arXiv subjects

Varun Sahni

Publications and source records attributed to Varun Sahni.

At least 91 records · Page 5Linked to original sources

arXiv2002

Exploring dark energy using the Statefinder

Observations of high redshift supernovae indicate that the universe is accelerating. The hypothesis of `Dark energy' (cosmological constant, scalar field tracker potentials, braneworld models, etc.) has been advanced to explain this phenomenon. Sensitive tests of dark energy which can differentiate between rival models are clearly the need of the hour. The statefinder pair $\lbrace r,s\rbrace$ is a geometrical diagnostic which can play this role. $r$ & $s$ depend upon the third time derivative of the scale factor $\stackrel{...}{a}$ and provide the next logical step in the hierarchy of the cosmological parameter set after $H$ and $q$. The statefinder pair $\lbrace r,s\rbrace$ can be determined to high accuracy from a SNAP type experiment and allows us to successfully differentiate between dark energy models having constant as well as time-varying equations of state.

astro-ph↗

arXiv2002

Supernova Constraints on Braneworld Dark Energy

Braneworld models of dark energy are examined in the light of observations of high redshift type Ia supernovae. Braneworld models admit several novel and even exotic possibilities which include: (i) The effective equation of state of dark energy can be more negative than in LCDM: $w \leq -1$; (ii) A class of braneworld models can encounter a `quiescent' future singularity at which the energy density and the Hubble parameter remain well behaved, but higher derivatives of the expansion factor ($\stackrel{..}{a}$, $\stackrel{...}{a}$ etc.) diverge when the future singularity is reached; (iii) The current acceleration of the universe is a {\em transient feature} in a class of models in which dark energy `disappears' after a certain time, giving rise to a matter dominated universe in the future. Since horizons are absent in such a space-time, a braneworld model with {\em transient acceleration} might help reconcile current supernova-based observations of an accelerating universe with the demands of string/M-theory. A maximum likelihood analysis reveals that braneworld models satisfy the stringent demands imposed by high redshift supernovae and a large region in parameter space agrees marginally better with current observations than LCDM. For instance, models with $w < -1 (> -1)$ provide better agreement with data than LCDM for $Ω_m \ggeq 0.3 (\lleq 0.25)$.

astro-ph↗

arXiv2002

New Vistas in Braneworld Cosmology

Traditionally, higher-dimensional cosmological models have sought to provide a description of the fundamental forces in terms of a unifying geometrical 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 singularity.

gr-qc↗

arXiv2002

New Cosmological Singularities in Braneworld Models

Higher-dimensional braneworld models which contain both bulk and brane curvature terms in the action admit cosmological singularities of rather unusual 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 ($\stackrel{..}{a}$, $\stackrel{...}{a}$ 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.

gr-qc↗

arXiv2002

The Cosmological Constant Problem and Quintessence

I 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 $k^4$. A cutoff at the Planck or electroweak scale leads to a cosmological constant which is, respectively, $10^{123}$ or $10^{55}$ times larger than the observed value, $ł/8πG \simeq 10^{-47}$ GeV$^4$. The absence of a fundamental symmetry which could set the value of $ł$ to either zero or a very small value leads to {\em the cosmological constant problem}. Most cosmological scenario's favour a large time-dependent $ł$-term in the past (in order to generate inflation at $z \gg 10^{10}$), and a small $ł$-term today, to account for the current acceleration of the universe at $z \lleq 1$. Constraints arising from cosmological nucleosynthesis, CMB and structure formation constrain $ł$ to be sub-dominant during most of the intermediate epoch $10^{10} < z < 1$. This leads to the {\em 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 $ł$ and in matter are almost equal. Time varying models of dark energy can, to a certain extent, ameliorate the fine tuning problem (faced by $ł$), 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.

astro-ph↗

arXiv2001

Relic Gravity Waves from Braneworld Inflation

We discuss a scenario in which extra dimensional effects allow a scalar field with a steep potential to play the dual role of the inflaton as well as dark energy (quintessence). The post-inflationary evolution of the universe in this scenario is generically characterised by a `kinetic regime' during which the kinetic energy of the scalar field greatly exceeds its potential energy resulting in a `stiff' equation of state for scalar field matter $P_ϕ\simeq ρ_ϕ$. The kinetic regime precedes the radiation dominated epoch and introduces an important new feature into the spectrum of relic gravity waves created quantum mechanically during inflation. The gravity wave spectrum increases with wavenumber for wavelengths shorter than the comoving horizon scale at the commencement of the radiative regime. This `blue tilt' is a generic feature of models with steep potentials and imposes strong constraints on a class of inflationary braneworld models. Prospects for detection of the gravity wave background by terrestrial and space-borne gravity wave observatories such as LIGO II and LISA are discussed.

gr-qc↗

arXiv2001

Anisotropy dissipation in brane-world inflation

We examine the behavior of an anisotropic brane-world in the presence of inflationary scalar fields. We show that, contrary to naive expectations, a large anisotropy does not adversely affect inflation. On the contrary, a large initial anisotropy introduces more damping into the scalar field equation of motion, resulting in greater inflation. The rapid decay of anisotropy in the brane-world significantly increases the class of initial conditions from which the observed universe could have originated. This generalizes a similar result in general relativity. A unique feature of Bianchi I brane-world cosmology appears to be that for scalar fields with a large kinetic term the initial expansion of the universe is quasi-isotropic. The universe grows more anisotropic during an intermediate transient regime until anisotropy finally disappears during inflationary expansion.

gr-qc↗

arXiv2001

Recycling the universe using scalar fields

We examine the behaviour of a closed oscillating universe filled with a homogeneous scalar field and find that, contrary to naive expectations, such a universe expands to larger volumes during successive expansion epochs. This intriguing behaviour introduces an arrow of time in a system which is time-reversible. The increase in the maximum size of the universe is closely related to the work done on/by the scalar field during one complete oscillatory cycle which, in turn, is related to the asymmetry in the scalar field equation of state during expansion and collapse. Our analysis shows that scalar fields with polynomial potentials $V(ϕ) = λϕ^q$, $q > 1$ lead to a growing oscillation amplitude for the universe: the increase in amplitude between successive oscillations is more significant for smaller values of $q$. Such behaviour allows for the effective recycling of the universe. A recycled universe can be quite old and can resolve the flatness problem. These results have strong bearing on cosmological models in which the role of dark matter is played by a scalar field. They are also relevant for chaotic inflationary models of the early universe since they demonstrate that, even if the universe fails to inflate the first time around, it will eventually do so during future oscillatory cycles. Thus, the space of initial conditions favourable for chaotic inflation increases significantly.

astro-ph↗

arXiv2001

Scalar field models for an accelerating universe

I describe a new class of quintessence+CDM models in which late time scalar field oscillations can give rise to both quintessence and cold dark matter. Additionally, a versatile ansatz for the luminosity distance is used to reconstruct the quintessence equation of state in a model independent manner from observations of high redshift supernovae.

astro-ph↗

arXiv2000

Reconstructing the Cosmic Equation of State from Supernova distances

Observations of high-redshift supernovae indicate that the universe is accelerating. Here we present a {\em model-independent} method for estimating the form of the potential $V(ϕ)$ of the scalar field driving this acceleration, and the associated equation of state $w_ϕ$. Our method is based on a versatile analytical form for the luminosity distance $D_L$, optimized to fit observed distances to distant supernovae and differentiated to yield $V(ϕ)$ and $w_ϕ$. Our results favor $w_ϕ\simeq -1$ at the present epoch, steadily increasing with redshift. A cosmological constant is consistent with our results.

astro-ph↗

arXiv2000

The Case for a Positive Cosmological Lambda-term

Recent observations of Type 1a supernovae indicating an accelerating universe have once more drawn attention to the possible existence, at the present epoch, of a small positive Lambda-term (cosmological constant). In this paper we review both observational and theoretical aspects of a small cosmological Lambda-term. We discuss the current observational situation focusing on cosmological tests of Lambda including the age of the universe, high redshift supernovae, gravitational lensing, galaxy clustering and the cosmic microwave background. We also review the theoretical debate surrounding Lambda: the generation of Lambda in models with spontaneous symmetry breaking and through quantum vacuum polarization effects -- mechanisms which are known to give rise to alarge value of Lambda hence leading to the `cosmological constant problem'. More recent attempts to generate a small cosmological constant at the present epoch using either field theoretic techniques, or by modeling a dynamical Lambda-term by scalar fields are also extensively discussed. Anthropic arguments favouring a small cosmological constant are briefly reviewed. A comprehensive bibliography of recent work on Lambda is provided.

astro-ph↗

arXiv2000

A New Cosmological Model of Quintessence and Dark Matter

We propose a new class of quintessence models in which late times oscillations of a scalar field give rise to an effective equation of state which can be negative and hence drive the observed acceleration of the universe. Our ansatz provides a unified picture of quintessence and a new form of dark matter we call "Frustrated Cold Dark Matter" (FCDM). FCDM inhibits gravitational clustering on small scales and could provide a natural resolution to the core density problem for disc galaxy halos. Since the quintessence field rolls towards a small value, constraints on slow-roll quintessence models are safely circumvented in our model.

astro-ph↗

arXiv1999

Evidence for Filamentarity in the Las Campanas Redshift Survey

We apply Shapefinders, statistical measures of `shape' constructed from two dimensional partial Minkowski functionals, to study the degree of filamentarity in the Las Campanas Redshift Survey (LCRS). In two dimensions, three Minkowski functionals characterise the morphology of an object, they are: its perimeter (L), area (S), and genus. Out of L and S a single dimensionless Shapefinder Statistic, F can be constructed (0 <=F <=1). F acquires extreme values on a circle (F = 0) and a filament (F = 1). Using F, we quantify the extent of filamentarity in the LCRS by comparing our results with a Poisson distribution with similar geometrical properties and having the same selection function as the survey. Our results unambiguously demonstrate that the LCRS displays a high degree of filamentarity both in the Northern and Southern galactic sections a result that is in general agreement with the visual appearance of the catalogue. It is well known that gravitational clustering from Gaussian initial conditions gives rise to the development of non-Gaussianity reflected in the formation of a network-like filamentary structure on supercluster scales. Consequently the fact that the smoothed LCRS catalogue shows properties consistent with those of a Gaussian random field (Colley 1997) whereas the unsmoothed catalogue demonstrates the presence of filamentarity lends strong support to the conjecture that the large scale clustering of galaxies is driven by gravitational instability.

astro-ph↗

arXiv1999

Disentangling the Cosmic Web I: Morphology of Isodensity Contours

We apply Minkowski functionals and various derived measures to decipher the morphological properties of large-scale structure seen in simulations of gravitational evolution. Minkowski functionals of isodensity contours serve as tools to test global properties of the density field. Furthermore, we identify coherent objects at various threshold levels and calculate their partial Minkowski functionals. We propose a set of two derived dimensionless quantities, planarity and filamentarity, which reduce the morphological information in a simple and intuitive way. Several simulations of the gravitational evolution of initial power-law spectra provide a framework for systematic tests of our method.

astro-ph↗

arXiv1998

Does Inflationary Particle Production suggest Omega_m < 1?

We study a class of FRW spacetimes with a nonminimally coupled light massive scalar field. Values of the coupling parameter xi<0 enhance long range power in the vacuum expectation value of the energy-momentum tensor and fundamentally alter the nature of inflationary particle production: the energy density of created particles behaves like an effective cosmological constant, leading generically to Omega_m < 1 in clustered matter and providing a possible resolution of the ``Omega problem'' for low density cosmological models.

hep-ph↗

arXiv1998

Morphology of Clusters and Superclusters in N-body simulations of Cosmological Gravitational Clustering

We analyse shapes of overdense regions (clusters and superclusters) in controlled N-body simulations of gravitational clustering with power law initial spectra P(k) \propto k^n, n = -3, -2, -1, 0. At values of the density just above the percolation transition the number of distinct (isolated) clusters peaks and we use this `natural threshold' to study the shapes and multiplicity function of clusters and superclusters. We find that the extent of both filamentarity and pancakeness increases as the simulation evolves, the former being appreciably larger than the latter at virtually all epochs and for all spectra considered by us. Our results also show that high density regions within very massive clusters/superclusters are likely to be noticeably filamentary or pancake/ribbon-like when compared to the less dense regions within these objects. We make a detailed study of two, moment-based `shape statistics' proposed, respectively, by Babul & Starkman (BS) and Luo & Vishniac (LV) and find that both LV and BS have certain built-in limitations: LV is biased towards oblate structures and tends to overemphasise this property; neither BS nor LV correctly describe the shape of strongly curved or topologically nontrivial objects. For instance, a thin filamentary torus and a ribbon are both described by BS and LV as being pancakes ! By contrast Shapefinders, a new shape diagnostic not constructed from density moments but from Minskowski functionals, does not suffer from these limitations and appears to faithfully reproduce the shapes of both simple and topologically complex objects.

astro-ph↗

arXiv1998

Filaments and Pancakes in the IRAS 1.2 Jy Redshift Catalogue

We explore shapes of clusters and superclusters in the IRAS 1.2 Jy redshift survey with three reconstructions spanning the range β= 0.1, 0.5, 1.0, where β= Ω^{0.6}/b, b is the bias factor and Ωthe present value of the dimensionless matter density. Comparing our results to Gaussian randomized reconstructions of the IRAS catalogue, we find structures having both planar and filamentary properties. For β= 0.5, 1.0 the largest structures in the survey have a distinct tendency to be filament-like} in general agreement with the results of N-body simulations.

astro-ph↗

arXiv1998

Shapefinders: A new shape diagnostic for large scale structure

We construct a set of shape-finders which determine shapes of compact surfaces (iso-density surfaces in galaxy surveys or N-body simulations) without fitting them to ellipsoidal configurations as done earlier. The new indicators arise from simple, geometrical considerations and are derived from fundamental properties of a surface such as its volume, surface area, integrated mean curvature and connectivity characterized by the Genus. These `Shapefinders' could be used to diagnose the presence of filaments, pancakes and ribbons in large scale structure. Their lower-dimensional generalization may be useful for the study of two-dimensional distributions such as temperature maps of the Cosmic Microwave Background.

astro-ph↗