IUCAA Preprints
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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 Morphology of the supercluster-void network in /\ CDM cosmology(2011-07-05) Shandarin, S.F.; Sheth, Jatush V.; Sahni, VarunWe report here the first systematic study of the supercluster-void network in the ΛCDM concordance cosmology in which voids and superclusters are treated on an equal footing. Superclusters are defined as individual members of an over-dense excur- sion set and voids are defined as individual members of a complementary under-dense excursion set at the same density threshold. We determine the geometric, topological and morphological properties of the cosmic web at a large set of density levels by computing Minkowski functionals for every supercluster and void using SURFGEN (Sheth et al. 2003). The properties of the largest (percolating) supercluster and the complementary void are found to be very different from properties of individual su- perclusters and voids. Individual superclusters totally occupy no more than about 5% of the total volume and contain no more than 20% of mass if the largest supercluster is excluded. Likewise, individual voids totally occupy no more than 14% of volume and contain no more than 4% of mass if the largest void is excluded. Although super- clusters are more massive and voids are more voluminous the difference in maximum volumes is not greater than by an order of magnitude. The genus value of individual superclusters can be ∼ 5 while the genus of individual voids can reach ∼ 40, implying significant amount of substructure in superclusters and especially in voids. One of our main results is that large voids, as defined through the density field (read dark matter distribution) can be distinctly non-spherical.Item Exploring the expanding universe and dark energy using the statefinder diagnostic(2011-07-05) Ujjaini, Alam; Sahni, Varun; Saini, Tarun Deep; et al.The coming few years are likely to witness a dramatic increase in high quality Sn 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 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 the 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 6 15 at the 3σ level if the value of Ωm is known exactly. The Statefinder gives reasonable results even when the value of Ωm is known to only ∼ 20% accuracy. In this case, marginalizing over Ωm and assuming a fiducial LCDM model allows us to rule out quintessence with w > −0.85 and the Chaplygin gas with κ 6 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.