Tarun Deep Saini

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.

Reconstructing the cosmic equation of state from supernova distances.

Observations of high-redshift supernovae indicate that the Universe is accelerating. Here we present a model-independent method for estimating the form of the potential V(phi) of the scalar field driving this acceleration, and the associated equation of state w(phi). Our method is based on a versatile analytical form for the luminosity distance D(L), optimized to fit observed distances to distant supernovae and differentiated to yield V(straight phi) and w(straight phi). Our results favor w(phi) approximately -1 at the present epoch, steadily increasing with redshift. A cosmological constant is consistent with our results.

Anisotropy dissipation in brane-world inflation

We examine the behavior of an anisotropic brane-world in the presence of inflationary scalar fields. We show that, contrary to naive expectations, a large anisotropy does not adversely affect inflation. On the contrary, a large initial anisotropy introduces more damping into the scalar field equation of motion, resulting in greater inflation. The rapid decay of anisotropy in the brane-world significantly increases the class of initial conditions from which the observed universe could have originated. This generalizes a similar result in general relativity. A unique feature of Blanchi type I brane-world cosmology appears to be that for scalar fields with a large kinetic term the initial expansion of the Universe is quasi-isotropic. The Universe grows more anisotropic during an intermediate transient regime until anisotropy finally disappears during inflationary expansion. ©2001 The American Physical Society.

Using Gravitational Lensing to Study H I Clouds at High Redshift

We investigate the possibility of detecting H I emission from gravitationally lensed H I clouds (akin to damped Lyα clouds) at high redshift by carrying out deep radio observations in the fields of known cluster lenses. These observations will be possible with current radio telescopes only if their lenses substantially magnify the flux of the H I emission. While at present this holds the only possibility of detecting the H I emission from such clouds, it has the disadvantage of being restricted to clouds that lie very close to the caustics of the lens. We find that observations at a detection threshold of 50 μJy at 320 MHz (possible with the Giant Meterwave Radio Telescope) have a greater than 20% probability of detecting an H I cloud in the field of a cluster, provided the clouds have H I masses in the range 5 × 108 M☉ M 2.5 × 1010 M☉. The probability of detecting a cloud increases if it has larger H I masses except in cases where the number of H I clouds in the cluster field is very small. The probability of detection at 610 and 233 MHz is comparable to that at 320 MHz, although a definitive statement is difficult owing to uncertainties in the H I content at the redshifts corresponding to these frequencies. Observations at a detection threshold of 2 μJy (possible in the future with the Square Kilometer Array) are expected to detect a few H I clouds in the field of every cluster, provided the clouds have H I masses in the range 2 × 107 M☉ M 109 M☉. Even if such observations do not result in the detection of H I clouds, they will be able to put useful constraints on the H I content of the clouds.

Reconstructing the properties of dark energy using standard sirens

Future space-based gravity wave (GW) experiments such as the Big Bang Observatory (BBO), with their excellent projected, one sigma angular resolution, will measure the luminosity distance to a large number of GW sources to high precision, and the redshift of the single galaxies in the narrow solid angles towards the sources will provide the redshifts of the gravity wave sources. One sigma BBO beams contain the actual source in only 68% of the cases; the beams that do not contain the source may contain a spurious single galaxy, leading to misidentification. To increase the probability of the source falling within the beam, larger beams have to be considered, decreasing the chances of finding single galaxies in the beams. Saini et al. T.D. Saini, S.K. Sethi, and V. Sahni, Phys. Rev. D 81, 103009 (2010)] argued, largely analytically, that identifying even a small number of GW source galaxies furnishes a rough distance-redshift relation, which could be used to further resolve sources that have multiple objects in the angular beam. In this work we further develop this idea by introducing a self-calibrating iterative scheme which works in conjunction with Monte Carlo simulations to determine the luminosity distance to GW sources with progressively greater accuracy. This iterative scheme allows one to determine the equation of state of dark energy to within an accuracy of a few percent for a gravity wave experiment possessing a beam width an order of magnitude larger than BBO (and therefore having a far poorer angular resolution). This is achieved with no prior information about the nature of dark energy from other data sets such as type Ia supernovae, baryon acoustic oscillations, cosmic microwave background, etc. DOI:10.1103/PhysRevD.87.083001

A Lens-Mapping Algorithm for Weak Lensing

We develop an algorithm for the reconstruction of the two-dimensional mass distribution of a gravitational lens from the observable distortion of background galaxies. From the measured reduced shear, the lens mapping is obtained, from which a mass distribution is derived. This is unlike other methods where the convergence κ is directly obtained. We show that this method works best for subcritical lenses but can be applied to a critical lens away from the critical lines. For finite fields, the usual mass-sheet degeneracy is shown to exist in this method. We show that the algorithm reproduces the mass distribution within acceptable limits when applied to simulated noisy data.