A large number of cosmological parameters have been suggested for obtaining information on the nature of dark energy. In this work, we study the efficacy of these different parameters in discriminating theoretical models of dark energy, using both cu
rrently available supernova (SNe) data, and simulations of future observations. We find that the current data does not put strong constraints on the nature of dark energy, irrespective of the cosmological parameter used. For future data, we find that the although deceleration parameter can accurately reconstruct some dark energy models, it is unable to discriminate between different models of dark energy, therefore limiting its usefulness. Physical parameters such as the equation of state of dark energy, or the dark energy density do a good job of both reconstruction and discrimination if the matter density is known to high accuracy. However, uncertainty in matter density reduces the efficacy of these parameters. A recently proposed parameter, Om(z), constructed from the first derivative of the SNe data, works very well in discriminating different theoretical models of dark energy, and has the added advantage of not being dependent on the value of matter density. Thus we find that a cosmological parameter constructed from the first derivative of the data, for which the theoretical models of dark energy are sufficiently distant from each other, and which is independent of the matter density, performs the best in reconstructing dark energy from SNe data.
We study a class of early dark energy (EDE) models, in which, unlike in standard dark energy models, a substantial amount of dark energy exists in the matter-dominated era. We self-consistently include dark energy perturbations, and show that these m
odels may be successfully constrained using future observations of galaxy clusters, in particular the redshift abundance, and the Sunyaev-Zeldovich (SZ) power spectrum. We make predictions for EDE models, as well as LCDM for incoming X-ray (eROSITA) and microwave (South Pole Telescope) observations. We show that galaxy clusters mass function and the SZ power spectrum will put strong constraints both on the equation of state of de today and the redshift at which EDE transits to present-day LCDM like behavior for these models, thus providing complementary information to the geometric probes of dark energy. Not including perturbations in EDE models leads to those models being practically indistinguishable from LCDM. An MCMC analysis of future galaxy cluster surveys provides constraints for EDE parameters that are competitive with and complementary to background expansion observations such as supernovae.
In this work, we study a class of early dark energy (EDE) models, in which, unlike in standard DE models, a substantial amount of DE exists in the matter-dominated era, self-consistently including DE perturbations. Our analysis shows that, marginaliz
ing over the non DE parameters such as $Omega_m, H_0, n_s$, current CMB observations alone can constrain the scale factor of transition from early DE to late time DE to $a_t geq 0.44$ and width of transition to $Delta_t leq 0.37$. The equation of state at present is somewhat weakly constrained to $w_0 leq -0.6$, if we allow $H_0 < 60$ km/s/Mpc. Taken together with other observations, such as supernovae, HST, and SDSS LRGs, the constraints are tighter-- $w_0 leq -0.9, a_t leq 0.19, Delta_t leq 0.21$. The evolution of the equation of state for EDE models is thus close to $Lambda$CDM at low redshifts. Incorrectly assuming DE perturbations to be negligible leads to different constraints on the equation of state parameters, thus highlighting the necessity of self-consistently including DE perturbations in the analysis. If we allow the spatial curvature to be a free parameter, then the constraints are relaxed to $w_0 leq -0.77, a_t leq 0.35, Delta_t leq 0.35$ with $-0.014 < Omega_{kappa} < 0.031$ for CMB+other observations. For perturbed EDE models, the $2sigma$ lower limit on $sigma_8$ ($sigma_8 geq 0.59$) is much lower than that in $Lambda$CDM ($sigma_8 geq 0.72$), thus raising the interesting possibility of discriminating EDE from $Lambda$CDM using future observations such as halo mass functions or the Sunyaev-Zeldovich power spectrum.
For a large class of dark energy (DE) models, for which the effective gravitational constant is a constant and there is no direct exchange of energy between DE and dark matter (DM), knowledge of the expansion history suffices to reconstruct the growt
h factor of linearized density perturbations in the non-relativistic matter component on scales much smaller than the Hubble distance. In this paper we develop a non-parametric method for extracting information about the perturbative growth factor from data pertaining to the luminosity or angular size distances. A comparison of the reconstructed density contrast with observations of large scale structure and gravitational lensing can help distinguish DE models such as the cosmological constant and quintessence from models based on modified gravity theories as well as models in which DE and DM are either unified, or interact directly. We show that for current SNe data, the linear growth factor at z = 0.3 can be constrained to 5%, and the linear growth rate to 6%. With future SNe data, such as expected from the JDEM mission, we may be able to constrain the growth factor to 2-3% and the growth rate to 3-4% at z = 0.3 with this unbiased, model-independent reconstruction method. For future BAO data which would deliver measurements of both the angular diameter distance and Hubble parameter, it should be possible to constrain the growth factor at z = 2.5 to 9%. These constraints grow tighter with the errors on the datasets. With a large quantity of data expected in the next few years, this method can emerge as a competitive tool for distinguishing between different models of dark energy.
