frequency wmap channels and the lowest planck hfi frequency channels . [ cols= " < , > , > , > , > , > , > " , ]     in the longer term , i.e. in the next ten years , we should expect to have the results from planck cmb measurements , galaxy catalogues from lsst and the sne measurements from snap . these will significantly improve the constraints on the de parameters . in certain models , as we show here on the example of our model  ii , cmb / lss cross - correlation can play a competitive role . as in the previous subsection , we begin by considering the linear de model with two different sets of the fiducial values : one where they match a cosmological constant ( @xmath166 ) and another where @xmath1 evolves but still consistent with present observations ( model  i ) . in fig . [ fig : lcdm_long ] and fig . [ fig : comb1_long ] we show the @xmath130 projected contours for the linear models . on these plots , the cross - correlation and the sne prediction includes the information from planck . combining with planck is equivalent to applying strong priors on all cosmological parameters . the constraints in the absence of any priors can be found in table  [ tab : long ] . planck and snap are by far the most dominant information sources for these models , with cross - correlation adding a relatively weak contribution .    for model ii we start by presenting the individual error contours for the three experiments ( fig . [ fig : m2_ind_long ] ) , with the purpose of explicitely showing degeneracy directions . we will see that , once we consider its combination with planck , the    relative utility of the cross - correlation is significantly higher for model  ii . the contours in fig . [ fig : comb2_long ] show that the cross - correlation can provide constraints on @xmath2 and @xmath28 that are competitive with those from snap . the improvement on planck is especially strong without the polarization data . the full list of parameter constraints is given in table  [ tab : long ] . our results confirm that sne measurements are more suitable for constraining variations in @xmath0 at low redshifts . at higher redshifts , the cross - correlation becomes useful and can provide an independent constraint @xmath28 . figure [ fig : alt_comb2_long ] illustrates how a different choice of model ii fiducial parameters affects the constraining capabilities of the different probes . the alternative model has @xmath167 instead of @xmath168 . was not modified as the transition time would be pushed to very high redshifts if it approached -1 . on the other hand , @xmath2 smaller than @xmath169 are strongly disfavored by current data . ] in this case we note the snap+planck constraint for @xmath28 is noticeably tighter than that from the planck / lsst correlation . also note that this is mainly due to improvement in the sensitivity of the sne , as the transition in this model happens at a lower redshfit . the size of the error on @xmath28 from the cross - correlation is only marginally increased compared to fig . [ fig : comb2_long ] . we have studied the potential of the cmb / lss correlation for constraining the evolution of the de equation of state . we proposed a new parameterization , a `` kink '' model which has the average equation of state @xmath2 as an explicit parameter . a direct control on the value of @xmath2 preserves the tight constraints on @xmath1 obtained from the distance to last scattering measurements , while allowing @xmath0 to vary in other ways .    using fisher analysis , we have made forecasts of the expected uncertainties in de parameters extracted from the upcoming cmb , sne and cmb / lss correlation data . we have considered both short- ( wmap , des , snls ) and long- ( planck , lsst , snap ) term prospects . we find that in long term the cross - correlation will provide competitive constraints on the evolution of @xmath0 , in particular , on the total change in @xmath1 , provided a sufficiently generic parameterization is used . we also note that the transition length parameter , @xmath19 , will not be well constrained even with the long - term combined data . our results encourage further investigation of the cmb / lss correlation as a probe of dark energy . the cross - correlation has a clear weakness  a large variance that hinders its utility as a precision cosmology probe . however , it also has certain attractive features , that in some cases can out weigh the lack of accuracy . these features are :    * the cross - correlation probes _ the rate _ of the growth of structure as well as the growth . * it is practically independent of reionization details ( @xmath92 ) and the details of the initial spectrum ( @xmath93 ) . * it probes the large scales ( @xmath170 ) , where the evolution of structure is safely inside the linear regime and there is no need for higher order corrections . * on linear scales contributing to the isw / lss correlation the galaxy bias is expected to be independent of scale . * cross - correlation is linear in bias , compared to the matter power spectrum that is quadratic . in fact , if one used a cross - correlation estimator that is normalized to the auto - correlations , that estimator would be independent of bias and the overall normalization of the primordial spectrum . * cross - correlation can probe the evolution of dark energy at relatively high redshifts , inaccessible by luminosity distance measurements .    in this work we have restricted our attention to quintessence models for which the effective sound speed is of order of unity , so that the dark energy perturbations only affect the evolution of the largest structures . however , if the dark energy clusters on smaller scales , it may leave a distinctive signature which can be detected with cross - correlation measurements . although current data do not provide any constraints on the dark energy sound speed @xcite , the constraints from the next generation of galaxy surveys have been studied in @xcite . we have only considered flat frw models . without the flatness assumption , cmb constraints on @xmath89 and @xmath90 weaken because of a well - known degeneracy @xcite , also relaxing constraints on @xmath0 . we will explore constraints on de using isw without the flatness prior in a future work . the model ii type parameterization of @xmath0 considered in the paper is not necessarily the most optimal for underscoring the power of cross - correlation constraints ( although clearly better suited for this purposed than model i ) . a more comprehensive study using a principal component approach @xcite is a subject of ongoing research . another potential use of the isw cross - correlation is to measure the amplitude of the scalar perturbations and indirectly constrain the amplitude of the tensor modes when combined with the normalization of cmb spectra @xcite . this is because the distribution of the large scale structures is not correlated with a stochastic background of gravitational waves . it has been also suggested @xcite that cmb / lss studies may help to differentiate between quintessence and models with modified gravity .    for a fixed total number of galaxies the information extracted from the isw studies depends on the choice of the redshift binning . the role of cross - 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we present an analysis of the constraining power of future measurements of the integrated sachs - wolfe ( isw ) effect on models of the equation of state of dark energy as a function of redshift , @xmath0 . to achieve this 
 , we employ a new parameterization of @xmath1 , which utilizes the mean value of @xmath0 ( @xmath2 ) as an explicit parameter . 
 this helps to separate the information contained in the estimation of the distance to the last scattering surface ( from the cmb ) from the information contained in the isw effect . 
 we then use fisher analysis to forecast the expected uncertainties in the measured parameters from future isw observations for two models of dark energy with very different time evolution properties . 
 for example , we demonstrate that the cross  correlation of planck cmb data and lsst galaxy catalogs will provide competitive constraints on @xmath0 , compared to a snap  like sne project , for models of dark energy with a rapidly changing equation of state ( e.g. `` kink '' models ) . 
 our work confirms that , while sne measurements are more suitable for constraining variations in @xmath0 at low redshift , the isw effect can provide important independent constraints on @xmath0 at high @xmath3 .