Ujjaini Alam

STATEFINDER: A NEW GEOMETRICAL DIAGNOSTIC OF DARK ENERGY

We introduce a new cosmological diagnostic pair {r, s} called the Statefinder. The Statefinder is a geometrical diagnostic and allows us to characterize the properties of dark energy in a model-independent manner. The Statefinder is dimensionless and is constructed from the scale factor of the Universe and its time derivatives only. The parameter r forms the next step in the hierarchy of geometrical cosmological parameters after the Hubble parameter H and the deceleration parameter q, while a is a linear combination of q and r chosen in such a way that it does not depend upon the dark energy density. The Statefinder pair {r, s} is algebraically related to the equation of state of dark energy and its first time derivative. The Statefinder pair is calculated for a number of existing models of dark energy having both constant and variable w. For the case of a cosmological constant, the Statefinder acquires a particularly simple form. We demonstrate that the Statefinder diagnostic can effectively differentiate between different forms of dark energy. We also show that the mean Statefinder pair can be determined to very high accuracy from a SNAP-type experiment.

Exploring the expanding Universe and dark energy using the statefinder diagnostic

The coming few years are likely to witness a dramatic increase in high-quality supernova data as current surveys add more high-redshift supernovae to their inventory and as newer and deeper supernova experiments become operational. Given the current variety in dark energy models and the expected improvement in observational data, an accurate and versatile diagnostic of dark energy is the need of the hour. This paper examines the statefinder diagnostic in the light of the proposed SuperNova Acceleration Probe (SNAP) satellite, which is expected to observe about 2000 supernovae per year. We show that the statefinder is versatile enough to differentiate between dark energy models as varied as the cosmological constant on one hand, and quintessence, the Chaplygin gas and braneworld models, on the other. Using SNAP data, the statefinder can distinguish a cosmological constant (w = -1) from quintessence models with w ≥ -0.9 and Chaplygin gas models with κ ≤ 15 at the 3a level if the value of Ω m is known exactly. The statefinder gives reasonable results even when the value of Ω m is known to only ∼20 per cent accuracy. In this case, marginalizing over Ω m and assuming a fiducial A-cold dark matter (LCDM) model allows us to rule out quintessence with w ≥ -0.85 and the Chaplygin gas with κ ≤ 7 (both at 3σ). These constraints can be made even tighter if we use the statefinders in conjunction with the deceleration parameter. The statefinder is very sensitive to the total pressure exerted by all forms of matter and radiation in the Universe. It can therefore differentiate between dark energy models at moderately high redshifts of z ≤ 10.

Is there supernova evidence for dark energy metamorphosis

We reconstruct the equation of state w(z) of dark energy (DE) using a recently released data set containing 172 Type Ia supernovae (SNe) without assuming the prior w(z) ≥−1 (in contrast to previous studies). We find that DE evolves rapidly and metamorphoses from dust-like behaviour at high z (w≃ 0 at z∼ 1) to a strongly negative equation of state at present (w≲−1 at z≃ 0). DE metamorphosis appears to be a robust phenomenon which manifests for a large variety of SNe data samples provided one does not invoke the weak energy prior ρ+p≥ 0. Invoking this prior considerably weakens the rate of growth of w(z). These results demonstrate that DE with an evolving equation of state provides a compelling alternative to a cosmological constant if data are analysed in a prior-free manner and the weak energy condition is not imposed by hand.

Nonparametric Dark Energy Reconstruction from Supernova Data

Understanding the origin of the accelerated expansion of the Universe poses one of the greatest challenges in physics today. Lacking a compelling fundamental theory to test, observational efforts are targeted at a better characterization of the underlying cause. If a new form of mass-energy, dark energy, is driving the acceleration, the redshift evolution of the equation of state parameter w(z) will hold essential clues as to its origin. To best exploit data from observations it is necessary to develop a robust and accurate reconstruction approach, with controlled errors, for w(z). We introduce a new, nonparametric method for solving the associated statistical inverse problem based on Gaussian process modeling and Markov chain Monte Carlo sampling. Applying this method to recent supernova measurements, we reconstruct the continuous history of w out to redshift z=1.5.

Nonparametric Reconstruction of the Dark Energy Equation of State

A basic aim of ongoing and upcoming cosmological surveys is to unravel the mystery of dark energy. In the absence of a compelling theory to test, a natural approach is to better characterize the properties of dark energy in search of clues that can lead to a more fundamental understanding. One way to view this characterization is the improved determination of the redshift-dependence of the dark energy equation of state parameter, w(z). To do this requires a robust and bias-free method for reconstructing w(z) from data that does not rely on restrictive expansion schemes or assumed functional forms for w(z). We present a new nonparametric reconstruction method that solves for w(z) as a statistical inverse problem, based on a Gaussian process representation. This method reliably captures nontrivial behavior of w(z) and provides controlled error bounds. We demonstrate the power of the method on different sets of simulated supernova data; the approach can be easily extended to include diverse cosmological probes.

Gaussian Process Modeling of Derivative Curves

Gaussian process (GP) models provide nonparametric methods to fit continuous curves observed with noise. In this article, we develop a GP-based inverse method that allows for the direct estimation of the derivative of a one-dimensional curve. In principle, a GP model may be fit to the data directly, with the derivatives obtained by means of differentiation of the correlation function. However, it is known that this approach can be inadequate due to loss of information when differentiating. We present a new method of obtaining the derivative process by viewing this procedure as an inverse problem. We use the properties of a GP to obtain a computationally efficient fit. We illustrate our method with simulated data as well as apply it to an important cosmological application. We include a discussion on model comparison techniques for assessing the quality of the fit of this alternative method. Supplementary materials for this article are available online.

RECONSTRUCTING COSMOLOGICAL MATTER PERTURBATIONS USING STANDARD CANDLES AND RULERS

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 growth 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 supernovae (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 Joint Dark Energy 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 baryon acoustic oscillation data which would deliver measurements of both the angular diameter distance and the Hubble parameter, it should be possible to constrain the growth factor at z = 2.5%-9%. These constraints grow tighter with the errors on the data sets. 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.

Constraining Perturbative Early Dark Energy with Current Observations

In this work, 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 constrain these models using current observations. We consider EDE models in which the dark energy equation of state is at least wm –0.1 at early times, which could lead to an EDE density of up to . Our analysis shows that marginalizing over the non-DE parameters such as Ωm, H 0, andns , current CMB observations alone can constrain the scale factor of transition from EDE to late-time dark energy to at 0.44 and width of transition to Δ t 0.37. The equation of state at present is somewhat weakly constrained to w 0 –0.6, if we allow H 0 < 60 km s–1 Mpc–1. Taken together with other observations, such as SNe, Hubble Space Telescope, and Sloan Digital Sky Survey luminous red galaxies, w 0 is constrained much more tightly to w 0 –0.9, while redshift of transition and width of transition are also tightly constrained to at 0.19 andΔ t 0.21. The evolution of the equation of state for EDE models is thus tightly constrained to ΛCDM-like behavior at low redshifts. Incorrectly assuming dark energy perturbations to be negligible leads to different constraints on the equation of state parameters—w 0 –0.8, at 0.33, andΔ t 0.31, thus highlighting the necessity of self-consistently including dark energy perturbations in the analysis. If we allow the spatial curvature to be a free parameter, then the constraints are relaxed to w 0 –0.77, at 0.35, andΔ t 0.35 with –0.014 < Ωκ < 0.031 for CMB + other observations. For perturbed EDE models, the 2σ lower limit on σ8 (σ8 ≥ 0.59) is much lower than that in ΛCDM (σ8 ≥ 0.72), thus raising the interesting possibility of discriminating EDE from ΛCDM using future observations such as halo mass functions or the Sunyaev-Zeldovich power spectrum.