Case Of Cosmological Constant Research Articles

Past horizons in Robinson-Trautman spacetimes with a cosmological constant

We study past horizons in the class of type II Robinson-Trautman vacuum spacetimes with a cosmological constant. These exact radiative solutions of Einstein's equations exist in the future of any sufficiently smooth initial data, and they approach the corresponding spherically symmetric Schwarzschild--(anti-)de Sitter metric. By analytic methods we investigate the existence, uniqueness, location, and character of the past horizons in these spacetimes. In particular, we generalize the Penrose-Tod equation for marginally trapped surfaces, which form such white-hole horizons, to the case of a nonvanishing cosmological constant, and we analyze the behavior of its solutions and visualize their evolutions. We also prove that these horizons are explicit examples of an outer trapping horizon and a dynamical horizon, so that they are spacelike past outer horizons.

Photon rockets in the (anti-)de Sitter universe

A class of exact solutions to Einstein's equations is presented, which describes accelerating photon rockets in the de Sitter and anti-de Sitter universes. These are particular members of the Robinson-Trautman family of axially symmetric spacetimes with pure radiation. In particular, generalizations of (type D) Kinnersley's rockets and (type II) Bonnor's rockets to the case of a nonvanishing cosmological constant are given. Some of the main physical properties of these solutions are investigated, and their relation to the C-metric solution which describes uniformly accelerated black holes is also given.

Anisotropic dark energy: dynamics of the background and perturbations

We investigate cosmologies where the accelerated expansion of the universe is driven by afield with an anisotropic equation of state. We model such scenarios within the Bianchi Iframework, introducing two skewness parameters to quantify the deviation ofpressure from isotropy. We study the dynamics of the background expansion in thesemodels. A special case of an anisotropic cosmological constant is analyzed indetail. The anisotropic expansion is then confronted with the redshift and angulardistribution of the type Ia supernovae. In addition, we investigate the effectson the cosmic microwave background (CMB) anisotropies for which the mainsignature appears to be a quadrupole contribution. We find that the two skewnessparameters can be very well constrained. Tightest bounds are imposed by theCMB quadrupole, but there are anisotropic models which avoid these boundscompletely. Within these bounds, the anisotropy can be beneficial as a potentialexplanation for various anomalous cosmological observations, especially in the CMBat the largest angles. We also consider the dynamics of linear perturbations inthese models. The covariant approach is used to derive the general evolutionequations for cosmological perturbations, taking into account imperfect sourcesin an anisotropic background. The implications for galaxy formation are thenstudied. These results might help to make contact between the observed anomaliesin CMB and large-scale structure and fundamental theories exhibiting Lorentzviolation.

Detection of the integrated Sachs-Wolfe effect and corresponding dark energy constraints made with directional spherical wavelets

Using a directional spherical wavelet analysis we detect the integrated Sachs-Wolfe (ISW) effect, indicated by a positive correlation between the first-year Wilkinson Microwave Anisotropy Probe (WMAP) and NRAO VLA Sky Survey (NVSS) data. Detections are made using both a directional extension of the spherical Mexican hat wavelet and the spherical butterfly wavelet. We examine the possibility of foreground contamination and systematics in the WMAP data and conclude that these factors are not responsible for the signal that we detect. The wavelet analysis inherently enables us to localize on the sky those regions that contribute most strongly to the correlation. On removing these localized regions the correlation that we detect is reduced in significance, as expected, but it is not eliminated, suggesting that these regions are not the sole source of correlation between the data. This finding is consistent with predictions made using the ISW effect, where one would expect weak correlations over the entire sky. In a flat universe the detection of the ISW effect provides direct and independent evidence for dark energy. We use our detection to constrain dark energy parameters by deriving a theoretical prediction for the directional wavelet covariance statistic for a given cosmological model. Comparing these predictions with the data we place constraints on the equation-of-state parameter w and the vacuum energy density Ω Λ . We also consider the case of a pure cosmological constant, that is, w = - 1. For this case we rule out a zero cosmological constant at greater than the 99.9 per cent significance level. All parameter estimates that we obtain are consistent with the standard cosmological concordance model values. Although wavelets perform very well when attempting to detect the ISW effect since one may probe only the regions where the signal is present, once all information is incorporated when computing parameter estimates, the performance of the wavelet analysis is comparable to other methods, as expected for a linear approach.

Boundary conditions in first order gravity: Hamiltonian and ensemble

In this work two different boundary conditions for first order gravity, corresponding to a null and a negative cosmological constant, respectively, are studied. Both boundary conditions allow one to obtain the standard black hole thermodynamics. Furthermore, both boundary conditions define a canonical ensemble. Additionally the quasilocal energy definition is obtained for the null cosmological constant case.

COSMOLOGICAL CONSTANT AND NONCOMMUTATIVITY: A NEWTONIAN POINT OF VIEW

We study a Newtonian cosmological model in the context of a noncommutative space. It is shown that the trajectories of a test particle undergo modifications such that it no longer satisfies the cosmological principle. For the case of a positive cosmological constant, spiral trajectories are obtained and corrections to the Hubble constant appear. It is also shown that, in the limit of a strong noncommutative parameter, the model is closely related to a particle in a Gödel-type metric.

CMB Analysis of Boomerang & Maxima & the Cosmic Parameters {Ωtot,Ωbh2, Ωcdmh2, ΩΛ, ns}

We show how estimates of parameters characterizing inflation-based theories of structure formation localized over the past year when large scale structure (LSS) information from galaxy and cluster surveys was combined with the rapidly developing cosmic microwave background (CMB) data, especially from the recent Boomerang and Maxima balloon experiments. All current CMB data plus a relatively weak prior probability on the Hubble constant, age and LSS points to little mean curvature (Ωtot = 1.08±0.06) and nearly scale invariant initial fluctuations (ns = 1.03±0.08), both predictions of (non-baroque) inflation theory. We emphasize the role that degeneracy among parameters in the Lpk = 212 ± 7 position of the (first acoustic) peak plays in defining the Ωtot range upon marginalization over other variables. Though the CDM density is in the expected range (Ωcdmh2 = 0.17 ± 0.02), the baryon density Ωbh2 = 0.030 ± 0.005 is somewhat above the independent 0.019 ± 0.002 nucleosynthesis estimates. CMB+LSS gives independent evidence for dark energy (ΩΛ = 0.66 ± 0.06) at the same level as from supernova (SN1) observations, with a phenomenological quintessence equation of state limited by SN1+CMB+LSS to wQ < −0.7 cf. the wQ=−1 cosmological constant case.

Global embedding ofD-dimensional black holes with a cosmological constant in Minkowskian spacetimes: Matching between Hawking temperature and Unruh temperature

We study the matching between the Hawking temperature of a large class of static D-dimensional black holes and the Unruh temperature of the corresponding higher dimensional Rindler spacetime. In order to accomplish this task we find the global embedding of the D-dimensional black holes into a higher dimensional Minkowskian spacetime, called the global embedding Minkowskian spacetime procedure (GEMS procedure). These global embedding transformations are important on their own, since they provide a powerful tool that simplifies the study of black hole physics by working instead, but equivalently, in an accelerated Rindler frame in a flat background geometry. We discuss neutral and charged Tangherlini black holes with and without cosmological constant, and in the negative cosmological constant case, we consider the three allowed topologies for the horizons (spherical, cylindrical/toroidal and hyperbolic).

Cosmology with exponential potentials

We examine in the context of general relativity the dynamics of a spatially flat Robertson–Walker universe filled with a classical minimally coupled scalar field ϕ of exponential potential V(ϕ) ∼ exp(−μϕ) plus pressureless baryonic matter. This system is reduced to a first-order ordinary differential equation for Ωϕ(wϕ) or q(wϕ), providing direct evidence on the acceleration/deceleration properties of the system. As a consequence, for positive potentials, passage into acceleration not at late times is generically a feature of the system for any value of μ, even when the late-times attractors are decelerating. Furthermore, the structure formation bound, together with the constraints Ωm0 ≈ 0.25 − 0.3, −1 ⩽ wϕ0 ⩽ −0.6, provides, independently of initial conditions and other parameters, the necessary condition , while the less conservative constraint −1 ⩽ wϕ ⩽ −0.93 gives . Special solutions are found to possess intervals of acceleration. For the almost cosmological constant case wϕ ≈ −1, the general relation Ωϕ(wϕ) is obtained. The generic (nonlinearized) late-times solution of the system in the plane (wϕ, Ωϕ) or (wϕ, q) is also derived.

Effective de Sitter brane via running radius

We present the solution for effective couplings on a running de Sitter brane. A renormalization group formalism is developed for linearized gravity in a two de Sitter brane model. It is shown that the effective tension remains a constant similarly to the zero cosmological constant case. We also discuss the suppression of higher derivative terms.

Linearized stability analysis of thin-shell wormholes with a cosmological constant

Spherically symmetric thin-shell wormholes in the presence of a cosmological constant are constructed applying the cut-and-paste technique implemented by Visser. Using the Darmois–Israel formalism the surface stresses, which are concentrated at the wormhole throat, are determined. This construction allows us to apply a dynamical analysis to the throat, considering linearized radial perturbations around static solutions. For a large positive cosmological constant, i.e., for the Schwarzschild–de Sitter solution, the region of stability is significantly increased, relatively to the null cosmological constant case, analysed by Poisson and Visser. With a negative cosmological constant, i.e., the Schwarzschild–anti de Sitter solution, the region of stability is decreased. In particular, considering static solutions with a generic cosmological constant, the weak and dominant energy conditions are violated, while for a0 ⩽ 3M the null and strong energy conditions are satisfied. The surface pressure of the static solution is strictly positive for the Schwarzschild and Schwarzschild–anti de Sitter spacetimes, but takes negative values, assuming a surface tension in the Schwarzschild–de Sitter solution, for high values of the cosmological constant and the wormhole throat radius.

Classical boundary-value problem in Riemannian quantum gravity and self-dual Taub-NUT–(anti)de Sitter geometries

The classical boundary-value problem of the Einstein field equations is studied with an arbitrary cosmological constant, in the case of a compact ( S 3) boundary given a biaxial Bianchi-IX positive-definite three-metric, specified by two radii ( a, b). For the simplest, four-ball, topology of the manifold with this boundary, the regular classical solutions are found within the family of Taub-NUT–(anti)de Sitter metrics with self-dual Weyl curvature. For arbitrary choice of positive radii ( a, b), we find that there are three solutions for the infilling geometry of this type. We obtain exact solutions for them and for their Euclidean actions. The case of negative cosmological constant is investigated further. For reasonable squashing of the three-sphere, all three infilling solutions have real-valued actions which possess a “cusp catastrophe” structure with a non-self-intersecting “catastrophe manifold” implying that the dominant contribution comes from the unique real positive-definite solution on the ball. The positive-definite solution exists even for larger deformations of the three-sphere, as long as a certain inequality between a and b holds. The action of this solution is proportional to − a 3 for large a (∼ b) and hence larger radii are favoured. The same boundary-value problem with more complicated interior topology containing a “bolt” is investigated in a forthcoming paper.

Instantons and wormholes in Minkowski and (A)dS spaces

Instanton and wormhole solutions are constructed in a d-dimensional gravity theory with an axion–dilaton pair of scalar fields. We discuss the cases of vanishing, positive and negative cosmological constant.

SPACE TIME FOAM

In the context of a model of space-time foam, made by N wormholes we discuss the possibility of having a foam formed by different configurations. An equivalence between Schwarzschild and Schwarzschild-Anti-de Sitter wormholes in terms of Casimir energy is shown. An argument to discriminate which configuration could represent a foamy vacuum coming from Schwarzschild black hole transition frequencies is used. The case of a positive cosmological constant is also discussed. Finally, a discussion involving charged wormholes leads to the conclusion that they cannot be used to represent a ground state of the foamy type.

LETTER: Cosmological Constant, Conical Defect and Classical Tests of General Relativity

We investigate the perihelion shift of the planetary motion and the bending of starlight in the Schwarzschild field modified by the presence of a $\Lambda$-term plus a conical defect. This analysis generalizes an earlier result obtained by Islam (Phys. Lett. A 97, 239, 1983) to the case of a pure cosmological constant. By using the experimental data we obtain that the parameter $\epsilon$ characterizing the conical defect is less than $10^{-9}$ and $10^{-7}$, respectively, on the length scales associated with such phenomena. In particular, if the defect is generated by a cosmic string, these values correspond to limits on the linear mass densities of $10^{19}g/cm$ and $10^{21}g/cm$, respectively.

Exhaustive study of cosmic microwave background anisotropies in quintessential scenarios

Recent high-precision measurements of the CMB anisotropies performed by the BOOMERanG and MAXIMA-1 experiments provide an unmatched set of data allowing us to probe different cosmological models. Among these scenarios, motivated by the recent measurements of the luminosity distance versus redshift relation for type Ia supernovas, is the quintessence hypothesis. It consists of assuming that the acceleration of the Universe is due to a scalar field whose final evolution is insensitive to the initial conditions. Within this framework we investigate the cosmological perturbations for two well-motivated potentials: the Ratra-Peebles and the SUGRA tracking potentials. We show that the solutions of the perturbed equations possess an attractor and that, as a consequence, the insensitivity to the initial conditions is preserved at the perturbed level. Then, we study the predictions of these two models for structure formation and CMB anisotropies and investigate the general features of the multipole moments in the presence of quintessence. We also compare the CMB multipoles calculated with the help of a full Boltzmann code with the BOOMERanG and MAXIMA-1 data. We pay special attention to the location of the second peak and demonstrate that it significantly differs from the location obtained in the cosmological constant case. Finally, we argue that the SUGRA potential is compatible with all the recent data with standard values of the cosmological parameters. In particular, it fits the MAXIMA-1 data better than a cosmological constant or the Ratra-Peebles potential.

Supersymmetry of topological Kerr-Newman-Taub- NUT-adSspacetimes

We extend the topological Kerr-Newman-adS solutions by includingNUT charge and find generalizations of the Robinson-Bertotti solutionto the negative cosmological constant case with different topologies.We show how all of these solutions can be obtained as limits of the general Plebanski-Demianski solution.We study the supersymmetry properties of all these solutions in thecontext of gauged N = 2, d = 4 supergravity. Generically theypreserve, at most, quarter of the total supersymmetry. In the Plebanski-Demianski case, although gauged N = 2, d = 4 supergravity does not have electro-magnetic duality, we find that the family of supersymmetricsolutions still exhibits an electro-magnetic duality in whichelectric and magnetic charges and mass and Taub-NUT charge are rotatedsimultaneously.

Wormhole Solutions in Superstring Theory

The wormhole is discussed in 4-dimensional superstring theory; the corresponding wormhole equation is deduced, from which both the analytical and numerical solutions are given with three different cases of cosmological constant.

Observational tests of x-matter models

We study gravitational lensing statistics, matter power spectra and the angular power spectra of the cosmic microwave background (CMB) radiation in x-matter models. We adopt an equation of state of x-matter which can express a wide range of matter from pressureless dust to the cosmological constant. A new ingredient in this model is the sound speed of the x-component, in addition to the equation of state w0 = px0/ρx0. Except for the cosmological constant case, the perturbations of x-matter itself are considered. Our primary interest is in the effect of non-zero sound speed on the structure formation and the CMB spectra. It is found that there exist parameter ranges where x-matter models are consistent with all current observations. The x-matter generally leaves imprints in the CMB anisotropy and the matter power spectrum, which should be detectable in future observations.

Exponential potentials and cosmological scaling solutions

We present a phase-plane analysis of cosmologies containing a baryotropic fluid with an equation of state ${p}_{\ensuremath{\gamma}}=(\ensuremath{\gamma}\ensuremath{-}1){\ensuremath{\rho}}_{\ensuremath{\gamma}},$ plus a scalar field $\ensuremath{\varphi}$ with an exponential potential $V\ensuremath{\propto}\mathrm{exp}(\ensuremath{-}\ensuremath{\lambda}\ensuremath{\kappa}\ensuremath{\varphi})$ where ${\ensuremath{\kappa}}^{2}=8\ensuremath{\pi}G$. In addition to the well-known inflationary solutions for ${\ensuremath{\lambda}}^{2}<2$, there exist scaling solutions when ${\ensuremath{\lambda}}^{2}>3\ensuremath{\gamma}$ in which the scalar field energy density tracks that of the baryotropic fluid (which for example might be radiation or dust). We show that the scaling solutions are the unique late-time attractors whenever they exist. The fluid-dominated solutions, where $V(\ensuremath{\varphi})/{\ensuremath{\rho}}_{\ensuremath{\gamma}}\ensuremath{\rightarrow}0$ at late times, are always unstable (except for the cosmological constant case $\ensuremath{\gamma}=0)$. The relative energy density of the fluid and scalar field depends on the steepness of the exponential potential, which is constrained by nucleosynthesis to ${\ensuremath{\lambda}}^{2}>20$. We show that standard inflation models are unable to solve this ``relic density'' problem.