2002 (IPP)
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Item Theoretical models of dark energy(2002-04-01) Sahni, VarunObservations of high redshift type Ia supernovae indicate that the universe is accelerating, fueled by an unknown form of dark energy having large negative pressure p < 0. The simplest example of dark energy is the cosmological constant (p ¼ q K=8pGÞ. The cosmological constant arises at a fundamental level from one-loop quantum effects which generate a K-term many orders of magnitude larger than the observed value of dark energy 10 47 GeV4 . This leads to the cosmological constant problem . Dynamical models of dark energy include scalar fields with exponential and power law potentials. Dark energy can also be generated in extra-dimensional braneworld models. Model-inde- pendent methods which attempt to reconstruct dark energy from supernova observations are discussed. 2002 Elsevier Science Ltd. All rights reservedItem Statefinder - anew geometrical diagnostic of dark energy(2002-02-21) Sahni, Varun; Saini, Tarun Deep; Starobinsky, A. A.We introduce a new cosmological diagnostic pair {r, s} called 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 s 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.Item Braneworld models of dark energy(2011-07-06) Sahni, Varun; Shtanov, YuriWe explore a new class of braneworld models in which the scalar curvature of the (induced) brane metric contributes to the brane action. The scalar curvature term arises generically on account of one-loop effects induced by matter fields residing on the brane. Spatially flat braneworld models can en- ter into a regime of accelerated expansion at late times. This is true even if the brane tension and the bulk cosmological constant are tuned to satisfy the Randall–Sundrum constraint on the brane. Braneworld models admit a wider range of possibilities for dark energy than standard LCDM. In these models the luminosity distance can be both smaller and larger than the lu- minosity distance in LCDM. Whereas models with dL ≤ dL(LCDM) imply w = p/ρ ≥ −1 and have frequently been discussed in the literature, mod- els with dL > dL(LCDM) have traditionally been ignored, perhaps because within the general-relativistic framework, the luminosity distance has this property only if the equation of state of matter is strongly negative (w < −1). Within the conventional framework, ‘phantom energy’ with w < −1 is beset with a host of undesirable properties, which makes this model of dark en- ergy unattractive. Braneworld models, on the other hand, have the capacity to endow dark energy with exciting new possibilities (including w < −1) without suffering from the problems faced by phantom energy. For a subclass of parameter values, braneworld dark energy and the acceleration of the universe are transient phenomena. In these models, the universe, after the current period of acceleration, re-enters the matter-dominated regime so that the deceleration parameter q(t) → 0.5 when t ≫ t0, where t0 is the present epoch. Such models could help reconcile an accelerating universe with the requirements of string/M-theory.