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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.Item Can dark energy be decaying?(2011-07-05) Ujjaini, Alam; Sahni, Varun; Starobinsky, A. A.We explore the fate of the universe given the possibility that the density associated with ‘dark energy’ may decay slowly with time. Decaying dark energy is modeled by a homogeneous scalar field which couples minimally to gravity and whose potential has at least one local quadratic maximum. Dark energy decays as the scalar field rolls down its potential, consequently the current acceleration epoch is a transient. We examine two models of decaying dark energy. In the first, the dark energy potential is modeled by an analytical form which is generic close to the potential maximum. The second potential is the cosine, which can become negative as the field evolves, ensuring that a spatially flat universe collapses in the future. We examine the feasibility of both models using observations of high redshift type Ia supernovae. A maximum likelihood analysis is used to find allowed regions in the {m, φ0} plane (m is the tachyon mass modulus and φ0 the initial scalar field value; m ∼ H0 and φ0 ∼ MP by order of magnitude). For the first model, the time for the potential to drop to half its maximum value is larger than ∼ 8 Gyrs. In the case of the cosine potential, the time left until the universe collapses is always greater than ∼ 18 Gyrs (both estimates are presented for Ω0m = 0.3, m/H0 ∼ 1, H0 ≃ 70 km/sec/Mpc, and at the 95.4% confidence level).Item Dark matter and dark energy(2011-07-06) Sahni, VarunAbstract. I briefly review our current understanding of dark matter and dark en- ergy. The first part of this paper focusses on issues pertaining to dark matter includ- ing observational evidence for its existence, current constraints and the ‘abundance of substructure’ and ‘cuspy core’ issues which arise in CDM. I also briefly describe MOND. The second part of this review focusses on dark energy. In this part I dis- cuss the significance of the cosmological constant problem which leads to a predicted value of the cosmological constant which is almost 10123 times larger than the ob- served value Λ/8πG ≃ 10−47 GeV4 . Setting Λ to this small value ensures that the acceleration of the universe is a fairly recent phenomenon giving rise to the ‘cosmic coincidence’ conundrum according to which we live during a special epoch when the density in matter and Λ are almost equal. Anthropic arguments are briefly dis- cussed but more emphasis is placed upon dynamical dark energy models in which the equation of state is time dependent. These include Quintessence, Braneworld models, Chaplygin gas and Phantom energy. Model independent methods to deter- mine the cosmic equation of state and the Statefinder diagnostic are also discussed. The Statefinder has the attractive property ... a /aH3 = 1 for LCDM, which is helpful for differentiating between LCDM and rival dark energy models. The review ends with a brief discussion of the fate of the universe in dark energy models.Item Case for dynamical dark energy revisited(2011-07-06) Alam, Ujjaini; Sahni, Varun; Starobinsky, A. A.We investigate the behaviour of dark energy using the recently released supernova data of Riess et al., 2004 and a model independent parameterization for dark energy (DE). We find that, if no priors are imposed on Ω0m and h, DE which evolves with time provides a better fit to the SNe data than ΛCDM. This is also true if we include results from the WMAP CMB data. From a joint analysis of SNe+CMB, the best-fit DE model has w0 < ∼ − 1 at the present epoch and the transition from deceleration to acceleration occurs at zT = 0.39±0.03. However, DE evolution becomes weaker if the ΛCDM based CMB results Ω0m = 0.27 ± 0.04, h = 0.71 ± 0.06 are incorporated in the analysis. In this case, zT = 0.57±0.07. Our results also show that the extent of DE evolution is sensitive to the manner in which the supernova data is sampled.Item Reconstructing dark energy(2006-10-23) Sahni, Varun; Starobinsky, A. A.This review summarizes recent attempts to reconstruct the expansion history of the Uni- verse and to probe the nature of dark energy. Reconstruction methods can be broadly classified into parametric and non-parametric approaches. It is encouraging that, even with the limited observational data currently available, different approaches give consistent results for the reconstruction of the Hubble parameter H(z) and the effective equation of state w(z) of dark energy. Model independent reconstruction using current data allows for modest evolution of dark energy density with redshift. However, a cosmological constant (= dark energy with a constant energy density) remains an excellent fit to the data. Some pitfalls to be guarded against during cosmological reconstruction are summarized and future directions for the model independent reconstruction of dark energy are explored.Item Dark energy(2006-01-10) Sahni, VarunThe cosmological constant problem as well as the case for dark energy are briefly reviewed and some theoretical models of dark energy are discussed in detail. These include: the cosmological constant, quintessence, the Chaplygin gas and Braneworld models. I also discuss model independent measures of dark energy and conclude by mentioning some properties of the Statefinder diagnostic which can successfully differentiate between different families of dark energy models.Item Two new diagnostics of dark energy(2008-11-03) Sahni, Varun; Starobinsky, A. A.We introduce two new diagnostics of dark energy (DE). The first, Om, is a combination of the Hubble parameter and the cosmological redshift and provides a null test of dark energy being a cosmological constant Λ. Namely, if the value of Om(z) is the same at different redshifts, then DE ≡ Λ, exactly. The slope of Om(z) can differentiate between different models of dark energy even if the value of the matter density is not accurately known. For DE with an unevolving equation of state, a positive slope of Om(z) is suggestive of Phantom (w < −1) while a negative slope indicates Quintessence (w > −1). The second diagnostic – acceleration probe ¯ q – is the mean value of the deceleration parameter over a small redshift range. It can be used to determine the cosmological redshift at which the universe began to accelerate, again without reference to the current value of the matter density. We apply the Om and ¯ q diagnostics to the Union data set of type Ia supernovae combined with recent data from the cosmic microwave background (WMAP5) and baryon acoustic oscillations.