arXiv subjects

Varun Sahni

Publications and source records attributed to Varun Sahni.

At least 73 records · Page 4Linked to original sources

arXiv2007

Smoothing Supernova Data to Reconstruct the Expansion History of the Universe and its Age

We propose a non-parametric method of smoothing supernova data over redshift using a Gaussian kernel in order to reconstruct important cosmological quantities including H(z) and w(z) in a model independent manner. This method is shown to be successful in discriminating between different models of dark energy when the quality of data is commensurate with that expected from the future SuperNova Acceleration Probe (SNAP). We find that the Hubble parameter is especially well-determined and useful for this purpose. The look back time of the universe may also be determined to a very high degree of accuracy (\lleq 0.2 %) in this method. By refining the method, it is also possible to obtain reasonable bounds on the equation of state of dark energy. We explore a new diagnostic of dark energy-- the `w-probe'-- which can be calculated from the first derivative of the data. We find that this diagnostic is reconstructed extremely accurately for different reconstruction methods even if Ω_m is marginalized over. The w-probe can be used to successfully distinguish between $Λ$CDM and other models of dark energy to a high degree of accuracy.

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arXiv2006

Exploring the Properties of Dark Energy Using Type Ia Supernovae and Other Datasets

We reconstruct dark energy properties from two complementary supernova datasets -- the newly released Gold+HST sample and SNLS. The results obtained are consistent with standard $Λ$CDM model within $2σ$ error bars although the Gold+HST data favour evolving dark energy slightly more than SNLS. Using complementary data from baryon acoustic oscillations and the cosmic microwave background to constrain dark energy, we find that our results in this case are strongly dependent on the present value of the matter density $Ω_m$. Consequently, no firm conclusions regarding constancy or variability of dark energy density can be drawn from these data alone unless the value of $Ω_m$ is known to an accuracy of a few percent. However, possible variability is significantly restricted if this data is used in conjunction with supernova data.

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arXiv2006

Reconstructing Dark Energy

This review summarizes recent attempts to reconstruct the expansion history of the Universe 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.

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arXiv2006

Quantum effects, soft singularities and the fate of the universe in a braneworld cosmology

We examine a class of braneworld models in which the expanding universe encounters a "quiescent" future singularity. At a quiescent singularity, the energy density and pressure of the cosmic fluid as well as the Hubble parameter remain finite while all derivatives of the Hubble parameter diverge (i.e., ${\dot H}$, ${\ddot H}$, etc. $\to \infty$). Since the Kretschmann invariant diverges ($R_{iklm}R^{iklm} \to \infty$) at the singularity, one expects quantum effects to play an important role as the quiescent singularity is approached. We explore the effects of vacuum polarization due to massless conformally coupled fields near the singularity and show that these can either cause the universe to recollapse or, else, lead to a softer singularity at which $H$, ${\dot H}$, and ${\ddot H}$ remain finite while ${\dddot H}$ and higher derivatives of the Hubble parameter diverge. An important aspect of the quiescent singularity is that it is encountered in regions of low density, which has obvious implications for a universe consisting of a cosmic web of high and low density regions -- superclusters and voids. In addition to vacuum polarization, the effects of quantum particle production of non-conformal fields are also likely to be important. A preliminary examination shows that intense particle production can lead to an accelerating universe whose Hubble parameter shows oscillations about a constant value.

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arXiv2006

Confronting Braneworld Cosmology with Supernova data and Baryon Oscillations

Braneworld cosmology has several attractive and distinctive features. For instance the effective equation of state in braneworld models can be both quintessence-like (w_0 \geq -1) as well as phantom-like (w_0 \leq -1). Models with w_0 \geq -1 (w_0 \leq -1) are referred to as Brane 2 (Brane 1) and correspond to complementary embeddings of the brane in the bulk. (The equation of state in Brane 1 can successfully cross the `phantom divide' at w = -1.) In this paper we compare the predictions of braneworld models to two recently released supernova data sets: the `Gold' data (Riess et al, 2004) and the data from the Supernova Legacy Survey (SNLS) (Astier et al, 2005). We also incorporate the recent discovery of the baryon acoustic peak in the Sloan Digital Sky Survey (Eisenstein et al, 2005) into our analysis. Our main results are that braneworld models satisfy both sets of SNe data. Brane 1 (with w_0 \leq -1) shows very good agreement with data for values of the matter density bounded {\em from below}: Ω_m \geq 0.25 (Gold) and $Ω_m \geq 0.2 (SNLS). On the other hand Brane 2 (with w_0 \geq -1) shows excellent agreement with data for values of the matter density which are bounded {\em from above}: Ω_m \leq 0.45 (Gold) and Ω_m \leq 0.35 (SNLS). The DGP model is excluded at 3σby SNLS and at 1σby the Gold dataset. Braneworld models with future `quiescent' singularities (at which the Hubble parameter and the matter density remain finite but higher derivatives of the expansion factor diverge) are excluded by both datasets.

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arXiv2005

Cosmic Mimicry: Is LCDM a Braneworld in Disguise ?

For a broad range of parameter values, braneworld models display a remarkable property which we call cosmic mimicry. Cosmic mimicry is characterized by the fact that, at low redshifts, the Hubble parameter in the braneworld model is virtually indistinguishable from that in the LCDM cosmology. An important point to note is that the Ω_m parameters in the braneworld model and in the LCDM cosmology can nevertheless be quite different. Thus, at high redshifts (early times), the braneworld asymptotically expands like a matter-dominated universe with the value of Ω_m inferred from the observations of the local matter density. At low redshifts (late times), the braneworld model behaves almost exactly like the LCDM model but with a renormalized value of the cosmological density parameter Ω_m^{LCDM}. The redshift which characterizes cosmic mimicry is related to the parameters in the higher-dimensional braneworld Lagrangian. Cosmic mimicry is a natural consequence of the scale-dependence of gravity in braneworld models. The change in the value of the cosmological density parameter is shown to be related to the spatial dependence of the effective gravitational constant in braneworld theory. A subclass of mimicry models lead to an older age of the universe and also predict a redshift of reionization which is lower than z_{reion} \simeq 17 in the LCDM cosmology. These models might therefore provide a background cosmology which is in better agreement both with the observed quasar abundance at z \gsim 4 and with the large optical depth to reionization measured by the Wilkinson Microwave Anisotropy Probe.

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arXiv2005

Cosmological Surprises from Braneworld models of Dark Energy

Properties of Braneworld models of dark energy are reviewed. Braneworld models admit the following interesting possibilities: (i) The effective equation of state can be w < -1 as well as w > -1. In the former case the expansion of the universe is well behaved at all times and the universe does not run into a future `Big Rip' singularity which is usually encountered by Phantom models. (ii) For a class of Braneworld models the acceleration of the universe can be a transient phenomenon. In this case the current acceleration of the universe is sandwiched between two matter dominated epochs. Such a braneworld does not have a horizon in contrast to LCDM and most Quintessence models. (iii) For a specific set of parameter values the universe can either originate from, or end its existence in a Quiescent singularity, at which the density, pressure and Hubble parameter remain finite, while the deceleration parameter and all invariants of the Riemann tensor diverge to infinity within a finite interval of cosmic time. (iv) Braneworld models of dark energy can loiter at high redshifts: $6 \lleq z \lleq 40$. The Hubble parameter decreasesduring the loitering epoch relative to its value in LCDM. As a result the age of the universe at loitering dramatically increases and this is expected to boost the formation of high redshift gravitationally bound systems such as $10^9 M_\odot$ black holes at $z \sim 6$ and lower-mass black holes and/or Population III stars at $z > 10$, whose existence could be problematic within the LCDM scenario. (v) Braneworld models with a time-like extra dimension bounce at early times thereby avoiding the initial `Big Bang singularity'. (vi) Both Inflation and Dark Energy can be successfully unified within a single scheme (Quintessential Inflation).

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arXiv2005

Did the Universe loiter at high redshifts ?

We show that loitering at high redshifts ($z \gsim 6$) can easily arise in braneworld models of dark energy which, in addition to being spatially flat, also accelerate at late times. Loitering is characterized by the fact that the Hubble parameter dips in value over a narrow redshift range which we shall refer to as the `loitering epoch'. During loitering, density perturbations are expected to grow rapidly. In addition, since the expansion of the universe slows down, its age near loitering dramatically increases. An early epoch of loitering is expected to boost the formation of high redshift gravitationally bound systems such as $10^9 M_\odot$ black holes at $z \sim 6$ and lower-mass black holes and/or Population III stars at $z > 10$, whose existence could be problematic within the LCDM scenario. Loitering models also help to reduce the redshift of reionization from its currently (high) value of $z_{\rm reion} \simeq 17$ in LCDM cosmology, thus alleviating a significant source of tension between observations of the high-redshift universe and theoretical model building. Currently a loitering universe accelerates with an effective equation of state $w < -1$ thus mimicking phantom dark energy. Unlike phantom, however, the late-time expansion of the universe in our model is singularity free, and a universe that loitered in the past will approach a LCDM model asymptotically in the distant future.

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arXiv2005

Exploring the Geometry, Topology and Morphology of Large Scale Structure using Minkowski Functionals

Modern redshift surveys such as the 2 degree field Galaxy Redshift Survey (2dFGRS) and the Sloan Digital Sky Survey (SDSS) reveal the fully 3 dimensional distribution of a million or so galaxies over a large cosmological volume. Visually galaxies appear to be distributed along sheet-like and/or filamentary superclusters. The CfA Great Wall, Southern Great Wall and the recently discovered SDSS Great Wall are very spectacular superclusters. Clearly theoretical predictions for galaxy clustering must be tested against these rich datasets. This can be achieved by means of the Minkowski Functionals (MFs). A MF-based approach provides an excellent description of superclusters and voids and allows one to quantify the properties of the cosmic web. In this review we give a summary of the progress made in this direction. After reviewing the status of observations and of numerical simulations, we comment upon the nature of bias which serves as a link between theoretical predictions and observations. We also summarise the methods developed for efficient numerical estimation of MFs for cosmological datasets and list several important results obtained using these methods. Specifically, we stress the discriminatory power of MFs and of the derived morphological statistics, the Shapefinders. Shapefinders are an excellent tool with which to study the shapes and sizes of superclusters and voids. We also discuss some of the important effects of scale-dependent bias which are brought out by a MF-based study of the mock catalogues of galaxies. Such effects, we note, should be accounted for before comparing theoretical models with observations.

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arXiv2004

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 without assuming the prior $w(z) \geq -1$ (in contrast to previous studies). We find that dark energy evolves rapidly and metamorphoses from dust-like behaviour at high $z$ ($w \simeq 0$ at $z \sim 1$) to a strongly negative equation of state at present ($w \lleq -1$ at $z \simeq 0$). Dark energy 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 $ρ+ p \geq 0$. Invoking this prior considerably weakens the rate of growth of $w(z)$. These results demonstrate that dark energy 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.

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arXiv2004

Rejoinder to "No Evidence of Dark Energy Metamorphosis", astro-ph/0404468

In a recent paper (astro-ph/0311364) Alam et al argued that the SNe data of Tonry et al 2003 and Barris et al 2003 appear to favour DE which evolves in time, provided no other priors are invoked. (The effect of invoking priors such as the age of the Universe, the values of $H_0$ and $Ω_m$ and CMB/LSS observations could modify this conclusion, as demonstrated in astro-ph/0403687 and other recent papers.) The approach adopted by Alam et al to reconstruct the properties of DE was severely (and, as we shall show below -- unfairly) criticized by Jönsson et al in astro-ph/0404468. In this paper we re-examine the parametrisation used in astro-ph/0311364 and show that, contrary to the claims of Jönsson et al, the results obtained from this reconstruction are robust and therefore representative of the true nature of dark energy.

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arXiv2004

The case for dynamical dark energy revisited

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 $Ω_{0m}$ and $h$, DE which evolves with time provides a better fit to the SNe data than $Λ$CDM. 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 $w_0 < -1$ at the present epoch and the transition from deceleration to acceleration occurs at $z_T = 0.39 \pm 0.03$. However, DE evolution becomes weaker if the $Λ$CDM based CMB results $Ω_{0m} = 0.27 \pm 0.04$, $h = 0.71 \pm 0.06$ are incorporated in the analysis. In this case, $z_T = 0.57 \pm 0.07$. Our results also show that the extent of DE evolution is sensitive to the manner in which the supernova data is sampled.

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arXiv2003

Braneworld models of dark energy

We 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 enter 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 luminosity distance in LCDM. Whereas models with $d_L \leq d_L(\rm LCDM)$ imply $w = p/ρ\geq -1$ and have frequently been discussed in the literature, models with $d_L > d_L(\rm LCDM)$ have traditionally been ignored, perhaps because within the general-relativistic framework, the luminosity distance has this property {\em only if} the equation of state of matter is strongly negative ($w < -1$). Matter with $w < -1$ is beset with a host of undesirable properties, which makes this model of dark energy unattractive within the conventional framework. Braneworld models, on the other hand, have the capacity to endow dark energy with exciting new possibilities without suffering from the problems faced by models with $w < -1$. For a subclass of parameter values, braneworld dark energy and the acceleration of the universe are {\em transient} phenomena. In these models, the universe, after the current period of acceleration, re-enters the matter dominated regime so that the deceleration parameter $q(t) \to 0.5$ when $t \gg t_0$, where $t_0$ is the present epoch. Such models could help reconcile an accelerating universe with the requirements of string/M-theory.

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arXiv2003

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 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 $w \geq -0.9$ and Chaplygin gas models with $κ\leq 15$ at the $3σ$ level if the value of $\om$ is known exactly. The Statefinder gives reasonable results even when the value of $\om$ is known to only $\sim 20%$ accuracy. In this case, marginalizing over $\om$ and assuming a fiducial LCDM model allows us to rule out quintessence with $w \geq -0.85$ and the Chaplygin gas with $κ\leq 7$ (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 $z \lleq 10$.

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arXiv2003

Can dark energy be decaying?

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 {\em 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 $\lbrace m, ϕ_0\rbrace$ plane ($m$ is the tachyon mass modulus and $ϕ_0$ the initial scalar field value; $m\sim H_0$ and $ϕ_0\sim M_P$ by order of magnitude). For the first model, the time for the potential to drop to half its maximum value is larger than $\sim 8$ Gyrs. In the case of the cosine potential, the time left until the universe collapses is always greater than $\sim 18$ Gyrs (both estimates are presented for $\om = 0.3$, $m/H_0 \sim 1$, $H_0 \simeq 70$ km/sec/Mpc, and at the 95.4% confidence level).

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arXiv2003

Measuring the Geometry and Topology of Large Scale Structure using SURFGEN: Methodology and Preliminary Results

We present 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, which generates a triangulated surface from a discrete data set representing (say) the distribution of galaxies in real (or redshift) space. Four Minkowski functionals -- surface area, volume, extrinsic curvature and genus -- describe the geometry and topology of the supercluster-void network. Ratio's of Minkowski functionals -- Shapefinders -- provide us with an excellent diagnostic of three dimensional shapes of clusters, superclusters and voids. Minkowski functionals and Shapefinders are determined for a triangulated iso-density surface using SURFGEN. SURFGEN is tested against both simply and multiply connected eikonal surfaces such as triaxial ellipsoids and tori. Remarkably, the first three Minkowski functionals are computed to better than 1% accuracy while the fourth (genus) is known exactly. SURFGEN also gives excellent results when applied to Gaussian random fields. Our results indicate that the surface modelling scheme SURFGEN is accurate and robust and can successfully be used to quantify the topology and morphology of the supercluster-void network in the universe. We apply SURFGEN to three cosmological models, $Ł$CDM, $\T$CDM and SCDM and obtain interesting new results pertaining to the geometry, morphology and topology of large scale structure.

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arXiv2003

Statefinder -- a new geometrical diagnostic of dark energy

We introduce a new cosmological diagnostic pair $\lbrace r,s\rbrace$ called Statefinder. The Statefinder is dimensionless and, like the Hubble and deceleration parameters $H(z)$ and $q(z)$, is constructed from the scale factor of the Universe and its derivatives only. The parameter $r(z)$ forms the next step in the hierarchy of geometrical cosmological parameters used to study the Universe after $H$ and $q$, while the parameter $s(z)$ is a linear combination of $q$ and $r$ chosen in such a way that it does not depend upon the dark energy density $Ω_X(z)$. The Statefinder pair $\lbrace r,s\rbrace$ is algebraically related to the the dark energy pressure-to-energy ratio $w=p/ε$ and its time derivative, and sheds light on the nature of dark energy/quintessence. Its properties allow to usefully differentiate between different forms of dark energy with constant and variable $w$, including a cosmological constant ($w = -1$). The Statefinder pair can be determined to very good accuracy from a SNAP type experiment.

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arXiv2003

Bouncing Braneworlds

We study cosmological braneworld models with a single timelike extra dimension. Such models admit the intriguing possibility that a contracting braneworld experiences a natural bounce without ever reaching a singular state. This feature persists in the case of anisotropic braneworlds under some additional and not very restrictive assumptions. Generalizing our study to braneworld models containing an induced brane curvature term, we find that a FRW-type singularity is once again absent if the bulk extra dimension is timelike. In this case, the universe either has a non-singular origin or commences its expansion from a quasi-singular state during which both the Hubble parameter and the energy density and pressure remain finite while the curvature tensor diverges. The non-singular and quasi-singular behaviour which we have discovered differs both qualitatively and quantitatively from what is usually observed in braneworld models with spacelike extra dimensions and could have interesting cosmological implications.

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