Non-vanishing Cosmological Constant Research Articles

Wavefunction of the Universe and Chern–Simons perturbation theory

The Chern–Simons exact solution of four-dimensional quantum gravity with nonvanishing cosmological constant is presented in metric variables as the partition function of Chern–Simons theory with nontrivial source. The perturbative expansion is given, and the wavefunction is computed to the lowest order of approximation for the Cauchy surface which is topologically a 3-sphere. The state is well-defined even at degenerate and vanishing values of the dreibein. Reality conditions for the Ashtekar variables are also taken into account, and remarkable features of the Chern–Simons state and their relevance to cosmology are pointed out.

Quintessence and Dark Matter Created by Weyl–Dirac Geometry

A spatially closed universe undergoing at present accelerated expansion, having a non-vanishing cosmological constant, and filled with luminous- and dark matter is described in terms of the Integrable Weyl–Dirac theory. It is shown that, during the dust-dominated period, dark matter and the quintessence pressure, the latter giving rise to acceleration: both are created by the Dirac gauge function. The behavior of two models: a nearly flat one and a well closed are considered in appropriate gauges, and plausible scenarios are obtained. The outcome of the present paper, together with results of a previous work,(31) provide a geometrically based, classical, singularity-free model of the universe, that has originated from a pure geometric Weyl–Dirac entity, passed a prematter period, the radiation-dominated era, and continues its development in the present dust period.

Stability analysis of anisotropic inflationary cosmology

The stability analysis of an anisotropic inflationary universe of the four dimensional Neveu-Schwarz--Neveu-Schwarz string model with a nonvanishing cosmological constant is discussed in this paper. The accelerating expansion solution found earlier is shown to be stable against the perturbations with respect to the dilaton and axion fields once the dilaton field falls close to the local minimum of the symmetry-breaking potential. This indicates that the Bianchi I space tends to evolve to an isotropic flat Friedmann-Robertson-Walker space. This expanding solution is also shown to be stable against the perturbation with respect to anisotropic spatial directions.

Boundary description of planckian scattering in curved spacetimes

We show that for an eikonal limit of gravity in a space-time of any dimension with a non-vanishing cosmological constant, the Einstein -- Hilbert action reduces to a boundary action. This boundary action describes the interaction of shock-waves up to the point of evolution at which the forward light-cone of a collision meets the boundary of the space-time. The conclusions are quite general and in particular generalize the previous work of E. and H. Verlinde. The role of the off-diagonal Einstein action in removing the bulk part of the action is emphasised. We discuss the sense in which our result is a particular example of holography and also the relation of our solutions in $AdS$ to those of Horowitz and Itzhaki.

Shell crossing in generalized Tolman-Bondi spacetimes

We study the occurrence of shell crossing in spherical weakly charged dust collapse in the presence of a non-vanishing cosmological constant. We find that shell crossing always occurs from generic time-symmetric regular initial data, near the center of the matter configuration. For non-time-symmetric initial data, the occurrence---or lack thereof---of shell crossing is determined by the initial velocity profile, for a given mass and charge distribution. Physically reasonable initial data inevitably leads to shell crossing (near the center) before the minimum bounce radius is reached.

Substructure and Halo Density Profiles in a Warm Dark Matter Cosmology

We performed a series of high-resolution collisionless N-body simulations designed to study the substructure of Milky Way-size galactic halos (host halos) and the density profiles of halos in a warm dark matter (WDM) scenario with a nonvanishing cosmological constant. The virial masses of the host halos range from 3.5 × 1012 to 1.7 × 1012 h-1 M☉, and they have more than 105 particles each. A key feature of the WDM power spectrum is the free-streaming length Rf,WDM, which fixes an additional parameter for the model of structure formation. We analyze the substructure of host halos using three Rf,WDM values: 0.2, 0.1, and 0.05 Mpc, and compare results to the predictions of the cold dark matter (CDM) model. We find that guest halos (satellites) do form in the WDM scenario, but are more easily destroyed by dynamical friction and tidal disruption than their counterparts in a CDM model. The small number of guest halos that we find in the WDM models with respect to the CDM one is the result of a lower guest halo accretion and a higher satellite destruction rate. These two phenomena operate almost with the same intensity in delivering a reduced number of guest halos at z = 0. For the model with Rf,WDM = 0.1 Mpc, the number of accreted small halos is a factor of 2.5 below that of the CDM model, while the fraction of destroyed satellites is almost twice as large as that of the CDM model. The larger the Rf,WDM value, the greater the size of these two effects and the smaller the abundance of satellites. Under the assumption that each guest halo hosts a luminous galaxy, we find that the observed circular velocity function of satellites around the Milky Way and Andromeda is well described by the Rf,WDM = 0.1 Mpc WDM model. In the Rf,WDM = 0.1-0.2 Mpc models, the surviving guest halos at z = 0, whose masses are in the range Mh ≈ 109-1011 h-1 M☉, have an average concentration parameter c1/5 = r(Mh)/r(Mh/5), which is approximately twice as small as that of the corresponding CDM guest halos. This difference very likely produces the higher satellite destruction rate found in the WDM models. The density profile of host halos is well described by the Navarro, Frenk, & White (NFW) fit, whereas guest halos show a wide variety of density profiles. A tendency to form shallow cores is not evident; the profiles, however, are limited by a poor mass resolution in the innermost regions where shallow cores could be expected.

Inflationary universe in higher derivative induced gravity

In an induced-gravity model, the stability condition of an inflationary slow-rollover solution is shown to be $\phi_0 \partial_{\phi_0}V(\phi_0)=4V(\phi_0)$. The presence of higher derivative terms will, however, act against the stability of this expanding solution unless further constraints on the field parameters are imposed. We find that these models will acquire a non-vanishing cosmological constant at the end of inflation. Some models are analyzed for their implication to the early universe.

Triad representation of the Chern-Simons state in quantum gravity

We investigate a triad representation of the Chern-Simons state of quantum gravity with a non-vanishing cosmological constant. It is shown that the Chern-Simons state, which is a well-known exact wavefunctional within the Ashtekar theory, can be transformed to the real triad representation by means of a suitably generalized Fourier transformation, yielding a complex integral representation for the corresponding state in the triad variables. It is found that topologically inequivalent choices for the complex integration contour give rise to linearly independent wavefunctionals in the triad representation, which all arise from the one Chern-Simons state in the Ashtekar variables. For a suitable choice of the normalization factor, these states turn out to be gauge-invariant under arbitrary, even topologically non-trivial gauge-transformations. Explicit analytical expressions for the wavefunctionals in the triad representation can be obtained in several interesting asymptotic parameter regimes, and the associated semiclassical 4-geometries are discussed. In restriction to Bianchi-type homogeneous 3-metrics, we compare our results with earlier discussions of homogeneous cosmological models. Moreover, we define an inner product on the Hilbert space of quantum gravity, and choose a natural gauge-condition fixing the time-gauge. With respect to this particular inner product, the Chern-Simons state of quantum gravity turns out to be a non-normalizable wavefunctional.

Bulk supersymmetry and brane cosmological constant

We consider a recent proposal to solve the cosmological constant problem within the context of brane world scenarios with infinite volume extra dimensions. In such theories bulk can be supersymmetric even if brane supersymmetry is completely broken. We propose a setup where unbroken bulk supersymmetry appears to protect the brane cosmological constant. This is due to a non-trivial scalar potential in the bulk which implies a non-trivial profile for a bulk scalar field. In the presence of the latter bulk supersymmetry appears to be incompatible with non-vanishing brane cosmological constant. Moreover, in this setup the corresponding domain wall interpolates between an AdS and the Minkowski vacua, so that the weak energy condition is not violated.

Neutralino relic density in a universe with a nonvanishing cosmological constant

We discuss the relic density of the lightest of the supersymmetric particles in view of new cosmological data, which favor the concept of an accelerating universe with a nonvanishing cosmological constant. Recent astrophysical observations provide us with very precise values of the relevant cosmological parameters. Certain of these parameters have direct implications on particle physics, e.g., the value of matter density, which in conjunction with electroweak precision data put severe constraints on the supersymmetry breaking scale. In the context of the constrained minimal supersymmetric standard model (CMSSM) such limits read as ${M}_{1/2}\ensuremath{\simeq}300\mathrm{GeV}--340\mathrm{}\mathrm{GeV},$ ${m}_{0}\ensuremath{\simeq}80\mathrm{GeV}--130\mathrm{}\mathrm{GeV}.$ Within the context of the CMSSM a way to avoid these constraints is either to go to the large $\mathrm{tan}\ensuremath{\beta}$ and $\ensuremath{\mu}>0$ region, or make ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\tau}}}_{R},$ the next to lightest supersymmetric particle (LSP), be almost degenerate in mass with the LSP.

Evidence for nonvanishing cosmological constant in nonSUSY superstring models

We reanalyse the computation of the cosmological constant $\Lambda$ at two loops in recently proposed Superstring models without massless gravitini, both in the theta-function based formalism and by a detailed computation in the more explicit hyperelliptic description of the underlying genus two Riemann surface. $\Lambda$ is expressed as the integral over the surface moduli of an amplitude which is zero if susy is not completely broken, but we find it to be nonvanishing in the susy breaking models which can be given an explicitly workable fermionic formulation. Thus unfortunately the issue of getting realistic and perturbatively viable models from Superstring Theory remains open.

Explicit Analytic Solutions of Classical Scalar Field Cosmology

A class of explicit and exact solutions is obtained for the equations governingthe evolution of spatially flat FLRW spacetimes in interaction with a classicalmassive scalar field in the presence of conformal coupling and of a quarticself-interaction potential. These solutions only exist for nonvanishing cosmologicalconstant. The equation of state is calculated self-consistently.

Tachyon-free non-supersymmetric type IIB orientifolds via brane-antibrane systems

We derive the rules to construct type IIB compact orientifolds in six and four dimensions including D-branes and anti-D-branes. Even though the models are non-supersymmetric due to the presence of the anti-D-branes, we show that it is easy to construct large classes of models free of tachyons. Brane-antibrane annihilation can be prevented for instance by considering models with branes and antibranes stuck at different fixed points in the compact space. We construct several anomaly-free and tachyon-free six-dimensional orientifolds containing D9-branes and anti-D5-branes. This setup allows to construct four-dimensional chiral models with supersymmetry unbroken in the bulk and in some D-brane sectors, whereas supersymmetry is broken (at the string scale) in some `hidden' anti-D-brane sector. We present several explicit models of this kind. We also comment on the role of the non-cancelled attractive brane-antibrane forces and the non-vanishing cosmological constant, as providing interesting dynamics for the geometric moduli and the dilaton, which may contribute to their stabilization.

Neutralino relic density with a cosmological constant confronts electroweak precision measurements

We discuss the relic density of the lightest of the supersymmetric particles (LSP) in view of new cosmological data, which favour the concept of an accelerating Universe with a non-vanishing cosmological constant. The new bound on the Cold Dark Matter density, Ω CDM h 0 2≲0.22 , puts stringent constraints on supersymmetry preferring low supersymmetry breaking scales, in sharp contrast to electroweak precision measurements favouring large supersymmetry breaking scales. Supersymmetric predictions are in agreement with cosmological data and electroweak precision data in the window of the parameter space: m 0<200 GeV , 300 GeV<M 1/2<400 GeV , putting bounds on sparticle masses, which may be evaded if m LSP <m τ ̃ R ≲1.2 m LSP .

Curvature invariants in type-III spacetimes

The results of Bicák and Pravda (1998 Class. Quantum Grav. 15 1539) are generalized for vacuum type-III solutions with, in general, a non-vanishing cosmological constant . It is shown that all curvature invariants containing derivatives of the Weyl tensor vanish if a type-III spacetime admits a non-expanding and non-twisting null geodesic congruence. A non-vanishing curvature invariant containing first derivatives of the Weyl tensor is found in the case of type-III spacetime with expansion or twist.

Conformally coupled induced gravity with gradient torsion

It is found that conformally coupled induced gravity with gradient torsion gives a dilaton gravity in Riemann geometry. In the Einstein frame of the dilaton gravity the conformal symmetry is hidden and a non-vanishing cosmological constant is not plausible due to the constraint of the conformal coupling.

Does loop quantum gravity imply Λ=0?

We suggest that in a recently proposed framework for quantum gravity, where Vassiliev invariants span the the space of states, the latter is dramatically reduced if one has a non-vanishing cosmological constant. This naturally suggests that the initial state of the universe should have been one with Λ=0.

Curvature invariants in type-N spacetimes

Scalar curvature invariants are studied in type-N solutions of the vacuum Einstein equations with, in general, a non-vanishing cosmological constant . Zeroth-order invariants, which include only the metric and Weyl (Riemann) tensor, either vanish or are constants depending on . All higher-order invariants containing covariant derivatives of the Weyl (Riemann) tensor are also shown to be trivial if a type-N spacetime admits a non-expanding and non-twisting null geodesic congruence. However, in the case of expanding type-N spacetimes we discover a non-vanishing scalar invariant, which is quartic in the second derivatives of the Riemann tensor. We use this invariant to demonstrate that both the linearized and third-order type-N twisting solutions recently discussed in literature contain singularities at large distances and thus cannot describe radiation fields outside bounded sources.

Strong Gravitational Lensing and Velocity Function as Tools to Probe Cosmological Parameters: Current Constraints and Future Predictions

Constraints on cosmological models from strong gravitational lensing statistics are investigated. We pay particular attention to the role of the velocity function in the calculation of the lensing probability. The velocity function derived from the observed galaxy luminosity function, which is used in most previous work, is unable to predict the large separation lensing events. In this paper, we also use the Press-Schechter theory to construct a velocity function theoretically. Model predictions are compared with the observed velocity function and the HST snapshot survey. Comparison with the latter observation shows that the predictions based on the theoretical velocity function are consistent with the observed large separation events in COBE normalized low-density models, especially with a non-vanishing cosmological constant. Adopting the COBE normalization, however, we could find no model which simultaneously satisfies both the observed velocity function and the HST snapshot survey. We systematically investigate various uncertainties in the gravitational lensing statistics including finite core radius, the distance formula, magnification bias, and dust obscuration. The results are very sensitive to these effects as well as theoretical models for the velocity function, implying that current limits on the cosmological parameters should be interpreted with caution. Predictions for future surveys are also presented.

Problems for supersymmetry breaking by the dilaton in strings from charge and color breaking

The general constraints on the parameter space of soft-breaking terms, in order to avoid dangerous charge and color breaking minima, are applied to the four-dimensional string scenario where the dilaton is the source of supersymmetry breaking (dilaton-dominated limit). The results indicate that the whole parameter space is essentially excluded on these grounds after imposing the present experimental data on the top mass. The inclusion of a non-vanishing cosmological constant does not improve substantially the prospects. Possible way-outs to this situation are briefly discussed.