Non-zero Cosmological Constant Research Articles

Expanding impulsive gravitational waves

We demonstrate explicitly that the known solutions for expanding impulsive spherical gravitational waves that have been obtained by a `cut and paste' method may be considered to be impulsive limits of the Robinson-Trautman vacuum type-N solutions. We extend these results to all the generically distinct subclasses of these solutions in Minkowski, de Sitter and anti-de Sitter backgrounds. For these we express the solutions in terms of a continuous metric. Finally, we also extend the class of spherical shock gravitational waves to include a non-zero cosmological constant.

On Zero‐Point Fluctuations, the Cosmological Constant, and the Graviton Mass

Recently attempts have been made to link vacuum zero-point fields (ZPF), with a nonzero cosmological constant (Λ), which is now treated as a cosmological free variable to be determined by observations. In another recent paper, Λ is related to a graviton mass. This is shown to be incorrect. Flat space propagators for both massless and massive spin-2 particles can be written (independently of gravity) in the context of flat space wave equations. However, they do not correspond to full general relativity with a graviton mass.

Measuring and modelling the redshift evolution of clustering: the Hubble Deep Field North

ABSTRA C T The evolution of galaxy clustering from za 0t oz . 4:5 is analysed using the angular correlation function and the photometric redshift distribution of galaxies brighter than IAB < 28:5 in the Hubble Deep Field North. The reliability of the photometric redshift estimates is discussed on the basis of the available spectroscopic redshifts, comparing different codes and investigating the effects of photometric errors. The redshift bins in which the clustering properties are measured are then optimized to take into account the uncertainties of the photometric redshifts. The results show that the comoving correlation length r0 has a small decrease in the range 0 & z & 1 followed by an increase at higher z. We compare these results with the theoretical predictions of a variety of cosmological models belonging to the general class of Cold Dark Matter scenarios, including Einstein‐de Sitter models, an open model and a flat model with non-zero cosmological constant. Comparison with the expected mass clustering evolution indicates that the observed high-redshift galaxies are biased tracers of the dark matter with an effective bias b strongly increasing with redshift. Assuming an Einstein‐de Sitter universe, we obtain b . 2: 5a tz . 2 and b . 5a tz . 4. These results support theoretical scenarios of biased galaxy formation in which the galaxies observed at high redshift are preferentially located in more massive haloes. Moreover, they suggest that the usual parameterization of the clustering evolution as jOr; zUajOr; 0UO1 1 zU 2O31eU is not a good description for any value of e . Comparison of the clustering amplitudes that we measured at z . 3 with those reported by Adelberger et al. and Giavalisco et al., based on a different selection, suggests that the clustering depends on the abundance of the objects: more abundant objects are less clustered, as expected in the paradigm of hierarchical galaxy formation. The strong clustering and high bias measured at z . 3 are consistent with the expected density of massive haloes predicted in the frame of the various cosmologies considered here. At z . 4, the strong clustering observed in the Hubble Deep Field requires a significant fraction of massive haloes to be already formed by that epoch. This feature could be a discriminant test for the cosmological parameters if confirmed by future observations.

Some properties of the Schwarzschild–de Sitter and Schwarzschild–anti-de Sitter spacetimes

Properties of the Schwarzschild--de Sitter and Schwarzschild--anti-de Sitter spacetimes are characterized by three phenomena, namely, by the ``effective potential'' of the motion of test particles and photons, the photon escape cones, and the embedding diagrams of $t=\mathrm{const}$ sections of central planes of both the ordinary and optical reference geometry of these spacetimes. The phenomena are related to the corresponding phenomena of the Schwarzschild spacetime, and differences caused by the asymptotic structure of the spacetimes with a nonzero cosmological constant are discussed. The properties of the embedding diagrams of the optical geometry are related to the dynamical behavior of test particles. The limits of the embeddability of the optical geometry are given and compared with the limits on the outer radius of the interior solutions of Einstein's equations with a nonzero cosmological constant for static, spherically symmetric configurations of uniform density. It is shown that, contrary to the pure Schwarzschild case, these limits do not fully coincide for repulsive cosmological constants.

Ages of Giant Elliptical Galaxies as Evidence for the Cosmological Constant

There is a compelling evidence for old ages of giant elliptical galaxies, about 3 Gyrs older than our Galaxy, from space ultraviolet observations and new population synthesis models. Alternative interpretation requires ad-hoc assumptions yet it produces poor fitting to observational data. If confirmed by future space UV mission, this would provide evidence for non-zero cosmological constant from time scale test.

Gravitational effects of quantumfields in the interior of a cylindrical black hole

The gravitational back-reaction is calculated for the conformally invariant scalar field within a black cosmic string interior with cosmological constant. Using the perturbed metric, the gravitational effects of the quantum field are calculated. It is found that near the horizon, the perturbations initially strengthen the singularity. This effect is similar to the case of spherical symmetry (without a cosmological constant). This indicates that the behaviour of quantum effects may be universal and not dependent on the geometry of the spacetime or the presence of a non-zero cosmological constant.

Constraints on and m from distant Type Ia supernovae and cosmic microwave background anisotropies

We perform a combined likelihood analysis of the latest cosmic microwave background anisotropy data and distant Type Ia supernova data of Perlmutter et al. bur analysis is restricted to cosmological models where structure forms from adiabatic initial fluctuations characterized by a power-law spectrum with negligible tensor component. Marginalizing over other parameters, our best-fitting solution gives Omega(m) = 0.25(-0.12)(+0.18) and Omega(Lambda) = 0.63(-0.23)(+0.18) (95 per cent confidence errors) for the cosmic densities contributed by matter and a cosmological constant, respectively. The results therefore strongly favour a nearly spatially flat Universe with a nonzero cosmological constant.

String duality and nonsupersymmetric strings

In recent work Kachru, Kumar, and Silverstein introduced a special class of nonsupersymmetric type II string theories in which the cosmological constant vanishes at the first two orders of perturbation theory. Heuristic arguments suggest the cosmological constant may vanish in these theories to all orders in perturbation theory leading to a flat potential for the dilaton. A slight variant of their model can be described in terms of a dual heterotic theory. The dual theory has a nonzero cosmological constant which is nonperturbative in the coupling of the original type II theory. The dual theory also predicts a mismatch between Bose and Fermi degrees of freedom in the nonperturbative D-brane spectrum of the type II theory.

Cold dark matter variant cosmological models — I. Simulations and preliminary comparisons

We present two matched sets of five dissipationless simulations each, including four presently favoured minimal modifications to the standard cold dark matter (CDM) scenario. One simulation suite, with a linear box size of 75 h−1 Mpc, is designed for high resolution and good statistics on the group/poor cluster scale, and the other, with a box size of 300 h−1 Mpc, is designed for good rich cluster statistics. All runs had 57 million cold particles, and models with massive neutrinos (CHDM-2ν) had an additional 113 million hot particles. We consider separately models with massive neutrinos, tilt, curvature, and a non-zero cosmological constant (Λ ≡ 3H20ΩΛ) in addition to the standard CDM model. We find that the dark matter in each of our tilted Ω0+ΩΛ = 1 (TΛCDM) model with Ω0 = 0.4, our tilted Ω01 model (TCDM), and our open Λ = 0 (OCDM) model with Ω = 0.5 has too much small-scale power by a factor of ∼2, while CHDM-2ν and SCDM are acceptable fits. In addition, we take advantage of the large dynamic range in detectable halo masses afforded by the combination of the two sets of simulations to test the Press–Schechter approximation. We find good fits at cluster masses for δc,g = 1.27–1.35 for a Gaussian filter and δc,t = 1.57 − 1.73 for a top hat filter. However, when we adjust δc to obtain a good fit at cluster mass scales, we find that the Press–Schechter model overpredicts the number density of haloes compared to the simulations by a weakly cosmology-dependent factor of 1.5–2 at galaxy and group masses. It is impossible to obtain a good fit over the entire range of masses simulated by adjusting δc within reasonable bounds.

Kaluza-Klein monopoles and gauged sigma models

We review some aspects of branes. In particular, we discuss the worldvolume theory describing the dynamics of the Kaluza-Klein monopole which turns out to be a gauged sigma model. We also briefly review some recent applications of gauged sigma models to the worldvolume description of massive branes, i.e. branes moving in a background with a nonzero cosmological constant.

Cosmic-String–Seeded Structure Formation

We describe the results of high-resolution numerical simulations of string-induced structure formation in open universes and those with a nonzero cosmological constant. For models with $\ensuremath{\Gamma}=\ensuremath{\Omega}h=0.1--0.2$ and a cold dark matter background, we show that the linear density fluctuation power spectrum has both an amplitude at ${8h}^{\ensuremath{-}1}\mathrm{Mpc}$, ${\ensuremath{\sigma}}_{8}$, and an overall shape which are consistent within uncertainties with those currently inferred from galaxy surveys. The cosmic string scenario with hot dark matter requires a strongly scale-dependent bias in order to agree with observations.

The End of the Age Problem, and the Case for a Cosmological Constant Revisited

The lower limit on the age of the universe derived from globular cluster dating techniques, which previously strongly motivated a non-zero cosmological constant, has now been dramatically reduced, allowing consistency for a flat matter dominated universe with a Hubble Constant, $H_0 \le 66 km s^{-1} Mpc^{-1}$. The case for an open universe versus a flat universe with non-zero cosmological constant is reanalyzed in this context, incorporating not only the new age data, but also updates on baryon abundance constraints, and large scale structure arguments. For the first time, the allowed parameter space for the density of non-relativistic matter appears larger for an open universe than for a flat universe with cosmological constant, while a flat universe with zero cosmological constant remains strongly disfavored. Several other preliminary observations suggest a non-zero cosmological constant, but a definitive determination awaits refined measurements of $q_0$, and small scale anisotropies of the Cosmic Microwave background. I argue that fundamental theoretical arguments favor a non-zero cosmological constant over an open universe. However, if either case is confirmed, the challenges posed for fundamental particle physics will be great.

Relation between Einstein and quantum field equations

We show that there exists a choice of scalar field modes, such that the evolution of the quantum field in the zero-mass and large-mass limits is consistent with the Einstein equations for the background geometry. This choice of modes is also consistent with zero production of these particles and thus corresponds to a preferred vacuum state preserved by the evolution. In the zero-mass limit, we find that the quantum field equation implies the Einstein equation for the scale factor of a radiation-dominated universe; in the large-mass case, it implies the corresponding Einstein equation for a matter-dominated universe. Conversely, if the classical radiation-dominated or matter-dominated Einstein equations hold, there is no production of scalar particles in the zero and large mass limits, respectively. The suppression of particle production in the large mass limit is over and above the expected suppression at large mass. Our results hold for a certain class of conformally ultrastatic background geometries and therefore generalize previous results by one of us for spatially flat Robertson-Walker background geometries. In these geometries, we find that the temporal part of the graviton equations reduces to the temporal equation for a massless minimally coupled scalar field, and therefore the results for massless particle production hold also for gravitons. Within the class of modes we study, we also find that the requirement of zero production of massless scalar particles is not consistent with a non-zero cosmological constant. Possible implications are discussed.

Morphological Evolution of Galaxies

We simulate the growth of large-scale structure for three different cosmological models, an Einstein-de Sitter model (density parameter Ω0 = 1), an open model (Ω0 = 0.2), and a flat model with nonzero cosmological constant (Ω0 = 0.2, cosmological constant λ0 = 0.8), using a cosmological N-body code (particle-particle/particle-mesh) with 643 dark matter particles in a comoving cubic volume of present comoving size 128 Mpc. The calculations start at z = 24 and end at z = 0. We use the results of these simulations to generate distributions of galaxies at the present (z = 0), as follows: Using a Monte Carlo method based on the present distribution of dark matter, we located ~40,000 galaxies in the computational volume. We then ascribe to each galaxy a morphological type based on the local number density of galaxies in order to reproduce the observed morphology-density relation. The resulting galaxy distributions are similar to the observed ones, with most ellipticals concentrated in the densest regions, and most spirals concentrated in low-density regions. By tying each galaxy to its nearest dark matter particle, we can trace the trajectory of that galaxy back in time by simply looking at the location of that dark matter particle at earlier time slices provided by the N-body code. This enables us to reconstruct the distribution of galaxies at high redshift and the trajectory of each galaxy from its formation epoch to the present. We use these galaxy distributions to investigate the problem of morphological evolution. Our goal is to determine whether the morphological type of galaxies is determined primarily by the initial conditions in which these galaxies form or by evolutionary processes (such as mergers or tidal stripping) occurring after the galaxies have formed and eventually altering their morphology, or a combination of both effects. Our main technique consists of comparing the environments in which galaxies are at the epoch of galaxy formation (taken to be at redshift z = 3) with the environment in which the same galaxies are at the present. Making the null hypothesis that the morphological types of galaxies do not evolve, we compare the galaxies that form in low-density environments but end up later in high-density environments to the ones that also form in low-density environments but remain in low-density environments. The first group contains a larger proportion of elliptical and S0 galaxies than the second group. We assume that the initial galaxy formation process cannot distinguish a low-density environment that will always remain low density from one that will eventually become high density. Therefore, these results are absurd and force us to discard the null hypothesis that morphological evolution does not occur. Our study suggests that ~75% of the elliptical and S0 galaxies observed at present formed as such, while the remaining ~25% of these galaxies formed as spiral galaxies and underwent morphological evolution for all three cosmological models considered (the percentages might be smaller for elliptical than for S0 galaxies). These numbers assume a morphological evolution process that converts one spiral galaxy into either a S0 or an elliptical galaxy. If the morphological evolution process involves mergers of spiral galaxies, these numbers be would closer to 85% and 15%, respectively. We conclude that most galaxies did not undergo morphological evolution, but a nonnegligible fraction did.

Structure Formation Seeded by Cosmic Strings

We describe the results of high-resolution numerical simulations of structure formation seeded by a cosmic string network with a large dynamical range taking into account, for the first time, modifications due to the radiation-matter transition [1]. The resulting linear power spectrum of density perturbations is calculated with either cold or hot dark matter backgrounds and compared with the linear power spectrum inferred from various galaxy surveys [2]. Finally, we investigate the performance of cosmic string models in open universes and those with a non-zero cosmological constant. This direct numerical approach marks a considerable quantitative advance by incorporating important aspects of the relevant physics not included in previous treatments.

A convenient set of comoving cosmological variables and their application

We present a set of cosmological called variables, which are particularly useful for describing the gas dynamics of cosmic structure formation. For ideal gas with gamma=5/3, the supercomoving position, velocity, density, temperature, and pressure are constant in time in a uniform, isotropic, adiabatically expanding universe. Expressed in terms of these supercomoving the cosmological fluid conservation equations and the Poisson equation closely resemble their noncosmological counterparts. This makes it possible to generalize noncosmological results and techniques to cosmological problems, for a wide range of cosmological models. These variables were initially introduced by Shandarin for matter-dominated models only. We generalize supercomoving variables to models with a uniform component corresponding to a nonzero cosmological constant, domain walls, cosmic strings, a nonclumping form of nonrelativistic matter (e.g. massive nettrinos), or radiation. Each model is characterized by the value of the density parameter Omega0 of the nonrelativistic matter component in which density fluctuation is possible, and the density parameter OmegaX of the additional, nonclumping component. For each type of nonclumping background, we identify FAMILIES within which different values of Omega0 and OmegaX lead to fluid equations and solutions in supercomoving variables which are independent of Omega0 and OmegaX. We also include the effects of heating, radiative cooling, thermal conduction, viscosity, and magnetic fields. As an illustration, we describe 3 familiar cosmological problems in supercomoving variables: the growth of linear density fluctuations, the nonlinear collapse of a 1D plane-wave density fluctuation leading to pancake formation, and the Zel'dovich approximation.

On the non-integrability of the SU(2) invariant Kähler-Einstein metrics

We study the dynamical system describing the metric on a Kähler manifold with an SU(2) action and a non-zero cosmological constant. We find that it is non-integrable in two senses: (i) it does not admit any first integral within a very wide class; (ii) it does not have the Painlevé property, and cannot be transformed into a system that enjoys it. We briefly indicate the implications of these results.

Exactly soluble sector of quantum gravity

Cartan's spacetime reformulation of the Newtonian theory of gravity is a generally-covariant Galilean-relativistic limit-form of Einstein's theory of gravity known as the Newton-Cartan theory. According to this theory, space is flat, time is absolute with instantaneous causal influences, and the degenerate `metric' structure of spacetime remains fixed with two mutually orthogonal non-dynamical metrics, one spatial and the other temporal. The spacetime according to this theory is, nevertheless, curved, duly respecting the principle of equivalence, and the non-metric gravitational connection-field is dynamical in the sense that it is determined by matter distributions. Here, this generally-covariant but Galilean-relativistic theory of gravity with a possible non-zero cosmological constant, viewed as a parameterized gauge theory of a gravitational vector-potential minimally coupled to a complex Schroedinger-field (bosonic or fermionic), is successfully cast -- for the first time -- into a manifestly covariant Lagrangian form. Then, exploiting the fact that Newton-Cartan spacetime is intrinsically globally-hyperbolic with a fixed causal structure, the theory is recast both into a constraint-free Hamiltonian form in 3+1-dimensions and into a manifestly covariant reduced phase-space form with non-degenerate symplectic structure in 4-dimensions. Next, this Newton-Cartan-Schroedinger system is non-perturbatively quantized using the standard C*-algebraic technique combined with the geometric procedure of manifestly covariant phase-space quantization. The ensuing unitary quantum field theory of Newtonian gravity coupled to Galilean-relativistic matter is not only generally-covariant, but also exactly soluble.

Impulsive gravitational waves generated by null particles in de Sitter and anti–de Sitter backgrounds

By boosting the metric of the Schwarzschild–de Sitter and Schwarzschild–anti-de Sitter space-times in the ultrarelativistic limit as the mass parameter vanishes, impulsive gravitational waves are obtained in backgrounds with a nonzero cosmological constant. We determine the geometry of these impulsive wave surfaces using various coordinate charts. In the de Sitter background they are spheres containing two null particles located at the poles. In the anti–de Sitter background they are hyperboloidal surfaces of constant negative curvature containing a single null particle on the axis of symmetry. The global structure and conformal diagrams for the complete manifolds are also determined.

Cosmological constant and advanced gravitational wave detectors

Interferometric gravitational wave detectors could measure the frequency sweep of a binary inspiral [characterized by its chirp mass] to high accuracy. The observed chirp mass is the intrinsic chirp mass of the binary source multiplied by $(1+z)$, where $z$ is the redshift of the source. Assuming a non-zero cosmological constant, we compute the expected redshift distribution of observed events for an advanced LIGO detector. We find that the redshift distribution has a robust and sizable dependence on the cosmological constant; the data from advanced LIGO detectors could provide an independent measurement of the cosmological constant.