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 New vistas in braneworld cosmology(2002-03-21) Sahni, Varun; Shtanov, YuriTraditionally, higher-dimensional cosmological models have sought to pro- vide a description of the fundamental forces in terms of a unifying geometri- cal construction. In this essay we discuss how, in their present incarnation, higher-dimensional ‘braneworld’ models might provide answers to a number of cosmological puzzles including the issue of dark energy and the nature of the big-bang singularityItem New cosmological singularities in braneworld models(2002-01-02) Yuri, Shtanov; Sahni, VarunHigher-dimensional braneworld models which contain both bulk and brane curvature terms in the action admit cosmological singularities of rather un- usual form and nature. These ‘quiescent’ singularities, which can occur both during the contracting as well as the expanding phase, are characterised by the fact that while the matter density and Hubble parameter remain finite, all higher derivatives of the scale factor ( .. a, ... a etc.) diverge as the cosmological singularity is approached. The singularities are the result of the embedding of the (3+1)-dimensional brane in the bulk and can exist even in an empty homogeneous and isotropic (FRW) universe. The possibility that the present universe may expand into a singular state is discussed.Item Measuring the geometry and topology of large scale structure using SURFGEN: Methodology and preliminary results(2002-03-22) Sheth, Jatush V.; Sahni, Varun; Shandarin, S.F.; et al.Observations of the universe reveal that matter within it clusters on a variety of scales. On scales between 10 - 100 Mpc, the universe is spanned by a percolating network of superclusters interspersed with large and almost empty regions – voids. This paper, the first in a series, presents a new ansatz which can successfully be used to determine the morphological properties of the supercluster-void network. The ansatz is based on a surface modelling scheme (SURFGEN), developed explicitly for the purpose, which generates a triangulated surface from a discrete data set representing (say) the dis- tribution of galaxies in real (or redshift) space. The triangulated surface describes, at progressively lower density thresholds, clusters of galaxies, superclusters of galaxies and voids. Four Minkowski functionals (MFs) – surface area, volume, extrinsic curva- ture and genus – describe the geometry and topology of the supercluster-void network. On a discretised and closed triangulated surface the MFs are determined using SUR- FGEN. Ratio’s of the Minkowski functionals provide us with an excellent diagnostic of three dimensional shapes of clusters, superclusters and voids. Minkowski function- als can be studied at different levels of the density contrast and therefore probe the morphology of large scale structure on a variety of length scales. Our method for determining the Minkowski functionals of a triangulated iso-density surface is tested against both simply and multiply connected eikonal surfaces such as triaxial ellipsoids and tori. The performance of our code is thereby evaluated using density distribu- tions which are pancake-like, filamentary, ribbon-like and spherical. Remarkably, the first three Minkowski functionals are computed to better than 1% accuracy while the fourth (genus) is known exactly. SURFGEN also gives very accurate results when ap- plied to Gaussian random fields. We apply SURFGEN to study morphology in three cosmological models, ΛCDM, τCDM and SCDM, at the present epoch. Geometrical properties of the supercluster-void network are found to be sensitive to the underlying cosmological parameter set. For instance, the percolating supercluster in ΛCDM turns out to be more filamentary but topologically simpler than superclusters in τCDM and SCDM. It occupies just 0.6% of the total simulation-box volume yet contains about 4% of the total mass. Our results indicate that the surface modelling scheme to calculate Minkowski functionals is accurate and robust and can successfully be used to quantify the topology and morphology of the supercluster-void network in the universe.Item Cosmological constant problem and quintessence(2011-07-06) Sahni, VarunI briefly review the cosmological constant problem and the issue of dark energy (or quintessence). Within the framework of quantum field theory, the vacuum expectation value of the energy momentum tensor formally diverges as k4. A cutoff at the Planck or electroweak scale leads to a cosmological constant which is, respectively, 10123 or 1055 times larger than the observed value, Λ/8πG ≃ 10−47 GeV4. The absence of a fundamental symmetry which could set the value of Λ to either zero or a very small value leads to the cosmological constant problem. Most cosmological scenario’s favour a large time-dependent Λ-term in the past (in order to generate inflation at z ≫ 1010), and a small Λ-term today, to account for the current acceleration of the universe at z < ∼ 1. Constraints arising from cosmological nucleosynthesis, CMB and structure formation constrain Λ to be sub-dominant during most of the intermediate epoch 1010 < z < 1. This leads to the cosmic coincidence conundrum which suggests that the acceleration of the universe is a recent phenomenon and that we live during a special epoch when the density in Λ and in matter are almost equal. Time varying models of dark energy can, to a certain extent, ameliorate the fine tuning problem (faced by Λ), but do not resolve the puzzle of cosmic coincidence. I briefly review tracker models of dark energy, as well as more recent brane inspired ideas and the issue of horizons in an accelerating universe. Model independent methods which reconstruct the cosmic equation of state from supernova observations are also assessed. Finally, a new diagnostic of dark energy – ‘Statefinder’, is discussed.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.