Constraining the Properties of Dark Energy

The presence of dark energy in the Universe is inferred directly from the accelerated expansion of the Universe, and indirectly, from measurements of cosmic microwave background (CMB) anisotropy. Dark energy contributes about 2/3 of the critical density, is very smoothly distributed, and has large negative pressure. Its nature is very much unknown. Most of its discernible consequences follow from its effect on evolution of the expansion rate of the Universe, which in turn affects the growth of density perturbations and the age of the Universe, and can be probed by the classical kinematic cosmological tests. Absent a compelling theoretical model (or even a class of models), we describe dark energy by an effective equation of state w=p_X/rho_X which is allowed to vary with time. We describe and compare different approaches for determining w(t), including magnitude-redshift (Hubble) diagram, number counts of galaxies and clusters, and CMB anisotropy, focusing particular attention on the use of a sample of several thousand type Ia supernova with redshifts z < 1.7, as might be gathered by the proposed SNAP satellite. Among other things, we derive optimal strategies for constraining cosmological parameters using type Ia supernovae. While in the near term CMB anisotropy will provide the first measurements of w, supernovae and number counts appear to have the most potential to probe dark energy.Comment: 6 pages, 3 figures; proceedings of 20th Texas Symposium on Relavistic Astrophysic

Constraints on the Inner Cluster Mass Profile and the Power Spectrum Normalization from Strong Lensing Statistics

Strong gravitational lensing is a useful probe of both the intrinsic properties of the lenses and the cosmological parameters of the universe. The large number of model parameters and small sample of observed lens systems, however, have made it difficult to obtain useful constraints on more than a few parameters from lensing statistics. Here we examine how the recent WMAP measurements help improve the constraining power of statistics from the radio lensing survey JVAS/CLASS. We find that the absence of theta>3'' lenses in CLASS places an upper bound of beta<1.25 (1.60) at 68% (95%) CL on the inner density profile, rho \propto r^{-beta}, of cluster-sized halos. Furthermore, the favored power spectrum normalization is sigma_8 >= 0.7 (95% CL). We discuss two possibilities for stronger future constraints: a positive detection of at least one large-separation system, and next-generation radio surveys such as LOFAR.Comment: Scatter in concentration included; virial mass used consistently; new Fig 3. Final version published in ApJ

Parameterization of Dark-Energy Properties: a Principal-Component Approach

Considerable work has been devoted to the question of how to best parameterize the properties of dark energy, in particular its equation of state w. We argue that, in the absence of a compelling model for dark energy, the parameterizations of functions about which we have no prior knowledge, such as w(z), should be determined by the data rather than by our ingrained beliefs or familiar series expansions. We find the complete basis of orthonormal eigenfunctions in which the principal components (weights of w(z)) that are determined most accurately are separated from those determined most poorly. Furthermore, we show that keeping a few of the best-measured modes can be an effective way of obtaining information about w(z).Comment: Unfeasibility of a truly model-independent reconstruction of w at z>1 illustrated. f(z) left out, and w(z) discussed in more detail. Matches the PRL versio

Probing Dark Energy Dynamics from Current and Future Cosmological Observations

We report the constraints on the dark energy equation-of-state w(z) using the latest 'Constitution' SNe sample combined with the WMAP5 and SDSS data. Based on the localized principal component analysis and the model selection criteria, we find that the LCDM model is generally consistent with the current data, yet there exists weak hint of the possible dynamics of dark energy. In particular, a model predicting w(z)-1 at z\in[0.5,0.75), which means that w(z) crosses -1 in the range of z\in[0.25,0.75), is mildly favored at 95% confidence level. Given the best fit model for current data as a fiducial model, we make future forecast from the joint data sets of JDEM, Planck and LSST, and we find that the future surveys can reduce the error bars on the w bins by roughly a factor of 10 for a 5-w-bin model.Comment: Accepted by PRD; minor changes from v

Hubble parameter reconstruction from a principal component analysis: minimizing the bias

A model-independent reconstruction of the cosmic expansion rate is essential to a robust analysis of cosmological observations. Our goal is to demonstrate that current data are able to provide reasonable constraints on the behavior of the Hubble parameter with redshift, independently of any cosmological model or underlying gravity theory. Using type Ia supernova data, we show that it is possible to analytically calculate the Fisher matrix components in a Hubble parameter analysis without assumptions about the energy content of the Universe. We used a principal component analysis to reconstruct the Hubble parameter as a linear combination of the Fisher matrix eigenvectors (principal components). To suppress the bias introduced by the high redshift behavior of the components, we considered the value of the Hubble parameter at high redshift as a free parameter. We first tested our procedure using a mock sample of type Ia supernova observations, we then applied it to the real data compiled by the Sloan Digital Sky Survey (SDSS) group. In the mock sample analysis, we demonstrate that it is possible to drastically suppress the bias introduced by the high redshift behavior of the principal components. Applying our procedure to the real data, we show that it allows us to determine the behavior of the Hubble parameter with reasonable uncertainty, without introducing any ad-hoc parameterizations. Beyond that, our reconstruction agrees with completely independent measurements of the Hubble parameter obtained from red-envelope galaxies.Comment: Modified to match journal versio

Gravitational Lensing as a Probe of Quintessence

A large number of cosmological studies now suggest that roughly two-thirds of the critical energy density of the Universe exists in a component with negative pressure. If the equation of state of such an energy component varies with time, it should in principle be possible to identify such a variation using cosmological probes over a wide range in redshift. Proper detection of any time variation, however, requires cosmological probes beyond the currently studied range in redshift of $\sim$ 0.1 to 1. We extend our analysis to gravitational lensing statistics at high redshift and suggest that a reliable sample of lensed sources, out to a redshift of $\sim$ 5, can be used to constrain the variation of the equation of state, provided that both the redshift distribution of lensed sources and the selection function involved with the lensed source discovery process are known. An exciting opportunity to catalog an adequate sample of lensed sources (quasars) to probe quintessence is now available with the ongoing Sloan Digital Sky Survey. Writing $w(z)\approx w_0 + z (dw/dz)_0$, we study the expected accuracy to which the equation of state today $w_0$ and its rate of change $(dw/dz)_0$ can simultaneously be constrained. Such a determination can rule out some missing-energy candidates, such as classes of quintessence models or a cosmological constant.Comment: Accepted for publication in ApJ Letters (4 pages, including 4 figures

Weak Lensing as a Calibrator of the Cluster Mass-Temperature Relation

The abundance of clusters at the present epoch and weak gravitational lensing shear both constrain roughly the same combination of the power spectrum normalization sigma_8 and matter energy density Omega_M. The cluster constraint further depends on the normalization of the mass-temperature relation. Therefore, combining the weak lensing and cluster abundance data can be used to accurately calibrate the mass-temperature relation. We discuss this approach and illustrate it using data from recent surveys.Comment: Matches the version in ApJL. Equation 4 corrected. Improvements in the analysis move the cluster contours in Fig1 slightly upwards. No changes in the conclusion

Is the Universe Inflating? Dark Energy and the Future of the Universe

We consider the fate of the observable universe in the light of the discovery of a dark energy component to the cosmic energy budget. We extend results for a cosmological constant to a general dark energy component and examine the constraints on phenomena that may prevent the eternal acceleration of our patch of the universe. We find that the period of accelerated cosmic expansion has not lasted long enough for observations to confirm that we are undergoing inflation; such an observation will be possible when the dark energy density has risen to between 90% and 95% of the critical. The best we can do is make cosmological observations in order to verify the continued presence of dark energy to some high redshift. Having done that, the only possibility that could spoil the conclusion that we are inflating would be the existence of a disturbance (the surface of a true vacuum bubble, for example) that is moving toward us with sufficiently high velocity, but is too far away to be currently observable. Such a disturbance would have to move toward us with speed greater than about 0.8c in order to spoil the late-time inflation of our patch of the universe and yet avoid being detectable.Comment: 7 pages, 7 figure

Gamma-ray burst contributions to constraining the evolution of dark energy

We explore the gamma-ray bursts' (GRBs') contributions in constraining the dark energy equation of state (EOS) at high ($1.8 < z < 7$) and at middle redshifts ($0.5 < z < 1.8$) and estimate how many GRBs are needed to get substantial constraints at high redshifts. We estimate the constraints with mock GRBs and mock type Ia supernovae (SNe Ia) for comparisons. When constraining the dark energy EOS in a certain redshift range, we allow the dark energy EOS parameter to vary only in that redshift bin and fix EOS parameters elsewhere to -1. We find that it is difficult to constrain the dark energy EOS beyond the redshifts of SNe Ia with GRBs unless some new luminosity relations for GRBs with smaller scatters are discovered. However, at middle redshifts, GRBs have comparable contributions with SNe Ia in constraining the dark energy EOS.Comment: 3 pages, 5 figures. Published in Astronomy and Astrophysics. Corrected referenc